MATHEMATICAL AND ARTISTIC ABILITIES, HUMAN RELATIONSHIPS AND AUTISM SPECTRUM

DISPOSITIONS(ASD)

Christine LawsonConsultant Psychologist

Chartered ScientistWarwickshire, UK

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CONTENTS

Acknowledgements 4

Abstract 5

Overview and Methodology 7

1. Introduction 21

1.1 Human Body Parts, Numerical Systems/Development and 21Human Figure Drawings

1.2 Facial Features, Small Numerosities, Human Figure Drawings 26and ASD

2. Method 31

2.1 Participants 312.2 Materials 312.3 Procedure 32

3. Results 33

3.1 Vignette: Young Person J. 333.2 Results: Young Person J. 34

3.3 Vignette: Young Person L. 373.4 Results: Young Person L. 37

3.5 Vignette: Young Person G. 403.6 Results: Young Person G. 40

3.7 Vignette: Young Person K. 433.8 Results: Young Person K. 44

3.9 Vignette: Young Person B. 473.10 Results: Young Person B. 47

3.11 Vignette: Young Person S. 503.12 Results: Young Person S. 51

3.13 Vignette: Young Person P. 543.14 Results: Young Person P. 54

4. Discussion 58

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4.1 Asperger Syndrome, ASD and Human Figure Drawings 584.2 Attentional Flexibility, Face/Body Processing and ASD 63

4.3 Working Memory, Mental Flexibility, Mathematical 77Abilities, Social Competence and ASD

4.4 Intuition, Systemizing, Certainty, Uncertainty, Equilibrium, 82Symmetry, Mathematical Abilities and ASD

4.5 Cognitive Flexibility, Self-Unification, Mathematical 92Abilities and ASD

4.6 Social Competence, Self-Perception, Positive Disposition, 99Mathematical Abilities and ASD

5. Conclusion 105

6. References 108

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Acknowledgements

My grateful thanks to the children, parents, school staff and any other individuals who contributed to investigations by the present author referred to previously and discussed here.

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Abstract

Background

Lawson(2003) described a boy diagnosed with Asperger syndrome and marked dyspraxia who produced drawings of people after forming specific Object Assembly items from the WISC-R(UK) and WAIS-R(UK) and apprehended quickly, small numerosities associated with dots and schematic facial features. Improvements concerning human figure drawings and arithmetic/mathematics were indicated alongside increasing maturity artistically and socially. Similar results were obtained with other children and adolescents of such a disposition(Lawson, 2004, 2005a, b, 2008a, c, 2009).

Aims

The author aimed to enhance cognitive flexibility and facilitate a non-algorithmic mode of functioning by facilitating perceptual and conceptual aspects relating to people and numbers within a holistic context by emphasising the significance of particular and relevant details and their interconnections for a broad range of young people with ASD.

Participants

Participants attended mainstream primary and secondary schools. They might draw people with omitted or poorly depicted features, isolated objects, specific individuals or cartoon characters. Some problematic aspects concerning their development related to dyspraxia, attention or arithmetic and their difficulties concerning relationships with people resulted in them being placed on the autism spectrum.

Procedure

Test Sessions: Participants were administered the WOND(Rust,1996), DAP(Naglieri, 1988), Picture Completion subtest(WISC-III UK, Wechsler, 1992), Test of Perception of Emotion from Facial Expression(Social Skills Training with Children and Adolescents, Spence, 1995), Dot Locations and Faces subtests(CMS, Cohen, 1995), Recall of Digits Forward and Backward subtest(BAS II, Elliot et al., 1996) and the WASI(Wechsler, 1999) as well as Cards with Dots or Facial Features(Lawson, 2001b).

Randomised and fast presentations were given with the cards containing dot arrangements followed by those with features from schematic faces in upright and inverted positions, with numerosities ranging from 1 to 5. After each card presentation a mask card was shown and following the absence of an immediate and correct numerical reply, time was allowed for the correct response. If the reply was incorrect or absent, after completion of all brief presentations, the failed items were offered until correct answers were elicited.

Training Sessions: The participants formed selected Object Assembly items, namely the Girl, Male Face(WISC-R, UK), Manikin, Female Profile and the Hand(WAIS-R, UK). Attention was directed to omissions in their drawings and size, proportion and

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dimension. Drawings of people were produced again of complete figures and sometimes separate features. The cards with dots and those with facial features were presented randomly with an emphasis on speed and accuracy until all items had received fast and correct replies.

Re-Test Sessions: The Picture Completion subtest(WISC-III UK), Test of Perception of Emotion from Facial Expression(Social Skills Training, Spence), Recall of Digits Forward and Backward(BAS II) and the DAP were administered and only those questions which had not been attempted or those which had received erroneous responses.

Results

At re-assessment, usually about six weeks after the last training session it was apparent that the young people had retained their enhanced drawing skills as demonstrated by their more integrated and realistic depictions. The suggested facilitation concerning expressive and representational abilities was accompanied by positive changes relating to their attainments and management of school and other situations.

Discussion

The comprehensive discussion within a neuropsychological context relates to cognitive development and specifically motor coordination, attention, memory, face and body processing, mental flexibility, intuition, systemizing, certainty and uncertainty, anxiety, symmetry, mathematical and artistic abilities, social competence and ASD.

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Overview and Methodology

Considering the complex nature of the areas under investigation as well as the participants concerned it appeared inappropriate to use one approach as this would lead to the acquisition of very limited data and consequently rather restricted discussions and conclusions. As discussed for example by Banister et al.(1994) and Cohen & Manion(1994) triangulation is a term that has been given to describe the use of various combinations of procedures, investigators, perspectives and so on. Triangulation is helpful specifically, when considering a more comprehensive perspective of issues within educational settings. Relying on one approach might lead to biases and distortions in the researchers view of the topic under investigation. A more recent discussion concerning triangulation has been contributed by Cohen et al.(2007).

In the research discussed here by the present author, reference has been made to investigations concerning developmental and acquired disabilities concerning children and adults in educational and clinical contexts with due consideration being given to the theoretical and philosophical aspects. Also ethical considerations have influenced my way of working with the young people throughout the investigation. Using several approaches a more comprehensive understanding has been facilitated leading to a firmer basis for the remediation of the difficulties under consideration.

As indicated by Swanson et al.(1981) when considering clinical interviews and the validity of verbal reflections, often individuals are quite capable of expressing their beliefs and thoughts. The discussion highlighted this point in relation to mathematical knowledge and hence the clinical interview was considered a useful approach for obtaining information concerning the facts and principles that people might use in their reasoning in the area of mathematics. It is acceptable to consider descriptions given by individuals of some of their cognitive processes even if they are unable to access or they have limited access to some of the sources in relation to their insights or to the necessary underlying processes for forming ideas. Also, some individuals may have a limited command of language or specific linguistic difficulties. The clinical interviewer can emphasise certain aspects concerning the topic under investigation and influence the type and level of analysis relating to the reporting of the participant. Introspective reports might be erroneous or restricted in certain respects and other types of assessments might provide appropriate and necessary additional information.

As emphasised by Swanson et al.(1981) the diagnostic process and cognitive psychological research concern discovery, theoretical specification and the precise assessment of competence. The clinical interview comprises research and measurement components for the assistance of individual diagnosis which involves the development of theories relating to individuals. In the research described here, the clinical interview was used for diagnostic and research purposes in a detailed investigative form in relation to the nature of the discussions and the contact time. The clinical interview was used alongside other methods involving the implementation of particular tests as well as specific materials and procedures developed by the present author, observations and professional reports as well as information given directly from parents, staff and others associated with the children and adolescents as well as the young people themselves.

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When working with these young individuals, collaboration and participation were emphasised in relation to the ‘new paradigm’ research concerning co-operative experiential inquiry as discussed by Reason & Rowan(1981) and Reason(1988). Crucial to co-operative experiential inquiry is an aware and self critical movement between experience and reflection which goes through various cycles as ideas, practice and experience are refined systematically. As highlighted by Reason & Rowan(1981), validity in research of this nature is concerned more with the personal and interpersonal aspects rather than method. It is necessary to consider the appropriateness of validity criteria in terms of more than what is right and to question what is useful and enlightening.

The children discussed here were very active participants. Through listening to them and observing their responses I was able to encourage very actively the development of their abilities. As I was involved with the young people for an extended period of time relatively deep collaborative working was possible. They were encouraged to reflect on their experiences with arithmetic/mathematics, drawings/art and social interactions in everyday contexts both during the sessions and outside of them. They made conscious and concerted efforts to understand issues arising during the sessions and hence they developed their own ideas and received encouragement for others. They were able to go through reflective cycles many times, gradually clarifying and refining their notions and maturing their ideas in a systematic way as well as very actively using their evolving knowledge.

Swanson et al.(1981) emphasised that the use and importance of data is relative always to theories and various hypotheses and assumptions relating to specific topics. Accounting for a variety of ideas concerning conceptual development and skill acquisition in certain areas it is possible for individuals to show improvement in their abilities in a variety of spheres. Enhancement of these abilities can be encouraged through the continuing development of innovative teaching methods and the associated reciprocal exchange of information via the participants’ interaction. In the work discussed here the present author has attempted to contribute to some specific aspects of development as indicated above and in the following summary.

Human body parts have been used as counting aids in the creation of some number systems in various cultures. Also, the fingers have been highlighted as being significant particularly in relation to early numerical development from a neuropsychological perspective by Butterworth(1999). Additionally, facial features are bodily aspects that have been noted in connection with number systems and in association with numerical disabilities by specific investigators. Badian(1983) considered that a deficiency in visual attention to precise detail as suggested in the human figure drawings of young children might offer information relating to later numerical abilities.

Hence, Lawson(2000c, 2001a) studied first year junior aged children and assessed them on their drawings of people, a standardised arithmetic test and specific rectangular and non-rectangular addition questions used earlier by Lawson(1986, 1989, 1990, 1995a, b, 2000a, b, 2001a) and based on findings by Friend(1979). The terms rectangular and non-rectangular referred to the arrangement of the digits in the addends. In relation to their attainments, the participants received different types of instruction or none if they had not demonstrated any major problems. The results

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suggested that directing the children’s attention to specific arithmetical details and associated numerical concepts or particular omissions and poorly depicted aspects concerning their drawings led to enhanced development and performances in both areas. These particular rectangular and non-rectangular addition problems were used as items in a dyscalculia test battery assessment by Lawson(1995b, 2000b, 2001a) and a more detailed analysis concerning the assessment implemented with specific young people was presented later by Lawson(2002, 2008b, 2010).

In Badian’s discussion concerning those who might be described as dyscalculic, the omission of the nose was noted and sometimes the inclusion of an incorrect number of fingers. A marked impairment of arithmetical skills as well as a lack of response to educational interventions were the criteria described for developmental dyscalculia in the children involved in a study by Shalev & Gross-Tsur(1993). Reference could be made to Shalev(2007) for a fairly recent discussion of aspects concerning developmental dyscalculia in the context of definitions, assessments and prevalence. Additionally, the discussion on developmental dyscalculia by Butterworth(2008) and the contribution concerning the genetics of learning abilities and disabilities by Kovas & Plomin(2008) are of interest here. Some of the young people in my investigations did have impairments which manifested themselves in relation to specific aspects of arithmetic and their responses had been limited in relation to remedial interventions. When considering the study by Lawson(2000c, 2001a), one boy omitted the nose on the drawings of a man, a woman and himself. After training which involved attention to numerical details all pictures included this feature. On one hand in each drawing the number of fingers was incorrect but on re-assessment this detail was shown accurately and there was a marked overall improvement on all three drawings. Another child drew a man without a nose but after successful tuition in relation to specific addition exercises which had been difficult for him, he included this feature in two dimensions and the bridge. His performance improved overall for his drawing of a man but it remained unchanged for the woman. Initially, both boys had performed well below their chronological age levels on an arithmetic test but marked improvements were shown on re-assessment.

Consequently, Lawson(2001b) investigated the apprehension of small numerosities in association with dots or facial features and children’s human figure drawings. Generally, the results indicated that these first year junior aged pupils could apprehend the numerosities associated with various arrangements of dots and small sets of schematic facial features. The amounts ranged from 1 to 5 and the expected trend was indicated with faster and more accurate responses occurring for the smaller set sizes. Also, the children drew a picture of a man, a woman and themselves with later analysis and assessment involving the system by Naglieri(1988). Children who had omitted the nose and/or whose performance was relatively poor overall on the drawing task were selected for a short training session. They were encouraged to reply with speed and accuracy to cards with dots and facial features until all items had received fast and accurate responses and then they were involved again with the drawing task. Hence, the participants had a considerable amount of practice with subitizing for sets involving 1 to 5 items.

Generally, the re-assessment results concerning the drawing tasks were indicative of a trend reflecting a marked increase usually in the number of included features concerning the face and other body parts. Also, the depictions tended to look more

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realistic although the training had involved only schematic faces. Overall, it was apparent that the dots and facial features tasks could be used to encourage the fast apprehension of small numerosities and to facilitate the inclusion of details in children’s human figure drawings.

In a further investigation by Lawson(2003) a case report was presented concerning a boy with a diagnosis of Asperger syndrome(AS) which is characterised by a qualitative impairment in social interaction and restricted, repetitive and stereotyped patterns of behaviour, interests and activities(American Psychiatric Association, 1994, 2000). There may be a delay in motor milestones and motor clumsiness is common although not an essential diagnostic feature(World Health Organisation, 1992). In fact, he had noticeable problems in relation to dyspraxia which concerns impairments in skilled movements. He was assessed on various aspects of his cognitive functioning, an arithmetic/mathematics test and human figure drawings. Then he participated in training sessions in which he formed faces, a hand and whole people using the Object Assembly items from the WISC-R(UK) and the WAIS-R(UK). After removal of the items he produced drawings of a man, a woman or himself and sometimes specific body parts. Also, he was involved with the dots and facial features tasks and responses concerning their associated numerosities. At re-assessment noticeable improvements were demonstrated on his three human figure drawings which were maintained and developed without further input. Also, his performance was enhanced quite markedly on the arithmetic/mathematics test. In later follow-up sessions it was indicated that he had been involved in a variety of activities in art at home including the creation of paintings with specific and integrated features. He continued to develop his interest and involvement in art at home, at school and elsewhere alongside increasing maturity and confidence in social situations.

Hence, it was felt that other children with a variety of disabilities and including specific difficulties concerning their drawings of people might benefit from the implementation and modification or elaboration of the approaches described above. They might present with various mathematical abilities and the training might facilitate improvements in this sphere. In a study by Lawson(2004) two children were presented in detail, specifically K. who was described as a boy with Asperger syndrome and L. as a boy with Asperger syndrome and dyspraxia which was relatively mild. Child L. had experienced other difficulties of a specific numerical nature so he was involved in training to address this issue and a presentation involving this work was given by Lawson(2005b). Also, L.’s problems associated with learning the multiplication tables have been discussed in detail with other case studies in the context of assessment and remediation in relation to numerical, arithmetical and other areas of mathematical development by Lawson(2008b, 2010). Furthermore, the non-rectangular addition problems highlighted earlier in the current discussion and the associated remedial approach designed by the present author were discussed in the contribution by Lawson(2008b, 2010). A recent presentation by Lawson(2009) concerned a boy G. who experienced difficulties particularly with these non-rectangular addition problems and he responded successfully to the remedial intervention. Also, G. had been diagnosed with Asperger syndrome. The two children, K. and L. as well as G. participated in similar assessments and training sessions and in addition to the follow-up sessions when they were administered formal assessments the participants were monitored over a longer interval. They demonstrated significant positive changes in relation to their specific areas of difficulty and presented with

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characteristics associated with the autism spectrum which were relatively less severe in quality and/or quantity.

The children in these studies by Lawson(2003, 2004, 2005b) were participants while they were attending primary schools or during the holiday period before the start of secondary education. The boy reported by Lawson(2003) had been monitored informally by the present author via contact with the home since the initial follow up sessions. The children presented by Lawson(2004, 2005b) were monitored and supported as appropriate during the following years after the re-assessment sessions. Unfortunately there may not be recognition of the difficulties associated with the autism spectrum for some individuals who are relatively able until they reach adolescence or adulthood. Hence they may not receive appropriate interventions to help them progress in some respects. The study by Lawson(2005a) concerned two young people, specifically a male adolescent B. and a female adolescent S., both with Asperger syndrome whose difficulties relating to the autism spectrum had not been acknowledged until after the commencement of their secondary education. They received similar assessments and interventions initially and they were monitored and supported as appropriate over the years following the re-assessment sessions. There were encouraging improvements concerning their attainments and management of situations both in and outside of the school environment.

Additionally, the presentations by Lawson(2008a, c) concerned two more young people, a boy J. who was diagnosed with Asperger syndrome during his primary school years and an adolescent male P. who was diagnosed with Asperger syndrome during the secondary stage of his education. The outcomes for these two young people were very positive in relation to their academic achievements and increased maturity and independence socially as J. progressed into adolescence and P. developed during the college stage of his education. Overall, the current discussion relates not only to those diagnosed with Asperger syndrome as indicated above who received similar assessments, interventions and ongoing monitoring and support as appropriate with encouraging results but also to a broad range of individuals of various ages with ASD. A more detailed contribution is offered here as an extension to the presentation by Lawson(2008c) and including information concerning G. as indicated above and discussed by Lawson(2009).

The detailed and comprehensive discussion presented here has been developed in relation to the work concerning the selected young people as well as others within the context of professional involvement by the author. Specifically, the discussion considers ASD, particularly Asperger syndrome and diagnostic criteria, human figure drawings, attentional/mental/cognitive flexibility, facial/bodily processing, working memory, mathematical abilities and associations with various artistic spheres, certainty/uncertainty, intuition, systemizing, equilibrium, symmetry, self-unification, social competence and self-perception.

There has been considerable controversy relating to the diagnostic criteria for Asperger syndrome and the autism spectrum. In the comprehensive discussion by Attwood(2006), diagnostic criteria are cited for AS as given by Gillberg(1991) which include motor clumsiness. Also, consideration is given to the aspect of language delay which is a particular area of controversy. Wing(2005) favours a multi-dimensional rather than a categorical approach in relation to the study of the autism spectrum. The

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significance of the impact of social difficulties is highlighted with an emphasis on the importance of studying particular dysfunctional aspects rather than diagnostic subgroups. Additionally, in an investigation by Skuse et al.(2009) involving individuals, aged around 8 years, the prevalence of mild deficits concerning social and communication competencies was shown to have a continuous distribution in the general schoolchild population. The categorisation of ASD in relation to specific diagnostic points was considered somewhat arbitrary and the findings were given in support of a dimensional approach concerning the autism spectrum. Also in relation to this study, reference could be made to the editorial by Constantino(2009). For various perspectives concerning different psychiatric diagnostic systems of classification including a dimensional approach and with specific consideration given to comorbidity, reference could be made to recent discussions by Aragona(2009a, b), Banzato(2009) and Zachar(2009).

Certainly in my own research, I had approached issues concerning those with ASD from the perspective of considering how areas of development that were presented as problematic could be assisted by regions of strength in order to facilitate progress in both spheres and associated aspects. Although specific categories had been ascribed to some individuals who were participants in my studies, it is important to note that all of the young people had social and communication difficulties which were associated with the autism spectrum, whatever label might or might not have been attributed to particular young people. Generally, I am in favour of a dimensional as opposed to categorical approach in relation to the diagnostic, therapeutic and remedial aspects of ways to facilitate development in those with ASD.

In a recent study by Staples & Reid(2010), it was suggested that there were variations in patterns or possible deficits concerning the fundamental movement skills of children and adolescents on the autism spectrum. One area where children’s motor coordination difficulties have been investigated concerns their drawings of people. The findings of Barnett & Henderson(1992) indicated that the drawings of the clumsy children aged between 5 and 13 years were inferior to those of their well coordinated controls for the representation of proportions, the depiction of features and the provision of detail in their figures. Additionally, the researchers noted that there was a tendency for a difficulty with drawing a circle for a head to be associated with the omission of the nose.

As highlighted in the case report of a boy with Asperger syndrome and marked dyspraxia described by Lawson(2003) there were several aspects in relation to his disposition that were clarified and strengthened through the assessment and teaching approach used in that study. As indicated, the results were very positive and it was felt that other young people with some similar difficulties should benefit from the same intervention. In contrast to that young man, most of the children discussed in the context of the studies by Lawson(2004, 2005a, b, 2008a, c, 2009) and here did not present with major disabilities in relation to dyspraxia although there were manifestations of problems concerning motor coordination to some extent in particular individuals. However, because of the selection criteria and as a result of the assessment with a variety of tasks it was apparent that they did have areas of weakness in common with him. One aspect concerned the amount of effort that they required to produce drawings of people and particularly without copying and in relation to this the generation of ideas when producing their depictions. Both of the

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young people in the study presented by Lawson(2005a) produced cartoon characters quite easily but they had to make an effort to produce realistic human figure drawings and in developing their ideas to add variety to their depictions. B. did not have marked problems in relation to motor co-ordination and S. wrote and drew with her right hand with reasonable dexterity.

As discussed by Jolley et al.(2000) in order for a child to produce a representation he/she needs to be able to hold in mind the perceptual and conceptual aspects of the topic during the drawing process. Also, the individual has to learn how to represent graphically three dimensional entities in two dimensions. In producing representations from memory as opposed to copying, more conscious effort is required in accessing relevant information and in the generation of ideas which are reflected then in the person’s drawings. Impairments or failures in the utilisation of their generative ability in relation to the production of varied groups of drawings had been suggested for children with autism who were relatively able but not savant artists(Lewis & Boucher, 1991).

The young people considered by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here were not involved in any copying activities during the sessions. They were encouraged to produce whole drawings of people which required more planning than would be required for the completion of pictures as highlighted by Leevers & Harris(1998). Also, they emphasised how even more effort was necessary for individuals to develop and apply new ideas to give variations to their depictions. Schematic faces were used with clearly defined facial features. A specific aim was to enhance flexible attention to human faces and certainly this aspect seemed to have developed in the young participants when considering how they produced increasingly detailed and realistic drawings of people and how they made progress in terms of their functioning in everyday contexts.

In relation to the young people described here and others who have been involved with my approach, when asked to produce a self drawing some of them said that they could not offer such a production. Certain individuals requested a mirror although this was not allowed during the sessions. In specific cases when the young people said that they could not do self drawings, if I indicated that they should draw a person similar to themselves in terms of age, sex and appearance usually they produced pictures which represented themselves. As the participants developed during the teaching/learning sessions and as indicated in follow-up sessions they became more aware of different aspects of themselves and the inter-relationships as well as their impact on other people and in different situations. Hence, they became more capable of managing their own behaviours in a broader variety of contexts.

As highlighted by Plaisted(2000), individuals with autism appear to demonstrate relatively good processing concerning unique characteristics of stimuli but relatively poor processing of similarities between stimuli. Various differences concerning attention in those with and without autism have been considered in relation to this aspect. In the investigations presented by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here the usual invariant quantity concerning the number of features in a face was manipulated via presentations of schematic faces. These varied in terms of the amount and position of facial features although their normal locations in relation to the outlines of the faces were kept constant for the upright and inverted

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positions. Hence, attentional switching was encouraged in relation to different groups of facial features and small numerosities and there was an emphasis on the simultaneous association between these two aspects. The aim was to enhance the fast processing of these co-occurring items and to promote mental flexibility and the generation of ideas by the participant. As highlighted by Gordon(2000) activities that are generated by the self tend to be more motivating for the individual and consequently result in enhanced learning. Also, spontaneity tends to facilitate variation in activities and opportunities for skill transference and concept generalisation.

Additionally, attentional flexibility is an aspect to consider in the context of the children’s performances on the Picture Completion subtest. Some of the items are pictures of familiar objects or animals and others represent parts of people or a whole body. Always something is missing which is usually a common feature of the object or individual or perhaps part of a familiar article that would be seen on or with a person. When assessed initially, sometimes the young people considered by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and presented here concentrated on the wrong aspects of the pictures and they appeared to have problems in directing their attention to other areas for consideration in relation to finding the missing item. During the training period they were involved with tasks where they had to attend to details concerning the physical characteristics of people. As the sessions progressed they appeared to attend more easily to different human aspects and to include these in their drawings. When re-assessed on the Picture Completion subtest, often with apparently little effort they directed their attention to the missing features and consequently they tended to respond very quickly and accurately.

Although none of the tasks in my research involved dynamic stimuli, the participants were involved very actively, physically and mentally with the tasks during the sessions and as they progressed this tended to be more so in relation to activities elsewhere. As indicated above, changes became apparent concerning their attentional capacities in terms of flexibility and this increased facilitation in their personal development was suggested outside of the sessions. When considering everyday situations, the young people became more capable of extracting appropriate contextual information and consequently, they developed more natural social responses and interactions.

When considering the young people discussed by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and presented here, some of their responses in relation to their perceptions of emotions from facial expressions indicated that they had misjudged the emotions on certain facial stimuli because they looked at one area of the face instead of processing the whole. Specifically they might have looked at the lower part and particularly the mouth as opposed to the eyes. They might have given erroneous responses or taken more time to identify a particular emotion. Even if they were correct on the static faces presented during the sessions they might have experienced difficulties sometimes in more realistic situations. During the individual sessions the children were not presented with neutral expressions when considering the detection of emotions from facial expressions as the assessment of emotions task used in the investigations involved only specific facial expressions. The memory for faces test did involve neutral expressions but the presentation time for each item was 2 seconds so that time was available for the participant to view the whole face. Additionally, the

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young people with ASD in my studies noted above indicated that they could use other bodily communications, as well as specifically facial aspects to facilitate their understanding of social interactions and sometimes aspects of the context or situation.

In consideration of the individuals discussed here who participated in my projects as well as others on the autism spectrum that I have been involved with over some years their presentations have been quite varied in degree and nature. Hence, only specific individuals were selected as participants for my interventions. A possible expectation concerning the approach described in the studies by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here was that flexible attention might be facilitated in relation to various groups of facial features and the associated information communicated by them in everyday situations. Stimulating the brain in such a way might enhance perceptual discrimination for certain facial characteristics and perceptual coherence in relation to configural and holistic aspects with associated implications specifically in the context of people and social settings. It is essential, not only to be able to process and interpret various types of information but to do so at a speed which is facilitative in relation to the situation.

In relation to other areas, mental flexibility has been highlighted by Dark & Benbow(1990, 1991, 1994) as being a salient characteristic of mathematically talented adolescents. Furthermore, Gray & Tall(1994) emphasised the development of ‘proceptual’ thought involving the merging of process and concept and the mental manipulation of symbolic information as being significant in the attainment of mature numerical and more advanced mathematical thought. For more recent discussions involving the proceptual notion reference could be made to Tall et al.(2001) and Gray & Tall(2007). Backward digit span can be considered as a working memory task involving the manipulation of stored numerical information as discussed for example, in relation to arithmetical cognition by Hoard et al.(1999) as well as more recently by Passolunghi & Cornoldi(2008).

Although the young people who participated in my project including those discussed by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) demonstrated some facility in relation to particular questions on both sections of the WOND, some difficulties were demonstrated on both parts. They improved their performances on both WOND sections after the training sessions involving the object assembly items, human figure drawings and the dots and facial features tasks. Improvements were shown on the Recall of Digits Forward and Backward although considerable effort was apparent sometimes in the manipulation and recall of accurate information. The pupils who had been involved in studies noted above had continued with mathematics tuition at school but they had not been in receipt of specific mathematical support from myself during the period of the projects.

Holding in mind information is an aspect of working memory and particularly the central executive(Baddeley & Logie, 1999) that has been highlighted concerning theory of mind acquisition involving metarepresentational abilities in those with typical development or autism(Baron-Cohen et al., 2000). Results of investigations involving backwards digit span(Davis and Pratt, 1995) and counting span(Keenan et al., 1998) have given support for working memory being a factor in the development of children's theories of mind. Also, school aged children and adolescents diagnosed

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with autism or Asperger syndrome who performed well on theory of mind tasks tended to respond better on digit span(Dahlgren et al., 2003).

As emphasised by Klin et al.(2000) appropriate social interactions between participants require engagement in holistic processing of information that changes rapidly such as that offered by facial expressions. Also, Lindner & Rosen(2006) found that children and adolescents with Asperger syndrome experienced more difficulty than the typically developing controls when required to identify emotions whether via static facial expressions, dynamic facial expressions or prosody. They highlighted the problems associated with an over reliance on verbal cues as a compensatory approach to managing social situations. As indicated above, the young people presented by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and considered here had marked difficulties concerning social interactions and aspects relating to intuition and the recognition of emotions so they tended to resort to a verbal and analytical processing mode in some situations.

In relation to the numerical aspects of the studies by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here, subitizing or ‘global counting’(Jarrold & Russell, 1997) were the processes indicated usually concerning the participants’ responses to the dot stimuli and the facial features but some ‘local counting’ occurred and slightly more so for the facial features. As they practised these tasks which included various arrangements of dots as well as facial features varying in amount but in their usual positions within schematic faces, the apparent tendency was towards more global counting and this included items beyond the expected subitizing range.

As highlighted by Laughlin(1997) with reference to Bastick(1982) intuition is characterised by various qualities including its non-analytic and gestalt aspects as well as affective and specifically empathic associations. Additionally, a more recent contribution noting the properties attributed to intuition by Bastick(1982) has been given by Claxton(2003). Also, in a discussion concerning beliefs described as intuitive or reflective, Sperber(1997) emphasises the representational and metarepresentational abilities of human individuals and the possible reciprocal movement between concepts of an intuitive or reflective nature in concept revision. Mental flexibility which has been noted earlier in the presentation here is a requirement for this aspect of development.

As discussed by Pring et al.(1995) in the context of savants and autism, a marked segmentation ability might characterise particularly individuals with a talent for art. Additionally, in an investigation by Drake et al.(2010) it was concluded that a skill concerning realistic drawing was related to a strong bias in local processing and repetitive behaviour tendencies. Some characteristics suggested in individuals with ASD, with or without artistic talent seemed to be apparent in typically developing children who were gifted artistically and selected here for their skill in producing realistic drawings. Furthermore, a facility for seeing wholes in terms of their parts might be associated with high abilities in other areas such as mathematics. Higher level functioning requires mental flexibility in relation to this mode and the ability to integrate perceptual and conceptual aspects into meaningful and coherent wholes. Also in this context, hypothetical thinking and the intuitive process are salient in the development of mature intellectual functioning and specifically in the studies

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described by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) concerning mathematics and art.

As highlighted by Maor(1991) the artist, Maurits Cornelis Escher and the musician, Johann Sebastian Bach appeared to share a similar mathematical intuition. In these individuals an acute sense was apparent relating to pattern, rhythm and regularity. The latter was temporal for Bach and spatial for Escher. The notion of symmetry is fundamental to the compositions of Bach as well as to the drawings of Escher. In mathematics, the definition of symmetry concerns the idea of invariance as noted by Zee(2007).

For individuals on the autism spectrum a desire for symmetry would appear to be intricately related to a desire for beauty and harmony. A sense of beauty and a state of harmony are so difficult apparently for those of such a disposition to experience in terms of their relationships with people. Baron-Cohen(2006) highlighted the “need for sameness” with reference to Kanner(1943) in addition to the social deficit as central to his hyper-systemizing theory of autism. However, an emphasis on a desire for symmetry or balance would seem a more fundamentally appropriate way of describing a characteristic pertinent to those on the autism spectrum.

During the course of my clinical work I have become very aware of a keen sense of justice expressed by individuals with AS. If they feel wronged themselves or they witness an act of injustice in relation to someone else it is crucial for them to see that the offender is reprimanded as soon as possible. Also, it is essential that the punishment is seen by them as very specifically appropriate to the offence and this applies also if they are the offenders. If the punishment is not perceived as being meaningful and justice is not seen to be done quickly, anxiety rises to a considerable degree in the person with AS and it does not recede until the balance is reset through the acknowledgement and appropriate redress concerning the offence and the perpetrator.

As noted in the present discussion, often some of the characteristics highlighted in relation to individuals on the autism spectrum concern their apparent ease in processing specific details in certain situations and particularly, a facility for attending to the more unusual aspects as opposed to the similarities between stimuli. Although these are very useful attributes in certain contexts, at other times an emphasis on more holistic processing and an appreciation of similarities is not only preferable but very significant, for example, in relation to appropriate social functioning. When considering the young people discussed by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) more positive emotions were shown as they continued with the training sessions. These more positive emotional experiences were demonstrated in connection with the specific tasks and reflected later as they chose to do activities in art as well as other areas including organised group activities and everyday social situations. Certainly they demonstrated more facility in terms of organising ideas in various ways and spontaneously taking different cognitive perspectives. It was suggested by the present author that particular approaches which promote abilities in certain areas might contribute to enhancing development in other spheres. Hence, the integration and transference of skills might be facilitated and the generalisation of concepts.

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As highlighted by Downing et al.(2004), the findings from their investigation with typically developing adults suggested that the human body, similarly to the face, might be given prioritisation in relation to attentional selection. Usually we know our own bodies immediately as we look at our body parts and we distinguish our bodies from those of other people. As indicated in the approach described by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) the young people with ASD were encouraged to think about body parts and to unify them in the formation of human cardboard characters or more complex aspects of the body as well as in human figure drawings. Specifically, they were helped to think about themselves and their own bodies as distinct from others and their bodies. Although the participants might have used some facial characteristics and cues to help them recognise individuals and understand their emotional presentations, they indicated that attending to bodily aspects was facilitative particularly in relation to functioning within social contexts. The subitizing tasks required them to apprehend immediately the numerosities associated with dots and with different groups of schematic facial features. Specifically, the non-algorithmic mode of functioning which is so crucial in many ways to human development and particularly in relation to social situations is an aspect that the author has aimed to facilitate in those individuals of such a disposition discussed in the studies mentioned here.

In numerical, arithmetical and other areas of mathematical processing it is essential to be able to ignore irrelevant information as quickly as possible and to direct attention to the relevant aspects of the task so that they can be integrated in the creation of a solution. As noted, the activities which I used in the specific approach highlighted here involved the fast processing of dots and facial features associated with small numerosities as well as the formation of human characteristics and parts of the body via the manipulation of cardboard components and the drawing of human figures. Overall, the aim was to help the promotion of cognitive development in the young participants with ASD through the coordination of ideas and to facilitate mental functioning at a higher level and in relation to themselves and others.

In a discussion concerning the mind, the brain and consciousness by Mittelstrass(2008) the difference is highlighted between the construction of scientific knowledge about oneself and the construction of understanding concerning the self by the individual. Also the contribution of the latter construction is emphasised in relation to the meaning of consciousness. Individuals with sufficient ability on the autism spectrum may be able to construct scientific knowledge about themselves but understanding themselves is more problematic. The ultimate aim of the approach presented by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) was to make a contribution to self-understanding and self-unification with the associated concern to promote the development of human relationships. Often because of poor social and communication skills and an unusual presentation young people with ASD may experience social isolation, discrimination or bullying.

Individuals with ASD tend to be seen as low in emotional warmth and low in social competence. They may be competent and very highly so in some areas but their cognitive profiles are likely to be uneven. Hence, it seemed poignant specifically to develop ways of helping individuals with ASD to function in a more unified mode in order to prevent prejudice. Those with ASD have been considered often as somewhat unusual in their presentation as they tend to centre on themselves and to lack the

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intuitive ability necessary for responding quickly and appropriately in social situations. The exceptional abilities of some individuals such as savants on the autism spectrum tend to be seen in the context of their perceived disabilities and contrasted with them.

In the approach discussed in detail by Lawson(2008b, 2010) an emphasis was placed on merging sensual experiences to promote learning, especially in relation to the multiplication tables. In the other studies by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) symbolic experiences have been brought together with the aim not only of promoting harmony within and across the specific areas concerned but elsewhere within a social context. The summation of all knowledge in a symmetric and synoptic mode in relation to a central notion is fundamental to ‘The Glass Bead Game’, with reference to the recent edition, that is, Hesse(2000). The interrelationships between different spheres of knowledge as emphasised in the ‘Game’ are essential to my approach discussed here and promoted for further consideration. For those on the autism spectrum, a primary aim concerning ways of enhancing their development is to facilitate harmonious unity within the individual. Something akin to the fundamental idea in the ‘Game’ is the underlying notion associated with the approach discussed here by the present author.

Attempts have been made to help facilitate the understanding of those with ASD and to create interventions with the aim of enhancing their progression throughout the lifespan. Alongside these positive moves the author would prefer the term ‘disorder’ to be eliminated from the classification of ASD with consideration being given to the alternative term ‘disposition’ as this highlights a particular style of functioning and does not centre on negative aspects.

Specific approaches which might facilitate the promotion of abilities in some areas might be used to enhance development in other spheres. The approach which I used involving human figure drawings, facial features, small numerosities, arithmetic and other aspects of mathematics was aimed at facilitating the perception of people and numbers within a holistic context by emphasising the significance of particular and relevant details and their interconnections. As noted by Matthews(1999) the drawing process is part of the child’s complex repertoire for expression and representation. Communications are involved with associated emotions and intentions relating to real and imaginable entities. Additionally, Callaghan(2008) emphasises how symbols are intentionally communicative. Also, aspects that are fundamental to the development of pictorial symbols are applicable to other symbolic systems. For a recent discussion concerning the development of representational and expressive drawing and their relationship, reference could be made to Jolley(2010). He highlights how often, drawing is considered a solitary activity. Also, the present author notes that this is true of mathematics. However, linking the two activities as I have encouraged via the approach presented here and promoting these activities, sometimes quite specifically in associated contexts within and outside of an educational environment in group situations as well as individually might help to facilitate social and emotional development.

Certain aspects considered in the approaches used with children in earlier studies contributed to the more comprehensive approach used with the children and adolescents in the following studies and discussed here. Expressive and

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representational abilities might be promoted in various areas as well as the possible facilitation or enhancement of hypothetical thought, intuition and representation of mental representations. The results presented in the investigations by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and considered here suggest that at least to some extent, positive changes in these abilities have occurred in relation to particular young people.

It has been indicated here, that certain individuals on the autism spectrum may have very strong reasoning abilities within specific contexts but their tendency to lack wisdom manifests itself clearly in social situations. Hence, some of those with ASD may be the recipients of markedly positive and negative reactions from other people. In relation to my own work, an intention has been to facilitate the development and more judicious application of knowledge within an interpersonal context for those experiencing social and communication difficulties.

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1. Introduction

1.1 Human Body Parts, Numerical Systems/Development and Human Figure Drawings

Human body parts have been used as counting aids in the creation of some number systems in various cultures. Also, the fingers have been highlighted as being significant particularly in relation to early numerical development from a neuropsychological perspective by Butterworth(1999). Additionally, facial features are bodily aspects that have been noted in connection with number systems and in association with numerical disabilities by specific investigators. Badian(1983) considered that a deficiency in visual attention to precise detail as suggested in the human figure drawings of young children might offer information relating to later numerical abilities.

Hence, Lawson(2000c, 2001a) studied first year junior aged children and assessed them on their drawings of people, a standardised arithmetic test and specific rectangular and non-rectangular addition questions used earlier by Lawson(1986, 1989, 1990, 1995a, b, 2000a, b, 2001a) and based on findings by Friend(1979). The terms rectangular and non-rectangular referred to the arrangement of the digits in the addends. In relation to their attainments, the participants received different types of instruction or none if they had not demonstrated any major problems. The results suggested that directing the children’s attention to specific arithmetical details and associated numerical concepts or particular omissions and poorly depicted aspects concerning their drawings led to enhanced development and performances in both areas. These particular rectangular and non-rectangular addition problems were used as items in a dyscalculia test battery assessment by Lawson(1995b, 2000b, 2001a) and a more detailed analysis concerning the assessment implemented with specific young people was presented later by Lawson(2002, 2008b, 2010).

The research concerning first grade children presented by Noël(2005) indicated that finger gnosia was good as a predictor of numerical skills and additionally, this was apparent for left-right orientation. Finger gnosia predicted performances to the same extent on numerical tasks irrespective of whether they were dependent on finger or magnitude representation. Also, in research by Rusconi et al.(2005) concerning adults, repetitive transcranial magnetic stimulation(rTMS) over the left angular gyrus was found to disrupt finger gnosis and number magnitude processing.

In a more recent investigation by Gracia-Bafalluy & Noël(2008) first grade children were selected for three groups. Those with poor finger gnosis were involved with a finger differentiation training programme(G1). A control intervention group of children with poor finger gnosis received story comprehension training(G2) and a group of children with high finger gnosis scores continued with the usual school lessons(G3). The finger differentiation training comprised two sessions a week, each of half an hour for eight weeks. Prior to the training period, children in G3 were superior in their performances when compared with those in G1 and G2 in relation to two numerical activities, one involving elaboration of the verbal numerical chain and the second involving counting collections of items. After the finger differentiation training period children in G1 had better finger gnosis than those in G2 after their

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story comprehension training and superior scores to those achieved originally by children in G3.

In the finger gnosis assessment the requirement for the children was for them to differentiate their fingers when touched and in the absence of visual cues. The specific task was that used by Noël(2005). Also, they performed two other tasks, namely ‘Draw a Man’(Goodenough & Pasquasy, 1967) and ‘Draw a Hand’. In the latter, the non-dominant hand of the child was positioned under the table so that it was not visible. The child was asked to draw a hand but without putting the pen down and without using his/her hand as a model. After the finger differentiation training the children in G1 performed better on the ‘Draw a Hand’ task than those in G2 after their training in story comprehension. A possible consideration was that the internal representations of the fingers and hands of the participants had improved but the other representations such as those involving the whole body had remained unchanged.

Additionally, after the finger differentiation intervention children in G1 were faster than those in G2 after their story comprehension intervention when requested to say how many fingers were raised in photographs of hands and the effect increased for more fingers. In fact, the children in G2 performed less well than those in either of the two other groups. After the finger differentiation intervention children in G1 were superior in performance for the subitizing task when compared with those in G2 after their story comprehension training. Also, the children in GI tended to be better at processing Arabic digits. Overall, it was suggested that the training in finger differentiation involving young children resulted in enhanced performances concerning finger gnosis, subitizing, counting raised finger representations and ordinality.

In Badian’s discussion concerning those who might be described as dyscalculic, the omission of the nose was noted and sometimes the inclusion of an incorrect number of fingers. A marked impairment of arithmetical skills as well as a lack of response to educational interventions were the criteria described for developmental dyscalculia in the children involved in a study by Shalev & Gross-Tsur(1993). Reference could be made to Shalev(2007) for a fairly recent discussion of aspects concerning developmental dyscalculia in the context of definitions, assessments and prevalence. Additionally, the discussion on developmental dyscalculia by Butterworth(2008) and the contribution concerning the genetics of learning abilities and disabilities by Kovas & Plomin(2008) are of interest here. Some of the young people in my investigations did have impairments which manifested themselves in relation to specific aspects of arithmetic and their responses had been limited in relation to remedial interventions. When considering the study by Lawson(2000c, 2001a), one boy omitted the nose on the drawings of a man, a woman and himself. After training which involved attention to numerical details all pictures included this feature. On one hand in each drawing the number of fingers was incorrect but on re-assessment this detail was shown accurately and there was a marked overall improvement on all three drawings. Another child drew a man without a nose but after successful tuition in relation to specific addition exercises which had been difficult for him, he included this feature in two dimensions and the bridge. His performance improved overall for his drawing of a man but it remained unchanged for the woman. Initially, both boys had performed well below their chronological age levels on an arithmetic test but marked improvements were shown on re-assessment.

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Additionally, it is interesting to note that in a recent study by Hsaio & Cottrell(2008) involving adults, two relatively long fixations were found to be sufficient for recognition of adult facial images of both sexes. The first fixation occurred just to the left of the nose centre and the second fixation was indicated around the centre of the nose.

Generally when considering the prominence of facial features, the nose contrasts less with the face than the eyes and mouth and this is apparent particularly for neonates and very young babies with their more limited visual acuity in comparison with the adult level, with reference to Slater & Butterworth(1997) and Slater(2001). In a recent study by De Heering et al.(2008) consideration has been given to the nature of the visual information that neonates depend on for facial recognition. Various skills in this respect have been suggested by investigators despite limitations in relation to their visual abilities and immaturity of cortical regions. In the study just mentioned above, supportive findings have been presented concerning a low spatial frequency being advantageous for recognition of faces in newborns and the suggestion that face specialisation emerges from gradual developmental processes.

Neonates and other infants appear able to process facial stimuli in dynamic or static states and to attend to internal and external facial features(Slater et al., 2000; Blass & Camp, 2004; Turati et al., 2006). In the study by Turati et al.(2006) inner or outer facial features of real adult female facial images were shown to offer sufficient cues for face recognition by neonates. Also, an advantage of the outer over the inner part of the face was suggested as neonates did not show recognition when the external features of a familiarised face were removed whereas removal of the inner facial region did not prevent recognition. Furthermore, recognition was disrupted by inversion of the face stimuli when only the inner region of the face was presented but not when the whole face was shown or only the outer features. Hence, it was suggested that neonates could use information for facial recognition concerning either the inner or outer features and either local or configural perceptual aspects.

Additionally, in a recent study by Leo & Simion(2009) the ability of neonates was investigated in relation to the recognition of configural changes in the context of real facial images. The newborn babies were assessed in terms of their sensitivity to the Thatcher illusion, with reference to Thompson(1980). This effect is produced by a 180º rotation of the eyes and mouth within a smiling facial image resulting in a grotesque transformation. Thatcherization is apparent only for the upright as opposed to the inverted image of the face. In the investigation by Leo & Simion(2009) an habituation procedure was used to study the ability of neonates in relation to the discrimination of an unaltered veridical facial image in comparison with the thatcherized version of the face. The results indicated that these newborn babies were able to discriminate an unaltered facial image from the thatcherized form of the same face for the presentation of stimuli in the canonical upright orientation. However, the participants were unable to make a discrimination between the same stimuli for the upside-down presentation. The results were given in support of the sensitivity at birth to second-order relational information, with reference to Maurer et al.(2002), that encodes the spatial information between facial features in processing upright faces.

Furthermore, in reviewing the literature Macchi Cassia et al.(2008) highlight the fact that neonates have shown a preference for top-heavy as opposed to bottom-heavy

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presentations and this is crucial in the attentional bias associated with faces. The description of faces as being top-heavy refers to the presence of more patterning in the upper section of the face involving the eyes and eyebrows in contrast to relatively less patterning in the lower part concerning the mouth. The study by Simion et al.(2002) is highlighted as one of the investigations demonstrating a preferential response in neonates relating to the top-heavy perceptual property in the context of geometrical nonfacelike stimuli.

However, as noted by Grossman & Vaish(2009), the findings of Farroni et al.(2005) were presented as challenging a suggested preference in neonates for top-heavy symmetrical patterns. Farroni and associates found that for schematic and naturalistic facial images the contrast polarity was a significant aspect for newborn babies. They demonstrated a preference for schematic and naturalistic upright facial images only in the positive polarity condition, that is, with dark eye and mouth regions and a lighter surrounding area. The preference was not shown for the condition of negative polarity where the eye and mouth regions were light and the surrounding area was dark. Also, placing dark patches, representing irises in white squares, on the schematic facial stimuli in the negative polarity presentation restored the preference for upright faces. Additionally, neonates preferred human faces under conditions of natural lighting such as daylight or overhead illumination as opposed to faces lit at the bottom. It was noted that a mechanism showing sensitivity to such natural lighting contexts might demonstrate sensitivity to the relatively darker areas around the eyes and mouth. Also, it would be expected that a device designed to facilitate eye contact identification in relation to an upright face would possess a bias toward stimuli with the potential to contain appropriate contrast polarity. For other perspectives which challenge the interpretations concerning the results found in the study by Farroni et al.(2005), reference could be made to Simion et al.(2007).

In a related context, Tomalski et al.(2009) considered whether human adults would show preferential orienting towards schematic face-like stimuli and whether this effect would be dependent on the contrast polarity concerning the stimuli. In two experiments it was shown that faster eye movements were elicited by upright schematic face-like patterns in comparison with inverted face-like patterns. Also, this was apparent only if they contained face- or gaze-relevant contrast information in the entire stimulus or solely in the eye area. The results were given in support of the preferential orienting pattern demonstrated in neonates as indicated in the study by Farroni et al.(2005).

Additionally, in a recent study by Grossman et al.(2008) infants aged 4 months viewed two sorts of dynamic events involving animated photorealistic faces which presented mutual or averted gazes in relation to the participants. Both types of gaze were followed by an eyebrow raise accompanied by a smile. Haemodynamic responses were assessed using near-infrared spectroscopy allowing spatial localisation concerning brain activation. Also, analysis of gamma-band oscillatory activity in the brain from electroencephalography provided temporal information concerning cortical processes. The results indicated two areas of the brain showing sensitivity to dynamic gaze direction as demonstrated by increased oxyHB concentration in the comparison of the mutual and averted gaze conditions. The specific regions which were the right superior posterior temporal and the right fronto-polar cortices have been implicated in these facial communication processes in adults. Additionally, similar cortical

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activations were produced by the mutual gaze itself as well as the eyebrow raise with the accompanying smile. The results were interpreted in terms of suggesting early specialisation of the cortical areas involved in the perception of cues concerning facial communication.

Macchi Cassia et al.(2008) consider another configural visual property in connection with faces termed congruency, which concerns the interdependency among various stimulus features, namely the shape and orientation of the outer contour and the spatial relationship associating the inner features. The limits of the pattern and spatial arrangement of these inner features are determined by the shape and orientation of the outer boundary. The results of their investigation indicated that within the context of nonfacelike stimuli, congruency gave rise to the same strength preference as that brought about by facedness. Also, the attentional biases relating to facedness and congruency were cumulative in their effect associated with the visual preferences of neonates. This was so in terms of an additive model which was true also for the summation of congruency with top heaviness in nonfacelike stimuli comprising more items in the upper section.

As highlighted by these investigators, when considering figural excellence stimulus dimensions such as symmetry, repetition and regularity are present to the greatest possible extent in congruent visual configurations. These are aspects to consider here not only in relation to faces but in the context of the human body and the interconnections of bodily parts as well as in association with human figure drawings. Gliga & Dehaene-Lambertz(2005) used high density event related potentials(ERPs) to investigate whether there was a similarity in the configural information processing for the perception of bodies and faces. Recordings were made of the responses given by adults and infants aged 3 months to static images of normal and distorted faces and bodies. The results were considered as indicating that rapid processing of configural information occurred for bodies as well as faces. At 3 months of age infants were able to discriminate perceptually distortions in human body configurations. They could recognise normal human facial and additionally, bodily configurations.

Also, in a recent study by Marshall & Shipley(2009) infants aged 5 months viewed point-light displays that depicted the human actions of walking, kicking, throwing and running. The displays involved upright canonical and spatially scrambled displays with disrupted global forms of the actions. Significant differences were noted between event-related potential(ERP) waveforms concerning the canonical and scrambled presentations at the mid-parietal, lateral parietal, temporal and occipital areas. These differences showed particular clarity at the lateral parietal electrode regions, P7 and P8, where a more positive waveform was apparent for the scrambled as opposed to the canonical stimuli. Hence, the results suggested that these infants were demonstrating a sensitivity to disruption of the human form in motion.

Additionally, in a recent investigation by Bristow et al.(2009) infants, aged 10 weeks were studied in relation to how they initially matched the articulatory movements that they saw with the sounds that they heard. High density ERPs were recorded in response to vowels produced in the auditory mode which followed a face presenting silent articulations which were congruent or incongruent with the auditory items. Results from the first experiment were in line with the findings concerning adults and indicated that auditory-visual integration was apparent during early perceptual stages.

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A similar mismatch response occurred in terms of timing and topography, whether the presentations of the preceding vowels were in the visual or aural mode. In the second experiment, audiovisual integration was investigated in relation to aspects that were linguistic, specifically vowel perception and non-linguistic, namely gender perception. A mismatch response was noted for both sorts of change at similar latencies. Their significantly different topographies were considered in terms of the cross-modal integration of these features being computed in parallel by two different networks. Specifically as indicated by brain source modelling, phoneme computations were lateralised towards the left and gender towards the right hemisphere. Hence, it was suggested that there was an early processing bias within each hemisphere. Other observations indicated repetition suppression in temporal brain areas and repetition enhancement in frontal brain regions. Also, reference could be made to the recent discussion by De Haan & Matheson(2009) concerning the emotional processing of facial and vocal information and their integration.

1.2 Facial Features, Small Numerosities, Human Figure Drawings and ASD

Usually the number of features in the face does not vary and there are many opportunities for infants to be sensitive to various distinctions concerning small groups of facial features. Results from a variety of studies have indicated that infants are able to make discriminations between sets of items associated with different numerosities. However, there has been much controversy in relation to the underlying processes concerning these discriminations and consequently, refinement of the experimental approaches. For relevant discussions and research including both small and large numerosities, reference could be made to Cohen & Marks(2002), Feigenson et al.(2002), Mix et al.(2002a, b), Wynn et al.(2002) and in association with a neuroconstructivist perspective to the presentation by Ansari & Karmiloff-Smith(2002). Also, contributions have been made in this area by Xu(2003), Lipton & Spelke(2003, 2004), Brannon et al.(2004), Clearfield(2004), Feigenson et al.(2004), Kobayashi et al.(2004), McCrink & Wynn(2004), Rousselle et al.(2004), Feigenson(2005), Feigenson & Carey(2005), Kobayashi et al.(2005), Wood & Spelke(2005), Clearfield & Westfahl(2006), Féron et al.(2006), Jordan & Brannon(2006), Mack(2006), Mix & Sandhofer(2007), Xu & Arriaga(2007), Cordes & Brannon(2008a), Izard et al.(2008), Jordan et al.(2008), Mix(2008), Rousselle & Noël(2008) as well as Sophian & Crosby(2008) and Moeller et al.(2009) using eye tracking.

Additionally, in a recent review by Cordes & Brannon(2008b) consideration has been given to the preverbal infant’s representation of number, area and time with particular aspects being discussed in relation to continuous variables and numerosity concerning small and large sets. Caution is highlighted when considering cognitive interpretations concerning studies with babies. Also, reference could be made to Kagan(2008) for a recent and detailed discussion emphasising controversial issues in this respect.

Recently, Cordes & Brannon(2009) carried out three experiments to investigate the representation of continuous variables in comparison with number in human infants. In the first experiment, using a larger sample of human infants the researchers were able to replicate the study by Clearfield & Mix(1999). They found that infants did notice contour length changes but also, they attended simultaneously to number and perimeter/area. In the second and third experiments number was compared with

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continuous extent, with large sets being used for comparison in the second study and a combination of small and large sets for the third experiment. In all three sections, the infant participants noticed numerical changes even when continuous variables were held constant. Specifically, the results of the third experiment suggested that given a sufficient ratio of change, a 4-fold number change, number was more salient than continuous extent for infants comparing small and large sets. Additionally, reference could be made to a recent and comprehensive discussion by Brannon & Cantlon(2009) concerning the origin of numerical thinking and a contribution by Jordan & Brannon(2009) relating to nonhuman and human numerical cognition as well as a review by Cantlon et al.(2009a). Also, Dehaene(2009) presented a detailed discussion concerning the origins of mathematical intuitions with particular consideration being given to arithmetic. He noted that more recent studies indicated that infants could attend to parameters which might be numerical or non-numerical. They did this to a variable extent and this depended on the experimental design and especially on how these parameters varied within the stimulus set.

The notion of subitizing has been considered in various investigations including discussions mentioned above as well as being analysed within the context of how children acquire words for small numbers by Benoit et al.(2004). As highlighted by these investigators, the term subitizing concerns the exact quantification of sets with few items without counting explicitly, internally or externally. After referring to some of the research mentioned above and other relevant investigations they described three specific skills associated with subitizing, namely perceptual, perceptual-preverbal and perceptual-verbal. The first, a perceptual skill they noted in relation to the ability of individuals, often suggested in infants to differentiate perceptually, arrays which differed by one item without the necessity for an emphasis on numerosity. As indicated above, various interpretations not based on numerosity have been proposed in association with the underlying processes. The second skill, with reference to Tan & Bryant(2000) concerned perceptual-preverbal subitizing where verbal naming was not necessary but the emphasis was on numerosity irrespective of the numerical perceptual configuration. The third category referred to as perceptual-verbal subitizing involved the use of number words in the expression of numerosity. This latter and more traditional use of the term subitizing is relevant particularly to the studies by the present author discussed below and to the current presentation.

As highlighted by Benoit et al.(2004) with reference to a study by Grice et al.(2001) which is described in more detail later by the present author, perceptual integration of features as in human facial perception seems to be primitive as well as variable in relation to different developmental disorders, in this case autism and Williams syndrome. Hence, subitizing might develop from a basic and early skill that binds spatially separate elements into a whole. Further lengthy progress then might follow involving the relationship between the elements and the whole as the individual coordinates these aspects and abstracts information of consequence to their numerical development. Hence, the present author felt that it might be helpful particularly to facilitate jointly perceptual integration in relation to numbers and facial features for those who might be experiencing difficulties concerning either or both aspects of their development. Also, progress might be enhanced in related areas such as social development.

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Consequently, Lawson(2001b) investigated the apprehension of small numerosities in association with dots or facial features and children’s human figure drawings. Generally, the results indicated that these first year junior aged pupils could apprehend the numerosities associated with various arrangements of dots and small sets of schematic facial features. The amounts ranged from 1 to 5 and the expected trend was indicated with faster and more accurate responses occurring for the smaller set sizes. Also, the children drew a picture of a man, a woman and themselves with later analysis and assessment involving the system by Naglieri(1988). Children who had omitted the nose and/or whose performance was relatively poor overall on the drawing task were selected for a short training session. They were encouraged to reply with speed and accuracy to cards with dots and facial features until all items had received fast and accurate responses and then they were involved again with the drawing task. Hence, the participants had a considerable amount of practice with subitizing for sets involving 1 to 5 items.

Generally, the re-assessment results concerning the drawing tasks were indicative of a trend reflecting a marked increase usually in the number of included features concerning the face and other body parts. Also, the depictions tended to look more realistic although the training had involved only schematic faces. Overall, it was apparent that the dots and facial features tasks could be used to encourage the fast apprehension of small numerosities and to facilitate the inclusion of details in children’s human figure drawings.

In a further investigation(Lawson, 2003) a case report was presented concerning a boy with a diagnosis of Asperger syndrome(AS) which is characterised by a qualitative impairment in social interaction and restricted, repetitive and stereotyped patterns of behaviour, interests and activities(American Psychiatric Association, 1994, 2000). There may be a delay in motor milestones and motor clumsiness is common although not an essential diagnostic feature(World Health Organisation, 1992). In fact, he had noticeable problems in relation to dyspraxia which concerns impairments in skilled movements. He was assessed on various aspects of his cognitive functioning, an arithmetic/mathematics test and human figure drawings. Then he participated in training sessions in which he formed faces, a hand and whole people using the Object Assembly items from the WISC-R(UK) and the WAIS-R(UK). After removal of the items he produced drawings of a man, a woman or himself and sometimes specific body parts. Also, he was involved with the dots and facial features tasks and responses concerning their associated numerosities. At re-assessment noticeable improvements were demonstrated on his three human figure drawings which were maintained and developed without further input. Also, his performance was enhanced quite markedly on the arithmetic/mathematics test. In later follow-up sessions it was indicated that he had been involved in a variety of activities in art at home including the creation of paintings with specific and integrated features. He continued to develop his interest and involvement in art at home, at school and elsewhere alongside increasing maturity and confidence in social situations.

Hence, it was felt that other children with a variety of disabilities and including specific difficulties concerning their drawings of people might benefit from the implementation and modification or elaboration of the approaches described above. They might present with various mathematical abilities and the training might facilitate improvements in this sphere. In a study by Lawson(2004) two children were

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presented in detail, specifically K. who was described as a boy with Asperger syndrome and L. as a boy with Asperger syndrome and dyspraxia which was relatively mild. Child L. had experienced other difficulties of a specific numerical nature so he was involved in training to address this issue and a presentation involving this work was given by Lawson(2005b). Also, L.’s problems associated with learning the multiplication tables have been discussed in detail with other case studies in the context of assessment and remediation in relation to numerical, arithmetical and other areas of mathematical development by Lawson(2008b, 2010). Furthermore, the non-rectangular addition problems highlighted earlier in the current discussion and the associated remedial approach designed by the present author were discussed in the contribution by Lawson(2008b, 2010). A recent presentation by Lawson(2009) concerned a boy G. who experienced difficulties particularly with these non-rectangular addition problems and he responded successfully to the remedial intervention. Also, G. had been diagnosed with Asperger syndrome. The two children, K. and L. as well as G. participated in similar assessments and training sessions and in addition to the follow-up sessions when they were administered formal assessments the participants were monitored over a longer interval. They demonstrated significant positive changes in relation to their specific areas of difficulty and presented with characteristics associated with the autism spectrum which were relatively less severe in quality and/or quantity.

The children in these studies by Lawson(2003, 2004, 2005b) were participants while they were attending primary schools or during the holiday period before the start of secondary education. The boy reported by Lawson(2003) had been monitored informally by the present author via contact with the home since the initial follow up sessions. The children presented by Lawson(2004, 2005b) were monitored and supported as appropriate during the following years after the re-assessment sessions. Unfortunately there may not be recognition of the difficulties associated with the autism spectrum for some individuals who are relatively able until they reach adolescence or adulthood. Hence they may not receive appropriate interventions to help them progress in some respects. The study by Lawson(2005a) concerned two young people, specifically a male adolescent B. and a female adolescent S., both with Asperger syndrome whose difficulties relating to the autism spectrum had not been acknowledged until after the commencement of their secondary education. They received similar assessments and interventions initially and they were monitored and supported as appropriate over the years following the re-assessment sessions. There were encouraging improvements concerning their attainments and management of situations both in and outside of the school environment.

Additionally, the presentations by Lawson(2008a, c) concerned two more young people, a boy J. who was diagnosed with Asperger syndrome during his primary school years and an adolescent male P. who was diagnosed with Asperger syndrome during the secondary stage of his education. The outcomes for these two young people were very positive in relation to their academic achievements and increased maturity and independence socially as J. progressed into adolescence and P. developed during the college stage of his education. Overall, the current discussion relates not only to those diagnosed with Asperger syndrome as indicated above who received similar assessments, interventions and ongoing monitoring and support as appropriate with encouraging results but also to a broad range of individuals of various ages with ASD. A more detailed contribution is offered here as an extension to the presentation by

30

Lawson(2008c) and including information concerning G. as indicated above and discussed by Lawson(2009).

Different researchers have referred to numerals as Arabic or Hindu-Arabic and I have retained the particular terms preferred by specific investigators when discussing their studies. Specifically, I should like to emphasise that I do acknowledge consideration in relation to the Indian numerical symbolic notation as highlighted for example, by Ifrah(1998).

In consideration of another aspect, drawings produced by the young people discussed here have been displayed at presentations noted in this contribution and with permission from the young people and their families. Specifically, the presentations have included Man, Woman and Self drawings produced under Test(T) and Re-Test(RT) conditions. Usually the young people participated in first Re-Test(RT1) sessions but some individuals participated in second Re-Test(RT2) sessions. Also, specific participants were not available for Re-Test sessions although they produced good selections of drawings which improved noticeably as they made progress. Furthermore, other drawings displayed at presentations included depictions of a variety of people, familiar and unfamiliar to the participants as well as scenes. Particular individuals developed their own interests and styles in relation to art and specific productions were displayed as appropriate.

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2. Method

2.1 Participants

Young people attending mainstream primary and secondary schools and some in the transition from primary to secondary education were selected as participants. Their drawings of people might be noticeably deficient in terms of omitted or poorly depicted features or they might draw only isolated objects but not people. They might depict only individuals of a very specific nature or produce characters in cartoon form. Various combinations of impairments might have been presented by the young people some of which concerned specifically dyspraxia, attention or arithmetic. However, all of the children and adolescents discussed here were experiencing difficulties particularly concerning relationships with people and they were diagnosed as being on the autism spectrum but for some of them not until their teenage years.

2.2 Materials

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)Man, Woman and Self

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)Mathematical Reasoning(MR) and Numerical Operations(NO)

British Ability Scales II(BAS II)-Elliot et al.(1996)Recall of Digits forward and Backward

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)Picture Completion

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)Vocabulary, Block Design, Similarities and Matrix Reasoning

Children’s Memory Scale-Cohen(1997)Dot Locations 1&2, Faces 1&2

Social Skills Training with Children and Adolescents-Spence(1995)Assessment of Perception of Emotion from Facial Expression

Object Assembly Items:Girl and Face(Male)-WISC-R(UK)-Wechsler(1976)Manikin, Profile(Female Face) and Hand-WAIS-R(UK)-Wechsler(1981)

Cards with Dots or Facial Features-Lawson(2001b)Cards had been prepared with dots on them representing numerosities from 1 to 5 arranged in geometric, linear and unorganised presentations with an overall total of 15 variations. Also, there was a pre-trial demonstration card with three dots placed in a diagonal line. The dots were in blue and contrasted clearly with the white background

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of the cards. Also, this was so for the schematic facial features which were in green and are described below.Specifically, there were prepared cards with schematic faces which included facial features varying in number and in relation to the specific characteristics. There were three cards representing each of the numerosities from 1 to 5 and hence 15 variations for each of the presentations involving upright and inverted faces. Also, one card contained a schematic facial outline without any features and on another card all main features were represented on a schematic face. These demonstration items were used to familiarise the participants with the experimental materials and procedure before the start of the trials. Additionally, there was a post stimulus mask card with a pattern not indicative of any numerosities.

2.3 Procedure

The Test, Training and Re-Test Sessions were arranged at convenient times in relation to the young people and their parents as well as the school routine and staff. Also, the number of sessions and their duration varied in order to meet the needs of the participants.

The assessments and re-assessments occurred within a therapeutic context as opposed to a formal educational or clinical setting. Specifically when the young people were re-assessed they were given only those questions to which they had given erroneous responses or those which they had not been able to attempt. Hence, different results might have been obtained if the tests had been administered in other conditions.

Test sessions: Participants were administered the WOND, DAP, Picture Completion subtest(WISC-III UK), Test of Perception of Emotion from Facial Expression(Social Skills Training, Spence), Dot Locations and Faces subtests(Children’s Memory Scale) and the Recall of Digits Forward and Backward subtest(BAS II). Also, the young people were presented with all four subtests from the WASI.

Cards with Dots or Facial Features: The participants were presented initially with the cards containing dots and the order of presentation was randomised in relation to the numerosities and types of dot arrangement. Then there was a varied presentation concerning the numerosities for the cards with schematic faces in upright followed by inverted positions. Initially each item was offered briefly and every card flashed up and down very quickly. The young people were required to give a number as soon as possible for these small sets of items and following an immediate and correct response they did not participate in further trials. Following the absence of an immediate reply time was allowed for the correct response after the brief presentation. After the short display of each item the mask card was shown to facilitate the inhibition of a possible post stimulus trace as highlighted by Starkey & Cooper(1995) and to encourage the fast apprehension of small numerosities. If an individual could not reply or he/she responded incorrectly, after completion of all brief presentations the failed items were offered again and for long enough to elicit a correct answer.

Training Sessions: After completing the assessments the young people participated in training sessions in which their attention was drawn to the details that they had omitted in their human figure drawings during the test session. This was achieved through questioning and prompting so that they had to produce an answer as opposed

33

to being given the names of the omitted features. Also, issues concerning size, proportion and dimension were highlighted as well as any other aspects that would give their drawings of people a more realistic appearance. The selected object assembly items mentioned earlier were used as aids in the production of more mature drawings. The participants were asked to assemble the items and their attention was directed to the details and issues noted above in order to facilitate improvements in their depictions. Then they were covered to prevent copying and uncovered as necessary for further discussions concerning difficult aspects after they had produced drawings again of complete figures and sometimes separate features.

Also, the young people were given training on the tasks involving cards with dots and facial features. The presentations of the items within the different sets were randomised and there was a variation in the order in which the groups were offered for each session. There was an emphasis on speed and accuracy until all items had received quick and correct replies.

Re-Test Sessions: The participants were administered again the WOND, Picture Completion subtest(WISC-III UK), Test of Perception of Emotion from Facial Expression(Social Skills Training, Spence), Recall of Digits Forward and Backward(BAS II) and the DAP.

3. Results

The formal re-assessment sessions occurred about six weeks after the last training session for J., L., G. and B. and there was a five week interval for K. There was no formal re-assessment for S. and the re-assessment for P. was several months after the final training session. The children and adolescents were followed up via informal sessions or contact with the families and school staff. The pictures of a man, a woman and the self indicated that they had retained their enhanced drawing skills and further improvements were apparent in terms of proportion concerning the various body parts in relation to each other and their integration. Also, the initial depictions of people by B. and S. had been cartoon figures but gradually their drawings had become more realistic in appearance. Also, although the human figure drawings of G. had continued to be of specific characters, they had become more detailed and more natural to some extent. There were marked differences at re-assessment for all of the children and adolescents. Additionally, the young people had been involved in various activities in art at home, at school and elsewhere including the production of drawings with specific and integrated features. As they were monitored during the following years it was apparent that they were demonstrating improvements in relation to their attainments and management of situations within educational environments and in a variety of other contexts.

3.1 Vignette: Young Person J.

Initially at school J.’s difficulties concerning relationships with other children were such that he was able to manage only a short time outside at break times before his negative interactions with other children resulted in him being required to stay in school. J. was contained in the classroom situation by careful control and positioning. It is of significance to note here that he tended not to draw people but on occasions

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when he drew human figures he demonstrated a poor depiction of facial features. As J. developed into adolescence he managed in school without support and coped with social situations at an individual and group level within and outside of school in structured and freer situations.

3.2 Results: Young Person J.

Chronological Age(CA)

Test(T) Session 8y 1m Re-Test(RT) Session 8y 3m

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RT

Mathematical Reasoning(MR) 109 115Numerical Operations(NO) 82 92WOND Composite(WC) 96 106

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Scaled ScoresT RT

Picture Completion 11 16

British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 28 38Recall of Digits Backward 44 49

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 69 Block Design 59Similarities 71 Matrix Reasoning 55

Verbal-VIQ 136Performance-FIQ 110Full Scale-FSIQ 126

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Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 5 6Female Child 5 6Adult Male 4 6Adult Female 6 6Total(24 Presented) 20 24

Items Identified Incorrectly(Correct Answer)

T RT

Male Child Male Child1. Angry(Sad) None

Female Child Female Child2. Disgusted(Afraid) None

Adult Male Adult Male2. Sad(Angry) None3. Nicely surprised(Sad)

Adult Female Adult FemaleNone None

Children’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 12 Immediate 3Short Delay 10 Delayed 10Total Score 15Long Delay 10

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 96 130Woman(W) 103 123Self(S) 97 138Total(M+W+S) 99 135

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Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 5 0 0 5Linear(DL) 4 0 1 5Unorganised(DU) 3 0 2 5

Total(D) 12 0 3 15

Faces(F)

Faces Upright(FU) 7 7 1 15Faces Inverted(FV) 8 5 2 15

Total(F) 15 12 3 30

Human Figure Drawings

Initially J. produced fairly simple drawings of a man, a woman and himself. Facial features were depicted at an elementary level and an incorrect number of fingers was indicated on one hand each on the woman and self drawings. During the subsequent sessions more details were included in the human figures, they were more in proportion, individual characteristics were highlighted and sometimes the people were shown engaged in activities. Also, on occasions J. drew some individual aspects, specifically hands and faces and these depictions included a considerable amount of detail. During the sixth session he produced an integrated scene with himself kicking a football and interacting with a teacher.

After a six week break J. participated in two further sessions when he was asked to draw a picture of a man, a woman and himself. In comparison with the depictions that he produced during the first session, the drawings contained a considerable amount of detail and the human figures displayed very individual characteristics. Specifically, the drawings were shown with more detailed noses and hands with five fingers including some fine aspects except for one club hand shown on the female figure. Also, he produced a detailed and integrated scene including an animal, people and objects.

When J. was seen during the following summer period he was able to produce drawings with people and objects which were integrated to form scenes. The people might be involved in interesting activities and drawn from various perspectives. J. was able to use his imagination in various ways such as depicting himself at the top of a rocket climbing frame although he knew that it was not possible for him to be completely at the top. Also, during that summer vacation he started attending some

37

sessions involving physical activities with a small group of children who were of a similar disposition. This was an achievement in itself as initially he had not been able to manage group activities with such demands. In relation to this, during the second individual session he chose to depict his favourite activity involving a parachute and he showed the other children involved with this task and the adult who was leading the group. Also, during the third session he drew a very good picture of a man and he decided that it would be someone standing at a bus stop near his home. He took great care with the drawing and he depicted a complete scene around the man involving a bus stop, road and houses. During the final session J. was keen to say that he had visited a wildlife park where he had been on a train with some members of his family. Then he drew a very detailed picture including objects and people and he wrote a few lines about his trip there.

3.3 Vignette: Young Person L.

Initially L. was described as a child who had been able to manage some small group activities within and outside of school but he did not have close friends. Generally he was doing well in terms of his academic work but some impairments were apparent as manifested in relation to particular tasks involving fine or gross motor co-ordination concerning respectively, his graphic skills and certain physical activities. As L. progressed into the secondary stage of his education he was described as being popular with his peers.

3.4 Results: Young Person L.

Chronological Age(CA)

Test(T) Session 8y 5m Re-Test(RT) Session 9y 0m

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RT

Mathematical Reasoning(MR) 114 126Numerical Operations(NO) 98 115WOND Composite(WC) 108 123

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Subtest Scaled Scores

T RT

Picture Completion 10 16

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British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 56 59Recall of Digits Backward 52 61

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 78 Block Design 72Similarities 68 Matrix Reasoning 62

Verbal-VIQ 142Performance-FIQ 131Full Scale-FSIQ 141

Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 4 6Female Child 4 6Adult Male 4 6Adult Female 6 6Total(24 Presented) 18 24

Items Identified Incorrectly(Correct Answer)

T RT

Male Child Male Child3. Nicely surprised(Happy) None5. Happy(Nicely surprised)

Female Child Female Child2. Nicely surprised(Afraid) None3. Afraid(Nicely surprised)

Adult Male Adult Male2. Disgusted(Angry) None3. Nicely surprised(Sad)

Adult Female Adult Female

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All correct NoneChildren’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 12 Immediate 9Short Delay 13 Delayed 12Total Score 13Long Delay 12

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 119 137Woman(W) 107 128Self(S) 109 137Total(M+W+S) 111 140

Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 2 1 2 5Linear(DL) 4 1 0 5Unorganised(DU) 3 2 0 5

Total(D) 9 4 2 15

Faces(F)

Faces Upright(FU) 13 0 2 15Faces Inverted(FV) 9 1 5 15

Total(F) 22 1 7 30

Human figure Drawings

During one session in the autumn period when L. was asked initially for depictions of people he produced a picture of a man, a woman and himself. His drawings were

40

fairly detailed but he omitted the ears on all of the figures and the shoulders were not clearly defined. Also, although the correct number of fingers was shown, the hands were disproportionately large in relation to the other body parts. As the sessions progressed L. drew people with more details and with aspects of their bodies more in proportion to each other. When he was re-assessed during the summer term marked improvements were demonstrated overall. Also, during the Easter break he produced drawings of two or three people engaged in activities and sometimes with speech bubbles.

3.5 Vignette: Young Person G.

As indicated, G.’s presentation suggested an association with the autism spectrum and he had received a diagnosis of Asperger syndrome. However, he had made progress since his transfer to a unit within a mainstream school where expertise concerning autism had been available from school staff. G. had one more year to complete before transferring to secondary education so issues relating to his specific difficulties in this context needed particular consideration. He had lax joints in his hands and in addition to this, his wrists and fingers were hyperextensible. G. had some difficulties with the conversational/social use of language and there were weaknesses concerning articulation. He was receiving speech and language therapy and occupational therapy. It is interesting to note here that G. tended to produce detailed depictions of objects, scenes or robots with any attempts at producing people tending to be representations of specific characters such as wizards or knights.

3.6 Results: Young Person G.

Chronological Age(CA)

Test(T) Session 10y 9m Re-Test(RT) Session 10y 11m

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RT

Mathematical Reasoning(MR) 92 94Numerical Operations(NO) 81 91WOND Composite(WC) 84 92

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Scaled Scores

T RT

Picture Completion 9 12

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British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 42 54Recall of Digits Backward 42 54

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 60 Block Design 66Similarities 72 Matrix Reasoning 46

Verbal-VIQ 128Performance-FIQ 109Full Scale-FSIQ 120

Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 4 6Female Child 4 6Adult Male 4 6Adult Female 6 6Total(24 Presented) 18 24

Items Identified Incorrectly(Correct Answer)

T RT

Male Child Male Child2. Nicely surprised(Afraid) None6. Afraid(Angry)

Female Child Female Child2. Nicely surprised(Afraid) None3. Afraid(Nicely surprised)

Adult Male Adult Male4. Nicely surprised(Afraid) None5. Angry(Disgusted)

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Adult Female Adult FemaleNone NoneChildren’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 16 Immediate 09Short Delay 13 Delayed 09Total Score 15Long Delay 14

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 83 114Woman(W) 76 98Self(S) 81 107Total(M+W+S) 74 108

Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 5 0 0 5Linear(DL) 3 1 1 5Unorganised(DU) 2 0 3 5

Total(D) 10 1 4 15

Faces(F)

Faces Upright(FU) 10 5 0 15Faces Inverted(FV) 8 5 2 15

Total(F) 18 10 2 30

Human Figure Drawings

During the initial assessment G. produced rather immature drawings for a man, woman and self and he said that the latter was not himself. The figures lacked

43

significant features such as noses, necks and fingers. Although he drew faces looking to the front for the initial assessment, during the following sessions at first he produced figures looking to the side and he indicated that they were looking at something. The bodies faced the front and in subsequent sessions he drew the faces in the same mode. Sometimes the figures represented specific characters that he had seen in videos and at other times they might be just any people or particular individuals such as an old woman. His choices were spontaneous and varied across and within the sessions. Sometimes he produced separate faces or hands and he included a considerable amount of detail in these depictions. Although he could produce individual hands, when they were part of a whole figure he tended to do blobs with the correct number of fingers or attempt to draw a mitt hand. He insisted that he could not draw himself even with the help of a mirror or photos of himself.

After a six week break G. participated in two further sessions when he was asked to draw a man, a woman and himself. Again he said that he could not draw himself but when instead he was asked to draw a boy he drew a person who was smaller than the man or the woman. In comparison with his initial productions all of the figures contained more details and individual characteristics. The bodies faced the front and this was so for the faces on which the main features were depicted including fine aspects of noses on all of the figures. On the man and self/boy drawings the hands were shown holding specific items and five fingers were indicated on one hand for the man. For the drawing of a woman five, two dimensional fingers were shown on hands which were depicted with definite and appropriate shapes. Generally, G. was able to produce easily pictures of people with specific details such as facial features including noses as well as hands with suitable shapes and five well defined fingers. Also, definite improvements were shown on individual body parts that he might produce on occasions such as faces or hands.

During the following summer vacation period, a year after he had been assessed initially G. attended four sessions. He drew pictures associated with his new school which were integrated and contained people and objects. Also, he produced other drawings which were complete scenes and he was able to make up stories associated with them. In addition to this, his mother indicated that he had drawn a sketch and then painted a picture of the garden. In fact when he attended for the third session he brought two pictures of his garden at home and in each painting there was a figure of a gnome fishing next to the pond. During the last session, again G. produced integrated pictures including a house which contained people that he had drawn in previous sessions. Then he drew specific characters, namely a professor and an opera singer who lived in the house and he depicted them in detailed contexts. Each time he drew integrated pictures, he was able to create short stories concerning the scenes.

G. settled in well during the following school year which was his first year of secondary education. Outside of school he continued to produce paintings, some with a gnome in his garden but different in other respects from his first painting. Also, he produced other pictures of complete scenes and with other themes.

3.7 Vignette: Young Person K.

When I was introduced to K. initially he had been unable to manage the classroom situation at school. He received individual help and he was due to transfer to

44

secondary education. He tended to draw objects and particularly cars but not people. As K. progressed through secondary school he developed relationships with young people of both sexes and he left when he was able to pursue a position within a small firm involving constructional work and there was the potential for him to follow a related college course.

3.8 Results: Young Person K.

Chronological Age(CA)

Test(T) Session 11y 6m Re-Test(RT) Session 11y 8m

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RT

Mathematical Reasoning(MR) 91 100Numerical Operations(NO) 84 90WOND Composite(WC) 87 97

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Scaled Scores

T RT

Picture Completion 13 18

British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 45 50Recall of Digits Backward 36 56

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 62 Block Design 59Similarities 56 Matrix Reasoning 67

Verbal-VIQ 114Performance-FIQ 123

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Full Scale-FSIQ 120

Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 6 *Female Child 6 *Adult Male 6 *Adult Female 6 *Total(24 Presented) 24 *

Items Identified Incorrectly

T None-All items identified correctlyRT Not re-tested

Children’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 9 Immediate 14Short Delay 11 Delayed 18Total Score 10Long Delay 11

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 100 109Woman(W) 97 117Self(S) 98 114Total(M+W+S) 97 115

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Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 4 1 0 5Linear(DL) 3 2 0 5Unorganised(DU) 3 1 1 5

Total(D) 10 4 1 15

Faces(F)

Faces Upright(FU) 12 2 1 15Faces Inverted(FV) 12 2 1 15

Total(F) 24 4 2 30

Human Figure Drawings

During the first session K. drew three figures, one each for a man, a woman and the self and it is significant particularly that he did produce a depiction of himself as he had said that he could not do this after the initial request. All of the figures were very small and they were similar in appearance overall and in terms of the specific details including the main features and the correct number of fingers on both hands that were shown in each drawing. However, it is important to note that on the drawings of the man and the woman there was a simple representation of the pupils for both eyes on each face. On the self drawing the eyes were shown as empty oval shapes. During subsequent sessions K. produced depictions with more detail on all three figures. They could be differentiated clearly from each other and sometimes they were shown with specific outfits and postures. Also, on occasions K. drew just faces and he chose to produce depictions of his mother and grandfather. Prior to the sessions he had produced many pictures of cars and when he was asked to draw anything of choice he depicted a racing car. However, a driver was not included and he said initially that he could not draw anyone in the vehicle although after saying this, he did produce a figure of a racing driver sitting in the car. Also, he demonstrated the ability to draw faces displaying particular emotions or complete figures with specific facial expressions. He started to draw pictures of complete scenes during the later sessions and these might include objects, animals and people as well as other features.

After a five week break K. participated in one further session for re-assessment during which he produced a picture of a man, a woman and himself. In comparison with his earlier attempts, he drew them with more ease and the depictions contained more details overall. Also, more individual characteristics were shown and it is interesting

47

to note that the eyes on the self drawing contained pupils as opposed to the empty oval shapes that were shown on the initial figures.

3.9 Vignette: Young Person B.

Initially, B. was described as a young man presenting with unsettled behaviour at home as well as at school where he was reported to be using inappropriate language in relation to other pupils and staff. He did not appear to see the consequences of his actions and he might be persuaded to fight with others in his peer group but he did not seem to be aware of his own strength. He progressed through his secondary education and participated in college courses with the aim pursuing work of a constructional nature. Also, he developed the ability to form positive relationships with other young males and females.

3.10 Results: Young Person B.

Chronological Age(CA)

Test(T) Session 13y 0m Re-Test(RT) Session 13y 3m

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RT

Mathematical Reasoning(MR) 98 103Numerical Operations(NO) 82 91WOND Composite(WC) 92 99

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Scaled Scores

T RT

Picture Completion 6 13

British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 35 45Recall of Digits Backward 40 48

48

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 60 Block Design 80Similarities 46 Matrix Reasoning 45

Verbal-VIQ 105Performance-FIQ 121Full Scale-FSIQ 114

Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 4 6Female Child 5 6Adult Male 5 6Adult Female 4 6Total(24 Presented) 18 24

Items Identified Incorrectly(Correct Answer)

T RT

Male Child Male Child2. Angry(Afraid) None5. Afraid(Nicely surprised)

Female Child Female Child4. Disgusted(Angry) None

Adult Male Adult Male5. Angry(Disgusted) None

Adult Female Adult Female2. Disgusted(Angry) None5. Angry(Sad)

Children’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 14 Immediate 10Short Delay 12 Delayed 9Total Score 14

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Long Delay 13Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 121 105Woman(W) 117 107Self(S) 114 116Total(M+W+S) 120 110

Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 4 1 0 5Linear(DL) 5 0 0 5Unorganised(DU) 4 0 1 5

Total(D) 13 1 1 15

Faces(F)

Faces Upright(FU) 10 3 2 15Faces Inverted(FV) 10 5 0 15

Total(F) 20 8 2 30

Human Figure Drawings

At first, when B. was asked to produce three human figure drawings he drew only the top halves of a man, a woman and himself. He indicated that usually he did not draw whole people but he said that he could do so. Then he produced three depictions which contained many features but they looked rather like cartoon figures. The test scores indicated above are for the whole figure drawings. The heads were disproportionately large in relation to the bodies and the hands were poorly depicted with an incorrect number of fingers on each hand on all drawings.

During the third session B. was able to acknowledge the nature of his initial depictions as being like cartoon figures and he noted omissions and aspects that were disproportionate. Then he took care in producing pictures of a man, a woman and himself which looked more natural and contained more details. Some features were drawn more in proportion to each other although this aspect would need attention

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particularly. Also, he had difficulty in drawing hands so he drew round his own hand twice. During the fourth and fifth sessions B. was able to produce better depictions of people in relation to detail, proportion and overall human characteristics. Also, during the fifth session, he drew pictures of two people together engaged in an activity or showing specific expressions. The figures were rather small and disproportionate as well as lacking some features. Also, he produced a scene in which a man was shown walking along a road. Specific characteristics were not indicated but the action was clear. During the sixth session immediately B. indicated that he had been doing some drawings since the last session and then quickly he produced a picture of a small male in combat clothes. Also, he drew a masculine figure with a rather alien appearance and then one drawing each of a man, a woman and himself. All drawings contained many details and consideration had been given to proportion although the heads were rather large on the female and self figures.

During the first session after this initial batch, that is the seventh session, B. produced a drawing of a man, and a woman but he said that he could not draw himself. He did produce a figure but he indicated that the depiction represented a friend. The people appeared more natural as opposed to the rather cartoon like depictions that he had produced when assessed originally. However, some major features were omitted such as the necks on all three characters and the ears on the woman. Generally the body parts were more in proportion to each other. Also, during the break B. had drawn freehand a hand and a foot and he brought these to the session. During the eighth session and after considering features that he had omitted in his drawings B. drew a picture of a man but he produced the figure within a context, specifically with a shining sun and a reflection of the man in the water.

3.11 Vignette: Young Person S.

At first when I became acquainted with S. she was described as a young person who had been displaying negative behaviours towards her peers and teachers. She was receiving individual tutoring outside of school and home and she did not attend mainstream classes. At home she spent a considerable amount of time alone although she did have one special friend and she saw this young lady at school as well as sometimes at home. S. had a hearing impairment and wore a hearing aid. Also, she had mild cerebral palsy and specifically left hemiplegia. The diagnosis of Asperger syndrome in adolescence was helpful for the understanding of her presentation by others. As she progressed through adolescence she was able to participate increasingly in activities and to manage situations both inside of school and elsewhere. The home environment was not problematic for her.

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3.12 Results: Young Person S.

Chronological Age(CA)

Test(T) Session 13y 6m Test(RT) Session *

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RTMathematical Reasoning(MR) 80 *Numerical Operations(NO) 75 *WOND Composite(WC) 75 *

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Scaled Scores

T RT

Picture Completion 10 *

British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 46 *Recall of Digits Backward 52 *

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 40 Block Design 44Similarities 39 Matrix Reasoning 39

Verbal-VIQ 85Performance-FIQ 87Full Scale-FSIQ 84

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Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 4 *Female Child 6 *Adult Male 4 *Adult Female 6 *Total(24 Presented) 20 *

Items Identified Incorrectly(Correct Answer)

T RT

Male Child Male Child2. Nicely surprised(Afraid) *5. Happy(Nicely surprised)

Female Child Female ChildNone *

Adult Male Adult Male2. Disgusted(Angry) *5. Angry(Disgusted)

Adult Female Adult FemaleNone *

Children’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 12 Immediate 8Short Delay 12 Delayed 9Total Score 13Long Delay 13

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 102 *Woman(W) 105 *Self(S) 103 *Total(M+W+S) 103 *

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Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 5 0 0 5Linear(DL) 5 0 0 5Unorganised(DU) 3 2 0 5

Total(D) 13 2 0 15

Faces(F)

Faces Upright(FU) 10 5 0 15Faces Inverted(FV) 10 5 0 15

Total(F) 20 10 0 30

Human Figure Drawings

During the first assessment session S. produced drawings of a man, a woman and herself taking about three minutes on each figure. All of the three characters were portrayed with facial features as depicted in cartoons rather than being realistic in form. Specifically, the eyes were shown closed as one dimensional slits and there were only simple indications for the noses and ears. Also, the hands were not drawn in a realistic mode. In particular, the correct number of fingers was not indicated on any of the hands and the fingers were shown in a rather pointed two dimensional form. The clothes were presented in some detail an all three figures but rigidity across the drawings was apparent to an extent in relation to certain aspects of the items.

During the third session, S. produced a drawing each of a man, a woman and herself. The depictions were fairly well proportioned although the heads were slightly large. The hands including the fingers were clearly shown and the figures contained a considerable amount of detail. They looked much more realistic when compared with the characters drawn during the initial session. During the fourth session, S. produced a drawing each of a man, a woman and herself. All of the figures were fairly well proportioned, quite detailed and very individual in their characteristics as well as being much more realistic in comparison with previous attempts. After completing the Object Assembly items at the start of the fifth session we discussed situations at school that S. experienced as problematic and the emotions that she felt as well as the reactions of staff and other pupils. Then she drew a picture of her in a class at school with simple figures for her peers as well as herself and the teacher but she depicted clear expressions of anger on her face and that of the teacher. Also, in a separate drawing she drew simple cartoon like faces with four different expressions showing when she was very angry, a little angry, a little calm and relaxed. During the sixth

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session S. drew a man, a woman and herself after looking at her previous efforts. They contained very specific details with rings in an eyebrow and lip of the man and with the woman shown as being clearly pregnant. She drew herself dressed in a particular outfit and overall the depictions were well proportioned and realistic in appearance. She gave the people names and then did the same for the figures she had produced during the fourth session.

3.13 Vignette: Young Person P.

Initially P. was described as a young man who had difficulties at home and at school. He had experienced incidents of bullying and consequently he had withdrawn from mainstream education. He participated in a small educational group outside of school. He had been diagnosed with dyslexia but showed some strength in mathematics. His main interest and strength concerned technology and as he matured he participated in a college course specialising in this area. He spent a lot of time on his computer at home but he did form some positive relationships at college and via the internet.

3.14 Results: Young Person P.

Chronological Age(CA)

Test(T) Session 14y 5m Re-Test(RT) Session 15y 0m

Wechsler Objective Numerical Dimensions(WOND)-Rust(1996)

Standard Scores

T RT

Mathematical Reasoning(MR) 125 132Numerical Operations(NO) 97 134WOND Composite(WC) 129 137

Wechsler Intelligence Scale for Children-Third Edition UK(WISC-III UK)-Wechsler(1992)

Scaled Scores

T RT

Picture Completion 8 15

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British Ability Scales II(BAS II)-Elliot et al.(1996)

Diagnostic Scales T Scores

T RT

Recall of Digits Forward 39 49Recall of Digits Backward 38 52

Wechsler Abbreviated Scale of Intelligence(WASI)-Wechsler(1999)

Subtest T Scores

Vocabulary 65 Block Design 69Similarities 65 Matrix Reasoning 54

Verbal-VIQ 126Performance-FIQ 119Full Scale-FSIQ 126

Social Skills Training with Children and Adolescents-Spence(1995)

Assessment of Perception of Emotion from Facial Expression

Number of Correct Items T RT

Male Child 6 6Female Child 6 6Adult Male 4 6Adult Female 6 6Total(24 Presented) 22 22

Items Identified Incorrectly(Correct Answer)

T RT

Male Child Male ChildNone None

Female Child Female ChildNone None

Adult Male Adult Male2. Afraid(Angry) None5. Angry(Disgusted)

Adult Female Adult FemaleNone None

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Children’s Memory Scale-Cohen(1997)

Scaled Scores Scaled Scores

Dot Locations FacesLearning 11 Immediate 6Short Delay 7 Delayed 7Total Score 11Long Delay 11

Draw a Person: A Quantitative Scoring System(DAP)-Naglieri(1988)

Standard Scores

T RT

Man(M) 109 130Woman(W) 112 124Self(S) 103 126Total(M+W+S) 109 131

Cards with Dots or Facial Features-Lawson(2001b)

Stimulus Type Presentation(P) and Response(R) Type

Brief P Brief P Prolonged P TotalImmediate Delayed Correct RCorrect R Correct R

Dots(D)

Geometric(DG) 4 1 0 5Linear(DL) 4 0 1 5Unorganised(DU) 4 1 0 5

Total(D) 12 2 1 15

Faces(F)

Faces Upright(FU) 9 5 1 15Faces Inverted(FV) 13 2 0 15

Total(F) 22 7 1 30

Human Figure Drawings

During the initial assessment session P. produced drawings of a man, a woman and himself. In overall appearance the figures tended to look like dolls and there were similarities in the characteristics although some distinguishing features were apparent in terms of dress and haircut on the male drawings and a longer hair style on the

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female. On all three depictions the eyes were round and lacked eyebrows and eyelashes. Also, there were blobs at the end of each arm on all figures with no clearly defined fingers.

During the third session and after completing the Object Assembly items as well as considering his initial human figure drawings, P. produced a picture of a man which contained many details in a more natural form but it was very small. Hence he was asked to produce another male figure which was larger. He was able to do this while retaining the features and similarly he produced a smaller female figure and then a larger one. During the fourth session and after completing the Object Assembly items as well as giving consideration to his earlier drawings P. produced a picture of himself. In comparison with his initial depiction the figure was larger and better proportioned. Also, there were more details and the overall impression was more natural.

After the summer vacation P. participated in the fifth session and following completion of the Object Assembly items and some consideration of his previous drawings he produced a picture of a man. He took great care with the depiction and included a considerable amount of detail. The shapes of the body parts were good generally but some difficulties were apparent in relation to proportion with the arms being rather short and the head somewhat large in comparison with the body. Overall the figure was a more realistic drawing of a man. During the sixth session and after completing the Object Assembly items with consideration given to details and proportion as well as reflection in relation to previous drawings P. completed pictures of a woman and himself. Generally he produced them more quickly and he included many details. Also, the body parts were more in proportion with each other and the overall appearances were more natural. During the seventh session and after completing the Object Assembly items P. produced a picture of a man with considerable detail and with the parts much more in proportion when compared with the figure that he had drawn during the fifth session.

During the eighth session which occurred several months after the seventh session P. drew carefully a picture of a man, then one of a woman and finally one of himself. He included many details and generally the depictions were well proportioned although overall they were rather small. His initial drawings had been larger but the people did not look very realistic. The human figures that he produced for this re-assessment session were much more natural in appearance.

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4. Discussion

4.1 Asperger Syndrome, ASD and Human Figure Drawings

As highlighted earlier, Asperger syndrome(AS) is a developmental disorder defined by the presence of characteristics within two main groups concerning a qualitative impairment in social interaction and restricted, repetitive and stereotyped patterns of behaviour, interests and activities(American Psychiatric Association, 1994, 2000). Motor milestones may be delayed to some extent and motor clumsiness is usual but this is not a necessary diagnostic feature(World Health Organisation, 1992). There has been considerable controversy relating to the diagnostic criteria for Asperger syndrome and the autism spectrum. Studies by Howlin(2003), Szatmari et al.(2003), Ghaziuddin & Mountain-Kinchi(2004) as well as an overview by Volkmar et al.(2004) and the presentation by Frith(2004) highlight relevant aspects concerning diagnostic criteria in this area. In addition, reference could be made to Klin et al.(2005), McConachie et al.(2005), Woodbury-Smith et al.(2005) and Wing(2005). In the comprehensive discussion by Attwood(2006), diagnostic criteria are cited for AS as given by Gillberg(1991) which include motor clumsiness. Also, consideration is given to the aspect of language delay which is a particular area of controversy. In relation to this point, Szatmari et al.(2009) considered a possible differentiation between those with AS and those on the autism spectrum(ASD) who were high-functioning in terms of a presence of structural language impairment for high-functioning individuals with ASD and its absence for individuals with AS. Structural language impairment which concerns deficits in grammar or syntax has been highlighted alongside other issues in a discussion concerning the diagnostic controversy by Sanders(2009).

Wing(2005) favours a multi-dimensional rather than a categorical approach in relation to the study of the autism spectrum. The significance of the impact of social difficulties is highlighted with an emphasis on the importance of studying particular dysfunctional aspects rather than diagnostic subgroups. Additionally, in an investigation by Skuse et al.(2009) involving individuals, aged around 8 years, the prevalence of mild deficits concerning social and communication competencies was shown to have a continuous distribution in the general schoolchild population. Social and communication deficits were shown to be associated with functional impairments at school concerning particularly, hyperactivity and conduct disorders. It was suggested that verbal IQ provided a protective facility in relation to social and communication impairments across the ability range in the girls but only in the below-average range for the boys. In the above-average verbal IQ range for boys, this protective advantage was not apparent. The categorisation of ASD in relation to specific diagnostic points was considered somewhat arbitrary and the findings were given in support of a dimensional approach concerning the autism spectrum. Also in relation to this study, reference could be made to the editorial by Constantino(2009). For various perspectives concerning different psychiatric diagnostic systems of classification including a dimensional approach and with specific consideration given to comorbidity, reference could be made to recent discussions by Aragona(2009a, b), Banzato(2009) and Zachar(2009).

Certainly in my own research, I had approached issues concerning those with ASD from the perspective of considering how areas of development that were presented as

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problematic could be assisted by regions of strength in order to facilitate progress in both spheres and associated aspects. Although specific categories had been ascribed to some individuals who were participants in my studies, it is important to note that all of the young people had social and communication difficulties which were associated with the autism spectrum, whatever label might or might not have been attributed to particular young people. Generally, I am in favour of a dimensional as opposed to categorical approach in relation to the diagnostic, therapeutic and remedial aspects of ways to facilitate development in those with ASD.

Dziuk et al.(2007) studied basic motor coordination and dyspraxic aspects relating to impairments in the performance of skilled gestures concerning individuals on the autism spectrum. Children and young adolescents with ASD including those with High Functioning Autism(HFA) and AS were assessed in relation to a standardised test for children of basic motor skills and a praxis examination which included gestures to command and to imitation as well as with tool use. After controlling for chronological age and IQ, basic motor skill concerning times to complete repetitive limb movements was found to be a significant predictor of praxis performance, namely praxis errors. The ASD group continued to demonstrate significantly poorer praxis in comparison with the control group after allowing for basic motor skill. Also, the praxis performance predicted strongly, the diagnostic features relating to autism as assessed on the Autism Diagnostic Observation Schedule(ADOS). Hence, as impairments in basic motor skills could not account completely for the dyspraxia in those with ASD and praxis with the ASD participants had a high correlation with impairments of a social, communicative and behavioural nature, the possibility was considered of dyspraxia being a core feature of autism or an underlying indicator of neurological abnormalities.

Furthermore, in a recent study by Staples & Reid(2010) fundamental movement skills were considered in children who were on the autism spectrum(ASD), aged around 9-12 years, in comparison with three groups of young people with typical development. The children in the ASD group were matched individually in relation to three developmental aspects, namely chronological age, movement skill performance and mental age. The researchers highlight the difference between what are termed movement skills and motor abilities with the former referring to goal-directed movements which can be described in accordance with the final outcome or the movement pattern used to achieve a goal. Fundamental movement skills are considered as the locomotor and object control skills which are seen to emerge after the child is able to walk and between the ages of 1-7 years. Motor abilities are not observed directly but noted via inference from movement skill performance with scoring in relation to general ability concerning balance or hand-eye coordination in contrast to using the movement pattern.

The controls matched with the ASD children on chronological age demonstrated a significantly better performance on the Test of Gross Motor Development(TGMD-2). When considering the comparison with the controls matched on movement skill, the children with ASD performed at a level similar to those who were approximately half their age. In relation to the controls who were matched in terms of the equivalence of their mental ages with the ASD group, those on the autism spectrum demonstrated more impairment than was expected after consideration of their levels of cognitive functioning. Overall, the results indicated that majority of the participants with ASD

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could perform the skills required by the TGMD-2. Their low scores were reflective of poor quality concerning how they performed these skills. There were consistent qualitative differences in relation to some of the skills with a particular difficulty being noted concerning the coordination of movements that involved both sides of their bodies or both arms and legs. In consideration of this finding and those from other studies highlighted in the discussion, the researchers suggested that the movement differences for those with ASD concerned two aspects associated with momentum/force and timing/coordination. Additionally, it was noted that in consideration of the third control group, there was a very close mental age match with the ASD participants. However, significantly poorer performances in relation to locomotor and object control skills were demonstrated by the children with ASD and these differences could not be attributed to levels of cognitive functioning. Hence, it was considered that these differences were suggestive of variations in patterns or possible deficits concerning the fundamental movement skills of children and adolescents on the autism spectrum.

One area where children’s motor coordination difficulties have been investigated concerns their drawings of people. The findings of Barnett & Henderson(1992) indicated that the drawings of the clumsy children aged between 5 and 13 years were delayed in comparison with those of the well coordinated controls. Generally for the more clumsy child, the poorer was the quality of the drawing and they did not catch up with their peers. The follow-up study results showed improvements for the clumsy children on all items except for those categorised under the heading of Motor Control and Co-ordination. Their drawings were inferior to those of the controls for the representation of proportions, the depiction of features and the provision of detail in their figures. Additionally, the researchers noted that there was a tendency for a difficulty with drawing a circle for a head to be associated with the omission of the nose.

As highlighted in the case report of a boy with Asperger syndrome and marked dyspraxia described by Lawson(2003) there were several aspects in relation to his disposition that were clarified and strengthened through the assessment and teaching approach used in that study. As indicated, the results were very positive and it was felt that other young people with some similar difficulties should benefit from the same intervention. In contrast to that young man, most of the children discussed in the context of the studies by Lawson(2004, 2005a, b, 2008a, c, 2009) and here did not present with major disabilities in relation to dyspraxia although there were manifestations of problems concerning motor coordination to some extent in particular individuals. However, because of the selection criteria and as a result of the assessment with a variety of tasks it was apparent that they did have areas of weakness in common with him. One aspect concerned the amount of effort that they required to produce drawings of people and particularly without copying and in relation to this the generation of ideas when producing their depictions. Both of the young people in the study presented by Lawson(2005a) produced cartoon characters quite easily but they had to make an effort to produce realistic human figure drawings and in developing their ideas to add variety to their depictions. B. did not have marked problems in relation to motor co-ordination and S. wrote and drew with her right hand with reasonable dexterity.

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As discussed by Jolley et al.(2000) in order for a child to produce a representation he/she needs to be able to hold in mind the perceptual and conceptual aspects of the topic during the drawing process. Also, the individual has to learn how to represent graphically three dimensional entities in two dimensions. In producing representations from memory as opposed to copying, more conscious effort is required in accessing relevant information and in the generation of ideas which are reflected then in the person’s drawings. Impairments or failures in the utilisation of their generative ability in relation to the production of varied groups of drawings had been suggested for children with autism who were relatively able but not savant artists(Lewis & Boucher, 1991). Also, in a study by Lee & Hobson(2006) children and adolescents with autism were asked to produce a man, a woman and a self drawing. The results showed that there was little to distinguish one human figure from another but their depictions of houses, namely a house, another house and their own houses showed clear distinctions. Participants with learning difficulties produced drawings mostly of people and houses which could be distinguished clearly from one another.

The young people considered by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here were not involved in any copying activities during the sessions. They were encouraged to produce whole drawings of people which required more planning than would be required for the completion of pictures as highlighted by Leevers & Harris(1998). Also, they emphasised how even more effort was necessary for individuals to develop and apply new ideas to give variations to their depictions.

Additionally of relevance here is research by Allen(2009) involving children on the autism spectrum and a control group of children matched on receptive language ability. The participants with ASD were unable to use the eye gaze of another person to understand the representations of abstract pictures whereas the typically developing individuals showed proficiency concerning this task. However, when the participants were asked to create their own drawings, those with ASD performed as well as the controls when, after a delay, they were required to identify their own perceptually identical pictures based on their intentions in relation to their drawings. Hence, it was suggested that children on the autism spectrum might not connect a picture drawn by another person to its referent in the real world but they are more likely to interpret drawings which they have produced themselves as symbols relating to real world referents.

The remedial approach used here was aimed at highlighting the inter-relationships concerning human characteristics in the context of activities including the manipulation of cardboard items to form human figures and the drawing of people. An intention was to facilitate the use of various aspects of memory and imagery as well as the promotion of spontaneity and creativity. As noted in the review by Taktek(2004) tasks with a main cognitive component as opposed to those which are predominantly motor seem to be sensitive to mental imagery. Drawing is an activity with a specific cognitive aspect involving fine visual-motor skills. An aspect fundamental to my approach was to facilitate the development of individuals with ASD within a real world context.

Additionally, in an investigation using fMRI by Miall et al.(2009) during scanning, adult participants viewed black and white cartoon line drawings of human faces, retained the items for a short-term memory period and then they produced drawings

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of the items without seeing their hands or the papers with their depictions. Assessments for specific encoding and retention of facial information involved comparing these two aspects for the presentation of cartoon faces with these processes for random dot stimuli displays. A comparison was made of the drawings involving conditions where the participants were able to use only memory of a previously viewed cartoon face in contrast to where both memory and concurrent viewing were available and in another condition with the requirement for depicting a new face, not seen previously by the viewers. The findings indicated marked activation concerning facially sensitive regions of the lateral occipital cortex and the fusiform gyrus for coding of cartoon faces but an absence of significant activation relating to the retention period. Also, strong activation was noted in both of these areas when the participants were drawing the presented cartoons. Additionally, the researchers considered that activity in the posterior parietal cortex and frontal regions associated with drawing from memory showed consistency with the encoding and retention of spatial information concerning the face being drawn as a visuo-motor action plan. The latter involved either the representation of a series of targets for ocular fixation or as spatial targets for the drawing action.

Furthermore, in a study by Chen et al.(2010) the researchers investigated whether adaptation to cartoon faces could affect perception of human faces. Adult participants were shown Japanese animation cartoon videos which included cartoon faces with atypically large eyes. The results indicated that adaptation to cartoon faces with big eyes had a significant effect in altering preferences for human faces with larger eyes. Also, with reference to Loffler et al.(2005) the investigators noted that information from this fMRI study with adults had suggested that synthetic, cartoon-like faces activated the fusiform face area approximately 84% as strongly as full greyscale human faces.

In relation to the approach described here by the present author, schematic faces were used with clearly defined facial features. A specific aim was to enhance flexible attention to human faces and certainly this aspect seemed to have developed in the young participants when considering how they produced increasingly detailed and realistic drawings of people and how they made progress in terms of their functioning in everyday contexts.

A comprehensive overview of drawing throughout life from a cognitive perspective has been given in the book edited by Lange-Küttner & Vinter(2008). Research presented by one of the contributors, Ross(2008) is given in support of conceptual as well as perceptual knowledge being reflected in children’s drawings. Specifically, it is suggested that the cognitive and physical aspects in relation to the production of drawings results in all episodes of drawing being self referential. Hence, retrospection by children in relation to their own drawings might facilitate their development in terms of self-awareness. Particularly in relation to drawings of the self, objective analysis concerning the content of the drawings may give an indication of knowledge about the self.

Ross(2008) highlights Duval & Wicklund’s(1972) ‘objective’ self-awareness theory which has undergone fundamental alterations since its initial formulation as discussed for example, by Silvia & Duval(2001) and Duval et al.(2001). Objective self-awareness refers to the state when the individual’s attentional focus is on the self as

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an object in the environment. In contrast, ‘subjective’ self-awareness occurs when attention is directed away from the self and the individual experiences the effects of environmental stimuli with perception and action originating from him/herself. As considered by Duval and colleagues orientation of attention to the self should happen when the self is figural, that is when it comprises a smaller portion of the psychological field. Additionally, as highlighted by Duval et al.(2001) self-focus can be increased by affect because of the establishment of a figure-ground relationship. Also, as noted by Duval and associates as well as Ross(2008) objective self-focus can be elicited by stimuli that highlight the self such as a significant audience or image of oneself in a mirror. In particular, self-evaluation is considered to follow on from objective self-reflection and consequently appropriate regulation of behaviour.

It is interesting to note that some of the young people that have been involved with my specific approach and others that I have known as well as some who have been reported in the literature have responded particularly well when doing presentations in front of their peers and/or other specific audiences. Also, in relation to the young people described here and others who have been involved with my approach, when asked to produce a self drawing some of them said that they could not offer such a production. Certain individuals requested a mirror although this was not allowed during the sessions. In specific cases when the young people said that they could not do self drawings, if I indicated that they should draw a person similar to themselves in terms of age, sex and appearance usually they produced pictures which represented themselves. As the participants developed during the teaching/learning sessions and as indicated in follow-up sessions they became more aware of different aspects of themselves and the inter-relationships as well as their impact on other people and in different situations. Hence, they became more capable of managing their own behaviours in a broader variety of contexts.

4.2 Attentional Flexibility, Face/Body Processing and ASD

As highlighted by Plaisted(2000), individuals with autism appear to demonstrate relatively good processing concerning unique characteristics of stimuli but relatively poor processing of similarities between stimuli. Various differences concerning attention in those with and without autism have been considered in relation to this aspect. In a study by Greenaway & Plaisted(2005), bottom-up processing which refers to selective attention which is guided involuntarily by aspects of the stimuli and top-down processing which is under voluntary control via the goals of the individual were considered in children and adolescents on the autism spectrum and typically developing controls(TD). A task using spatial cues and a series of visual search tasks with task-irrelevant distracters were employed in the investigation. Participants in the TD group demonstrated similar top-down modulation for the colour and the onset singleton items used as distracters. When considering individuals in the ASD group, top-down modulation was shown to be typical for the colour stimuli but impaired for the onset stimuli. The researchers concluded that top-down modulation could be typical for children on the autism spectrum but it depended on the properties of stimuli. As noted, these young people might present with excellent control of attention in certain situations but in others the opposite might be true. The prioritisation of dynamic stimuli for individuals with ASD was considered to be implicated in relation to their difficulties in processing information within social contexts.

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Additionally, in a more recent investigation by Keehn & Joseph(2008), children and adolescents with ASD were shown to demonstrate less sensitivity to novel onset items in comparison with a TD group. Hence, an impairment in relation to the processing of dynamic stimuli was suggested for those on the autism spectrum and supportive evidence was given for an association with the social and communication difficulties indicated in those with ASD.

Furthermore, Joseph et al.(2009) matched children and adolescents with ASD on chronological age and nonverbal IQ with TD controls. They were engaged in a standard static search task as well as a dynamic search task involving targets and distracters which changed locations randomly every 500ms to prevent memory being used in the search. It was indicated that memory for rejected distracters did not heighten the visual search abilities suggested for those with ASD. Overall, it was considered that their apparent superiority in visual search did not arise from differences in how they used their attention during searching but from anomalously augmented visual perception of stimulus characteristics. Furthermore, participants with ASD whose performances suggested an enhanced ability concerning discrimination between targets and distracters in the static condition were reported to present with higher levels relating to the social symptoms as assessed on the Autism Diagnostic Observation Schedule(ADOS).

Also of relevance here is a recent study by Smith & Milne(2009) concerning change blindness, a phenomenon which suggests that a restricted number of items within the visual scene receive attention from the observer at any specific time. Children and adolescents with ASD were compared with a TD group. As noted by these researchers and in the present discussion, it had been suggested that individuals on the autism spectrum concentrated their attention on aspects of the visual scene which had less contextual relevance, demonstrated superior perceptual discrimination and noticed details that tended to not capture the attention particularly of more typical observers. The participants were asked to detect continuity errors which had been introduced deliberately into a short film. Significantly more errors were detected by the ASD individuals in comparison with the TD participants. There was a greater detection of errors involving central as opposed to marginal aspects of the scene for both groups but this effect was more so for the TD individuals. No difference was shown in the number of errors, whether social or non-social, detected by either of the participant groups. Overall, the results of the study were considered as indicative of heightened awareness of the visual scene for individuals on the autism spectrum. Proposed explanations including possible combinations in relation to ASD might involve superior top-down attentional control, enhanced bottom-up perceptual discrimination or inefficient filtering concerning visual information.

In a study by Riby & Hancock(2009a) involving eye-tracking techniques two tasks were used to investigate attention to pictures which contained faces. The participants comprised individuals diagnosed previously with autism and assessed as severe or mild-moderate on the Childhood Autism Rating Scale(CARS) for this investigation and aged 6-17 years as well as young people with Williams syndrome, aged 6-12 years. Those in each group were matched with TD individuals in relation to nonverbal ability. In one task, the participants were required to view images of natural scenes. Then, half of the images were manipulated by the addition of an ‘incongruent’ item which was a picture of a small face. The term ‘incongruent’, with reference to

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Underwood and Foulsham(2006) meant that the item was placed in an unusual position within the image. In the other task, participants viewed nine scrambled scenes which were arranged so that the character’s face appeared once in each of the nine possible location squares. Also, there were nine scenes in which the faces had been omitted. The results indicated that in comparison with the TD individuals, those with Williams syndrome demonstrated prolonged face gaze across tasks whereas the participants with autism showed reduced face gaze. Also, individuals with autism who were relatively more able demonstrated increased face gaze in comparison with those who were less able in terms of level of functioning in relation to the autism spectrum, indicated in this study by the CARS scores.

Furthermore, Ames & Jarrold(2009) considered the difficulties suggested for those with ASD in the comprehension of non-verbal cues communicated by other individuals and providing symbolic information concerning relationships between themselves, other people and events in the environment. Specifically, the study investigated whether these aspects were a reflection of underlying issues related to the identification of temporal co-occurrence, memory processes, associative skills or non-temporal inference. The participants were involved with four tasks and those with ASD were adolescents whose intellectual abilities were below the level of expectation for their chronological ages. There were two control groups with one comprising relatively younger TD children matched on verbal mental ability with the ASD individuals. The second control group was formed of adolescents described as having moderate learning difficulties and they were selected as having equivalent verbal mental abilities and chronological ages in comparison with the ASD individuals. The results indicated non-social inferential difficulties in the participants with ASD when there was a requirement concerning the temporal co-occurrence of items. It was considered that these difficulties might be associated with attentional abnormalities reported in those with ASD.

Also in another recent study, Amirault et al.(2009) investigated the dynamics of attentional processes in adult males with ASD in comparison with TD controls. The attentional blink paradigm offers information concerning the temporal dynamics of attention, particularly about the temporal allocation of attention and the duration of an attentional period. Specifically, the attentional blink refers to the decrease of discrimination accuracy in relation to a second target presented in a close temporal delay after the discrimination of a first target. The high functioning ASD participants compared with the controls exhibited a noticeable increase in the attentional blink duration. Hence, a deficit was considered in the rapid allocation of attentional resources.

Additionally, in a study by Rinehart et al.(2010) individuals with high-functioning autism(HFA), aged around 7-16 years were matched with typically developing controls on chronological age, sex and full-scale IQ. Also, participants with Asperger disorder(AD), aged approximately 7-20 years were matched with a similar control group on the same variables. The temporal characteristics of information processing and selective attention were considered in these groups in the context of the attentional blink using the rapid serial visual presentation(RSVP) paradigm. The results indicated that the attentional blink was of a similar magnitude in those with HFA as well as the individuals with AD as found in the controls. Hence it was considered that automatic inhibitory processes were intact in those with HFA as well

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as individuals with AD. It was noted that, in relation to this aspect of cognition consideration could be given to the differentiation of these conditions from other fronto-striatal conditions such as attention deficit hyperactivity disorder(ADHD). Also, the findings were considered as giving strength to the idea of a cognitive dissociation between HFA and AD in tasks assessing controlled inhibitory processes supported by fronto-striatal executive functioning. Additionally, individuals in the HFA group were found to be less able at detecting black Xs but their performances concerning responses to white letters were comparable with their controls. These aspects were considered in the context of a possible difficulty in dual-task processing or superiority in visual search influenced by a visual-motion deficit.

Furthermore, Belmonte et al.(2010) used fMRI in an investigation concerning the performances of boys, aged around 11-15 years on a non-social visual attention task. Boys with autism spectrum conditions(ASC) and high-functioning presentations as well as clinically unaffected brothers of individuals with ASC showed impairment on a visual divided-attention task which required the conjunction of attributes from fast and simultaneous presentations of spatially disjoint stimuli and the suppression of spatially intervening distractors. Additionally, both groups in comparison with neurotypically developing controls showed atypical fronto-cerebellar activation as a function of distractor congruence. Also, there was a correlation between the degree of this atypical frontal activation and psychometric measures of autistic traits in the ASC boys and the sibling participants. A correlational analysis across brain areas indicated a decrease in the overall functional correlation in those with ASC but not in the sibling individuals. As highlighted by the researchers, the ASC and sibling participants did activate their fronto-cerebellar attentional systems but these activations were too late for use during the behavioural response for the trial of interest in their study. Specifically, the activations were manifested in the immediately following trials.

In relation to this finding, a consistency was noted concerning clinical behavioural observations and self-reports in which the importance had been emphasised of explicit instructions and response preparation time for unpredictable stimuli. As discussed later in this presentation, uncertainty is an aspect that is problematic, particularly for those with ASC and planning is essential to help reduce the associated anxiety. Planning should facilitate quicker responses to situations under consideration and as indicated below, the promotion of fast and flexible responses is fundamental to my approach to facilitate development of those on the autism spectrum.

In the investigations presented by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here the usual invariant quantity concerning the number of features in a face was manipulated via presentations of schematic faces. These varied in terms of the amount and position of facial features although their normal locations in relation to the outlines of the faces were kept constant for the upright and inverted positions. Hence, attentional switching was encouraged in relation to different groups of facial features and small numerosities and there was an emphasis on the simultaneous association between these two aspects. The aim was to enhance the fast processing of these co-occurring items and to promote mental flexibility and the generation of ideas by the participant. As highlighted by Gordon(2000) activities that are generated by the self tend to be more motivating for the individual and consequently result in enhanced

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learning. Also, spontaneity tends to facilitate variation in activities and opportunities for skill transference and concept generalisation.

Additionally, attentional flexibility is an aspect to consider in the context of the children’s performances on the Picture Completion subtest. Some of the items are pictures of familiar objects or animals and others represent parts of people or a whole body. Always something is missing which is usually a common feature of the object or individual or perhaps part of a familiar article that would be seen on or with a person. When assessed initially, sometimes the young people considered by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and presented here concentrated on the wrong aspects of the pictures and they appeared to have problems in directing their attention to other areas for consideration in relation to finding the missing item. During the training period they were involved with tasks where they had to attend to details concerning the physical characteristics of people. As the sessions progressed they appeared to attend more easily to different human aspects and to include these in their drawings. When re-assessed on the Picture Completion subtest, often with apparently little effort they directed their attention to the missing features and consequently they tended to respond very quickly and accurately.

Although none of the tasks in my research involved dynamic stimuli, the participants were involved very actively, physically and mentally with the tasks during the sessions and as they progressed this tended to be more so in relation to activities elsewhere. As indicated above, changes became apparent concerning their attentional capacities in terms of flexibility and this increased facilitation in their personal development was suggested outside of the sessions. When considering everyday situations, the young people became more capable of extracting appropriate contextual information and consequently, they developed more natural social responses and interactions.

In relation to facial and other human characteristics, detailed discussions concerning various aspects of development in face processing have been given by contributors to the text edited by Schwarzer & Leder(2003). Also of relevance here are recent discussions by Pascalis et al.(2009) and Grossman & Farroni(2009) as well as the contribution highlighted earlier by De Haan & Matheson(2009). In the book edited by Schwarzer & Leder(2003) just mentioned above, Tanaka et al.(2003) note how a number of studies concerning individuals of various ages on the autism spectrum have indicated that aspects of face processing for this group might be different in comparison with those who are not on the spectrum.

More recently, Back et al.(2007) studied individuals with ASD in relation to their ability to make inferences concerning mental states and using dynamic and static female facial stimuli. In the first experiment participants with ASD aged 10-14 years performed above chance level for recognising mental states but not as well as those in the control group. Overall, no difference was demonstrated for accuracy scores relating to mental states presented via dynamic or static faces. Individuals with ASD performed more poorly for recognition of mental states when the eye region was static and neutral in comparison with the condition when information from the eyes was present. The researchers indicated that their investigation was the first developmental study that considered the recognition of individual mental states and contrasted it with previous studies by others which had investigated the accuracy rates of participants

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across all mental states. In the second experiment individuals with ASD aged 11-15 years performed as well as the typically developing participants for the recognition of mental states when the eyes were presented in isolation or within the context of the entire face. Also, results from the first experiment indicated that the participants in both groups were significantly less able in the recognition of mental states when the mouth region was static and neutral in comparison with the complete dynamic facial presentation. Hence, there was a suggested contribution in relation to the mouth region for all participants in the attribution of mental states.

Additionally, of interest here is a recent study by Grossman et al.(2009) in which a group of adolescents with ASD were compared with typically developing(TD) participants in an investigation concerning the ability to integrate auditory-visual(AV) information of meaningful phrase-length language in a task involving onset asynchrony detection. The stimuli comprised video clips of complete phrases involving simple, commonly occurring words. The video clips were digitally manipulated so that the video items preceded the audio presentations over a range of 0-500ms. The results indicated that the individuals with ASD were as accurate as the TD group in indicating whether there was synchrony or not between the speech sounds and their corresponding mouth movements within the context of a whole adult female face, that is, at integrating the auditory and visual aspects in this task. Hence, it was suggested that the meaningful nature of language presented in the absence of background noise provided the basis for more success with AV integration in those with ASD than single non-word syllables or competing auditory stimulation.

Also, in another recent study by Klin et al.(2009), young children, aged 2 years with ASD were matched with typically developing toddlers on non-verbal mental age and chronological age and developmentally delayed toddlers without autism on verbal mental age and chronological age. The children were presented with five types of point-light displays of biological motions with the point-lights positioned at body joints. Each animation showed an upright and an inverted figure accompanied by a soundtrack which matched the actions of the upright figure. Four of them involved only moving point-lights with an accompanying human voice of an actor engaged in routines relevant to experiences of childhood. The fifth animation included a different sound with the actor in this presentation playing pat-a-cake and the sound of clapping was heard at the same time that two point lights, that is, the actor’s hands collided. It was noted that the collision of the point-lights and the resultant clapping sound created a causal physical contingency, with the movements of the point-light hands causing the occurrence of a noise, as opposed to co-occurrence which was the situation for the speech sounds and movements in the other animations.

The results indicated that the children with ASD showed no viewing preference in relation to the upright and inverted figures for the animations involving co-occurrence of speech sounds and animations. In contrast, the typically developing and developmentally delayed children without autism demonstrated preferential attention to upright animations. However, for the animation containing a physical contingency the youngsters with ASD showed a significant viewing preference for the upright figure, whereas no significant change in preferential viewing was demonstrated for those in the typically developing group and developmentally delayed group without autism. It was considered that the individuals with ASD failed in orienting to point-light displays of biological motion and their viewing behaviour when they were

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looking at these displays might be explained in terms of a response to non-social physical contingencies, which were not taken into account by the children in the control groups. The issue of synchrony was considered in relation to the pat-a cake condition as the motions matched the soundtrack only when the figure was upright. Additionally, further analysis involving all of the animations was highlighted in terms of the children with ASD having their attention drawn to presentations with auditory-visual synchrony which was not apparent for the controls. The apparent sensitivity to synchrony in relation to biological motion stimuli in this study for the children with ASD was noted as being consistent with ongoing fixations on the synchronies between lip motion and speech sound. Also, the lack of preferential attention regarding biological motion was considered as showing consistency with reduced attention to the eyes and less expertise concerning social interactions indicated later in development. Synchrony is an aspect to be given consideration in relation to balance and symmetry and in the context of ASD as highlighted later in the present discussion.

Additionally, in research by Atkinson(2009) adults on the autism spectrum(ASD) were compared with participants described as typically developing(TD), matched on chronological age and IQ. They were required to classify basic emotions from point-light and full-light presentations of bodily movements and to discriminate the direction relating to coherent motion in random-dot kinematograms. The ASD individuals were reliably less accurate in the classification of emotions irrespective of the type of stimulus display as well as in the perception of coherent motion. The ASD participants with higher motion coherence thresholds were less accurate in the classification of movements relating to body movements, particularly in the point-light presentations. This relationship was not apparent for the TD individuals.

Also of relevance here is a review and synthesis by Kaiser & Shiffrar(2009) concerning the visual perception of motion by individuals with ASD. They highlight contrasting results from various studies involving those on the autism spectrum compared with neurotypical participants for visual sensitivity to coherent motion in random-dot kinematograms as well as in psychophysical investigations which have implemented point-light displays of human motion. The researchers bring together a number of aspects from a variety of sources to suggest the possibility that differences in individuals relating to impairments in the motor system or perception-action coupling may make a contribution to visual sensitivity and impairments concerning social behaviour.

Additionally, reference could be made to the contribution by Plaisted Grant & Davis(2009) concerning perception and apperception in individuals on the autism spectrum. Variations in their perceptual and attentional skills in contrast to those with a neurotypical presentation were discussed with consideration being given to particular theories in relation to investigations involving perceptual grouping and motion coherence. Their own recent and ongoing research was highlighted and discussed in the context of magnocellular and parvocellular functioning.

In a more recent study, Brieber et al.(2010) used event-related fMRI to investigate the neural mechanisms associated with the detection of random and coherent motion processing. Male adolescents with ASD, mostly with a diagnosis of Asperger syndrome and a few diagnosed with HFA, aged 13-19 years were matched with

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typically developing individuals on chronological age and full-scale IQ as well as verbal IQ but there was a significant difference between the groups on performance IQ. When considering the behavioural data obtained via the involvement of participants in a motion detection threshold task outside of the scanner, no significant differences were noted between the ASD and control group performances. The results concerning the neural aspects indicated that for the participants with ASD there was increased activation in the left primary visual cortex across the conditions in comparison with the controls. Also, a significant interaction effect between group and condition was noted in the superior parietal cortex, extending to the precuneus as a result of reduced activation in the coherent versus random motion condition for the ASD group. Additionally, neural activity was not differentially modulated by particular motion tasks in participants with ASD. In relation to the analyses concerning functional connectivity, positive correlations were found between the primary visual cortex and the extrastriate cortex, region V5 within both hemispheres but there were not any significant between-group differences in the patterns of functional connectivity along the dorsal stream. Hence, the findings were given as suggesting that motion processing in individuals with ASD resulted in deviant activations in the dorsal stream at the lower and higher processing levels.

Furthermore, an investigation by Cook et al.(2009) concerned the comparison of psychophysical thresholds for biological and non-biological motion detection in adults males on the autism spectrum and neurotypical controls. The participants viewed animations of a biological stimulus, that is, a moving hand or a non-biological stimulus, namely, a falling tennis ball. Increased relative sensitivity to biological in contrast to non-biological motion demonstrated by the control individuals was not shown by those on the autism spectrum. No difference was found between the two groups of participants in relation to their perceptual thresholds for non-biological motion so the difference appeared to be specific to biological motion. Also, in contrast to some studies the experimental task used in this investigation did not have a requirement concerning global motion integration or the processing of emotional content.

In a study by Murphy et al.(2009) adults who were on the autism spectrum, the ASD group and neurotypical controls were required to detect movement direction in relation to human point-light walkers which were presented in natural as well as spatially scrambled forms in a background of noise. In addition to direction discrimination activities in studies where the walkers moved on the same spot while facing left or right, in the investigation by Murphy et al.(2009) they moved across the screen. Hence, information concerning coherent translatory motion was available for both conditions but only the walker in the normal presentation offered configurational and kinematic aspects relating to the human body. The results indicated a strong and highly significant effect in association with walker type on performance. These improvements concerning response times and error decreases as well as sensitivity increases were demonstrated for the normal intact walker presentations. In particular, these improvements were apparent for both of the participant groups. Hence, the researchers considered that the individuals on the autism spectrum were able to integrate local visual information into a global percept of the human form in motion. The discussion highlighting differences in relation to studies concerning biological motion perception for those with ASD noted variations associated with age, diagnosis and the type of tasks used in the investigations.

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Additionally, Chawarska & Shic(2009) used an eye-tracking approach to investigate visual scanning and recognition of coloured static images of affectively neutral female faces. The participants comprised young children aged 2 years and 4 years with ASD who were matched with TD controls on the basis of chronological age. At both age levels the TD children performed similarly in relation to the scanning and recognition of faces. Irrespective of age, the children with ASD spent a longer time examining the external facial features, the hair, cheeks and forehead, compared with the TD controls. Furthermore, for those with ASD aged 2 years a similar proportion of active scanning time was given in attention to inner features of the face as that allocated by the TD children. However, for the youngsters with ASD aged 4 years significantly less time was indicated for attention to the internal facial features, namely the eyes, nose and mouth and more time looking away from the face and at the body, background and screen in comparison with both TD age groups and the younger children with ASD. Irrespective of the age of the children with ASD, it was indicated that they allocated more looking time to the eyes than any other part of the static facial images. As the researchers noted with reference to findings elsewhere, similar results had been reported in older children and adults with ASD, in neurotypical adults and in very young TD infants. Also, the investigators indicated that for those with ASD a similar proportion of time was allocated to the eyes and nose areas in comparison with their TD peers and this result was similar to reported findings for older children. Additionally, for these young children with ASD less attention to the mouth was suggested in contrast to the attentional allocation of their TD peers. Furthermore, using a visual paired comparison procedure it was indicated that neither of the ASD age groups provided strong evidence to support facial recognition in response to stimuli which were described as full-head images which included additional facial identity cues such as hair.

In another investigation by Riby & Hancock(2009b) eye tracking techniques were used to study how individuals with Williams syndrome or autism, diagnosed previously with the condition and assessed as severe or mild-moderate on the Childhood Autism Rating Scale(CARS) for this project, attended to social scenes and movie extracts which contained human actors or cartoon characters. The proportion of gaze time was considered in relation to fixation on faces, bodies and the scene background. The participants with Williams syndrome, aged 8-28 years were each matched with two typically developing individuals, aged 8-28 years, one of comparable chronological age and the other of comparable non-verbal ability. The participants with autism were within the age range of 6-18 years and they were matched individually with typically developing individuals of comparable chronological age and non-verbal age.

The results indicated preferential attention to the faces of characters for less time in the participants with autism and for more time in those with Williams syndrome in comparison with the typically developing individuals. The relatively reduced gaze behaviours were demonstrated for the human actor and cartoon images as well as the movies for those with autism but the relatively prolonged gaze behaviours of those with Williams syndrome was shown only for the human actors. When considering specifically, gaze behaviours in relation to the eye and mouth regions for the movies of human actors, reduced fixations to the eye but not the mouth regions were apparent for the participants with autism. In line with more typically developing individuals,

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for those with Williams syndrome more attention was indicated in relation to the eye as opposed to the mouth areas for the human actor movies but a greater proportion of face gaze was shown in attention to these facial areas in comparison with the other two groups of participants.Additionally, in an investigation by Norbury et al.(2009) male adolescents on the autism spectrum(ASD), aged around 13-16 years were matched with typically developing(TD) male controls, aged within a similar range. The eye-movements of the participants were recorded while they watched videos of peers interacting in familiar situations. Within the ASD group, the viewing patterns were compared of the young people with and without impairments in language. For the participants with ASD and age-appropriate language abilities, less time was spent viewing the eyes and there was slower fixation of the eyes in comparison with the TD individuals. When considering those with ASD and language impairments, no differences were found in relation to their viewing patterns in comparison with their TD peers. No association with eye-movement patterns and social outcomes was found for either language phenotype. A relationship across the autism spectrum was indicated between increased fixations to the mouth and greater communicative competence. The importance of attention to eyes and mouths was noted for the development of language and competence in communication. Also, variations in fixation time relating to the eyes might be insufficient to disrupt social competence in everyday interactive contexts.

Furthermore, in a study by Freeth et al.(2010a) adolescents, aged 11-16 years, described as high-functioning and on the autism spectrum(ASD) were compared with typically developing controls. Visual fixation patterns were investigated while the participants viewed complex photographic scenes which contained one person. There were two scene presentations with different durations, specifically with the first one lasting for 5 seconds and the second one for 2 seconds. The participants in both groups spent a similarly large proportion of their viewing time fixating the face of the person. However, time-course analyses indicated differences in the viewing patterns shown by the two groups. Attention to the face appeared to have higher priority for the typically developing individuals in comparison with the ASD group. Those with typical development were faster in their initial fixations of the face when the scene presentations were presented each for 5 seconds and they looked more at the top facial regions early as opposed to late in viewing for both presentation duration conditions. The participants with ASD were quicker in their initial fixations concerning one of the main objects when the presentation of the scenes was for 5 seconds and fixations concerning the top facial regions were distributed more evenly throughout the viewing time for both presentation duration conditions. Rapid gaze cueing by the gaze direction of the person in the scene was demonstrated by both participant groups but an immediate increase in gaze duration in relation to the object looked at after gaze cueing was apparent only for the typically developing individuals. Hence, as concluded by the researchers, the variations in fixation timings shown in their investigation might be a reason for individuals with ASD to miss many social cues that are subtle and change quickly and which are perceived relatively easily by those who are typically developing within an everyday context.

In another study by Freeth et al.(2010b), the investigators considered whether a person and his or her direction of gaze presented in a complex naturalistic scenic context resulted in biases of perception, attention and memory in typically developing

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and high-functioning adolescents on the autism spectrum(ASD). The participants with ASD were boys, aged from 13-16 years and they were matched with typically developing controls in relation to chronological age, gender and full-scale IQ. A series of photographic scenes, each of which contained a person were presented via a computerised image manipulation programme. By using the programme the participants were able to manoeuvre the scenes laterally behind a static window. The borders of the latter partially occluded the scenes. The direction of gaze relating to the person in the scenes spontaneously cued the attention of participants in both groups, with preference judgements being affected and the causation of biases in memory. Also, it was indicated that a person’s gaze direction cued visual search accurately to the exact location of gaze for the participants with ASD and the typically developing individuals. Hence, it was suggested that for adolescents, with male participants being selected for this study, both with and without ASD, there were biases in preference, memory and attention that resulted from the gaze direction of another person when viewed in a complex naturalistic scene. Although there were similarities in performance between the groups as noted above, the researchers highlighted the fact that the individuals with ASD performed differently from those with typical development when viewing scenes in which the location of the person was on the left-hand side. The effect relating to gaze direction concerning preference was markedly weaker for the participants with ASD in comparison with the controls.

Freeth et al.(2010a) commented on how their study had similarities with research findings by Fletcher-Watson(2009). In this investigation adolescents and young adults, aged 16-23 years with ASD, more specifically with high-functioning autism or Asperger syndrome were considered in relation to typically developing(TD) controls, aged 17-48 years. Eye-movements were measured during a viewing period of 3 seconds with presentations involving static complex social and non-social scenes as well as social and non-social elements within a scene. Initially, the analyses identified the viewing time to various regions and then specifically, the location of the first fixation in a trial which was an indication of attentional priority and how a task instruction affected scan paths. Also, it was considered to what extent gaze-following was apparent and how much the low-level properties of a scene influenced the scan paths of the participants.

The TD individuals demonstrated a marked bias for fixating the scene in which the person was present and specifically, the person. Also, the ASD participants showed preferential looking in relation to the scene in which the person was present as opposed to the presentation in which the person was absent. For the TD individuals this bias was apparent in the first fixation. The ASD participants demonstrated a preference for social information in the first fixation that was not as strong or it was absent. Hence, there was an indication of a reduced attentional prioritisation for the social aspects of a scene. Both groups showed increased fixation in relation to the person in the scene in response to an instruction to discriminate gender. The TD individuals demonstrated spontaneous gaze-following in respect of the object domain in the free-viewing condition but this was not indicated in the ASD participants. Also, both groups made fixations which were not markedly predictable from the low-level stimulus properties. Hence, it was considered that via sensitive measures, problems with social attention were indicated in those with ASD across the lifespan and there was support for suggested neurodevelopmental atypicalities in such individuals

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throughout life. Also, these subtle aspects of people on the autism spectrum might be reflected in how they managed everyday scenarios.

Additionally, in a recent study by New et al.(2010) consideration was given to social attention in relation to ASD in an investigation involving participants who were children, adolescents and young adults with ASD and typically developing controls(TD). The children and adolescents in the ASD group were aged approximately 7-14 years with IQ scores ranging from low average to above average and those in the TD control group were about 8-11 years of age with above average IQ scores. The TD young adults were undergraduates. The participants observed alternating versions of a static complex natural scene on each trial and they had to notice the difference between these presentations. A target object in each scene belonged to one of four semantic categories, namely people, animals, plants and artifacts. Two alternate versions of the scene comprised one in which the target object was deleted and filled in with the surrounding background and another in which the target object underwent a left to right reflection. Some of the TD controls viewed the same scenes as the children, adolescents and young adults with ASD, others observed inverted versions of each scene and a selection of the controls viewed blurred images.

Change detection performance was assessed as an indication of attentional prioritisation. For the participants with ASD, their performances indicated a similar social attentional prioritisation for animate categories as the controls. The researchers considered that this finding could not be explained by lower level visual properties as the effect was not present when blurred or inverted images were used as stimuli in the presentations. Also, it was noted that there was an association for increasing age with faster detection of changes concerning people relative to artifacts. The small but significant increase in the animate attentional bias with age in the individuals with ASD was highlighted in relation to the lack of an overall developmental trajectory for the TD controls. Hence, it was suggested that some compensatory strategies in processing might be available as those with ASD developed and these might be sensitive to interventions.

When considering the young people discussed by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and presented here, some of their responses in relation to their perceptions of emotions from facial expressions indicated that they had misjudged the emotions on certain facial stimuli because they looked at one area of the face instead of processing the whole. Specifically they might have looked at the lower part and particularly the mouth as opposed to the eyes. They might have given erroneous responses or taken more time to identify a particular emotion. Even if they were correct on the static faces presented during the sessions they might have experienced difficulties sometimes in more realistic situations. During the individual sessions the children were not presented with neutral expressions when considering the detection of emotions from facial expressions as the assessment of emotions task used in the investigations involved only specific facial expressions. The memory for faces test did involve neutral expressions but the presentation time for each item was 2 seconds so that time was available for the participant to view the whole face. Additionally, the young people with ASD in my studies noted above indicated that they could use other bodily communications, as well as specifically facial aspects to facilitate their understanding of social interactions and sometimes aspects of the context or situation.

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Generally, styles of processing of upright and inverted faces have been considered in relation to each condition and developmental stages as highlighted in various contributions to the book edited by Schwarzer & Leder(2003). Also, reference could be made to a recent discussion and study by Picozzi et al.(2009) concerning the effect of inversion on the recognition of realistic face and nonface stimuli presented visually to young children.

In a review by McKone & Yovel(2009) concerning investigations with neurotypical young adults, the effect of feature inversion was shown to vary considerably across studies in relation to whether the feature change was shape only or included colour/brightness, how many faces were in the stimulus set and whether the stimulus was presented in a facial context. For changes relating only to shape in the context of a face, the effects were as large as inversion effects associated with spacing. Small feature inversion effects were apparent only when a task could be solved efficiently outside of whole-face processing. Overall, the findings indicated there was not a dissociation between the shape of features and the spacing among them. This conclusion was noted as being consistent with other results from studies involving a variety of methodologies including investigations concerning developmental aspects, those using neuroimaging as well as research concentrating on individual differences and those involved with neuropsychological approaches. The authors suggested that holistic/configural processing in relation to upright faces integrated the spacing between the features of the face and the precise shape of the main facial features.

Furthermore, in a study by Mondloch et al.(2010) 20 versions of a single female face with variations only in the spacing among the features were used as stimuli. Adults and children, aged 10 years as well as patients treated for bilateral congenital cataract, aged 12-27 years were required to judge 120 pairs of faces as to whether they were the same or different. Half of the pairs comprised items that were different. The findings indicated that discrimination of facial features was easy for the adults and this was so, even after the experience of early visual deprivation due to their cataracts and there was only a small effect resulting from inversion. The children, aged 10 years nearly reached the adult levels of accuracy although they did not perform quite as well as the adults. The discrimination ability in the three groups was not affected by the application of make-up or large variations in luminance, for example when faces had brown eyes in contrast to blue eyes. Overall, the results were given in support of features and their spacing being significant in the context of facial recognition. However, it was suggested that typically, discrimination of features was easier in comparison with spatial cues and a prominent role in the real world seemed likely for featural discrimination concerning recognition of faces.

As indicated by Sagiv & Bentin(2001) schematic faces might enhance holistic processing through the provision of a clearly defined facial gestalt and by obscuring the physiognomic value of facial components. Whether upright or inverted the physiognomic value of schematic faces is based on their gestalt. Inhibition of processing the gestalt might result from inversion but not the induction of an alteration in processing strategy. Holistic processing was facilitated in the studies by Lawson(2003, 2004 2005a, b, 2008a, c, 2009) and discussed here via fast presentations of schematic faces in upright and inverted positions. Different groups of facial features, varying in amount but not in colour which was constant across features and always positioned normally within the context of a facial outline were displayed

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to the participants. Hence, top heaviness and congruency in relation to faces as discussed by Macchi Cassia et al.(2008) would be more salient aspects for some groups than for others. The presentations were offered frequently and in similar amounts so that expertise was developed in relation to processing all of the available feature combinations in upright and inverted conditions and their associated numerosities.

The importance of fast presentations to highlight the difficulties concerning holistic processing of facial emotion in those with autism has been demonstrated in a study by Celani et al.(1999). As emphasised by these investigators with reference to several studies, the recognition of emotions expressed in the face is dependent on analytical processing which concerns inferential understanding of facial expressions and holistic processing which facilitates direct knowledge of their emotional meaning. In the study by these researchers children and adolescents with autism were matched on verbal mental age with individuals with Down syndrome and typically developing controls. In the first activity the young people were required to match faces on the basis of emotional expression or identity. The target picture was presented for only 750msec and it was not visible when the sample pictures were shown to the participants. The aim was to inhibit the use of perceptual, piecemeal strategies. In the second activity the participants rated the valence of an isolated stimulus such as facial, emotional expression or an emotional situation without representations of people. The aim was to compare the tendencies of those with and without autism to assess facial pleasantness using facial expression of emotion as a meaningful indicator. In comparison with the typically developing controls and those with Down syndrome individuals with autism demonstrated significantly poorer performances on both facial, emotional expression subtasks. On the identity and emotional situation activities no significant differences were found between the groups.

An overview of behavioural, event related potential(ERP) and functional imaging data concerning face processing and the autism spectrum has been given by Jemel et al.(2006). In relation to behavioural studies it was concluded that although the tendency in face processing for this specific group of individuals might be towards local aspects this orientation might be overcome by the demands of particular tasks. After reviewing the ERP data, it was concluded that typical category specific and dimension specific modulations of ERP activity appeared diminished or absent when considering the autism spectrum. Also, in relation to fMRI investigations of brain activity during facial image processing typical fusiform face area(FFA) and amygdala activation was not mandatory for those within this group. Overall, there seemed to be considerable variability in terms of the mode and ability to process faces when considering those on the autism spectrum. Also, the review by Sasson(2006) is of interest here as well as a recent analysis by Jeste & Nelson III(2009) concerning the use of ERPs in relation to understanding the autism spectrum. Additionally, reference could be made to Dawson & Bernier(2007) and Pelphrey & Carter(2007) for fairly recent discussions relating to the development of social and communication skills concerning individuals with ASD. Also of relevance here is the book edited by Striano & Reid(2009) on social cognition. Specifically, there is a section concerning the autism spectrum but there are considerations given to this aspect in other chapters.

Additionally, a recent contribution by Annaz et al.(2009) concerns the development of face recognition and particularly the holistic aspects in children and young

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adolescents. Specifically, the participants comprised those with autism in the high-functioning(HFA) and low-functioning(LFA) categories, Down syndrome and Williams syndrome as well as typically developing(TD) young people. Apart from variations in onset delays and developmental rates, atypical profiles were indicated in those with specific conditions and they were different for the particular conditions. The researchers used the term holistic processing to refer to a gestalt fusion process between different visual elements in an array. It was considered that this apparently early and strong aspect of face recognition was executed in low-level vision by lateral processes of excitation and inhibition. Also, this process could be accessed by the technique used in this investigation, namely a part-whole manipulation of facial stimuli. The process of gestalt fusion was contrasted with a template-matching process which they considered could be accessed by the manipulation of stimulus orientation, which was a procedure used in this study. Specifically, in the HFA group inversion effects were absent but part-whole effects were present. When considering the LFA group, performance was more accurate for the inverted facial stimuli in comparison with the upright presentations. Also, there was better discrimination for the eyes and the noses in the inverted faces whereas the orientation did not affect performance for the discrimination of mouths.

Also, in a recent study by Scherf et al.(2008) children and adults who were high functioning and with autism(HFA) were compared with typically developing individuals(TD) on activities concerning perceptual discrimination. There was a face inversion task and a classification level task which required particularly fine discriminations involving three groups of stimuli. Specifically these were socially loaded faces, perceptually homogenous novel objects, greebles and common objects which were perceptually heterogenous. The results indicated that the children with HFA presented with typical developmental levels of expertise in relation to common object recognition. In contrast, they demonstrated poorer recognition concerning the perceptually homogenous objects including faces and particularly greebles. Hence in relation to face recognition skills, it was considered that individuals with autism had a generalised deficit concerning visuospatial processing that might affect them negatively in relation to configural processing and for recognition of within group perceptually homogenous objects.

When considering those individuals discussed here who participated in my projects as well as others on the autism spectrum that I have been involved with over some years their presentations have been quite varied in degree and nature. Hence, only specific individuals were selected as participants for my interventions. A possible expectation concerning the approach described in the studies by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here was that flexible attention might be facilitated in relation to various groups of facial features and the associated information communicated by them in everyday situations. Stimulating the brain in such a way might enhance perceptual discrimination for certain facial characteristics and perceptual coherence in relation to configural and holistic aspects with associated implications specifically in the context of people and social settings. It is essential, not only to be able to process and interpret various types of information but to do so at a speed which is facilitative in relation to the situation.

4.3 Working Memory, Mental Flexibility, Mathematical Abilities, Social Competence and ASD

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In relation to other areas, mental flexibility has been highlighted by Dark & Benbow(1990, 1991, 1994) as being a salient characteristic of mathematically talented adolescents. Also, Bull et al.(1999) noted the difficulties with 7 year olds concerning perseveration or altering psychological set for those demonstrating rather limited facility with numerical development. In another study with children aged around 7 years, Bull & Scerif(2001) highlighted problems they described as relating to inhibitory processes and switching to new strategies for individuals of relatively limited mathematical ability. Their interpretation of the results relating to domain-specific inhibition has been challenged by Censabella & Noël(2005). Also, in a further study by Censabella & Noël(2008) children aged 10 years with mathematical disabilities and arithmetic fact retrieval disabilities did not show inhibition deficits relating to suppression of irrelevant information from working memory, inhibition of prepotent responses or interference control. Hence, inhibition was not considered to be causal for mathematical disabilities although it was acknowledged that inhibition of a more passive sort as in associative networks might be at fault in mathematical disabilities.

Also, factors contributing to social and interpersonal competence have been considered significant in relation to academic progress at an early age as discussed by Ladd et al.(1999) including specifically aspects of a mathematical nature by Blair & Razza(2007). Additionally, reference could be made to Blair et al.(2008) for a recent contribution in relation to executive functions and mathematical development.

Furthermore, Gray & Tall(1994) emphasised the development of ‘proceptual’ thought involving the merging of process and concept and the mental manipulation of symbolic information as being significant in the attainment of mature numerical and more advanced mathematical thought. For more recent discussions involving the proceptual notion reference could be made to Tall et al.(2001) and Gray & Tall(2007). As clarified by Tall et al.(2001) the notion of ‘procept’ is considered principally as a cognitive construct with a pivotal role available for the symbol. Hence, a focus on process concerning computation or manipulation can be transferred to a concept which may be thought of as an entity for manipulation.

Backward digit span can be considered as a working memory task involving the manipulation of stored numerical information as discussed for example, in relation to arithmetical cognition by Hoard et al.(1999) as well as more recently by Passolunghi & Cornoldi(2008). Also, backward recall of digits presented visually in left to right display conditions has been found to be worse for children with autism in comparison with typically developing and deaf children(Hermelin & O’Connor, 1975). As highlighted by Poirier & Martin(2008) in their recent discussion concerning working and immediate memory in relation to the autism spectrum, the children in the study by Hermelin & O’Connor(1975) were considered as high functioning although the diagnostic criteria have altered since the time of this investigation.

Additionally, in a study by Alloway et al.(2009) primary aged children with a diagnosis of Asperger syndrome(AS) were investigated alongside others with specific neurodevelopmental conditions. They were administered the Automated Working Memory Assessment(AWMA; Alloway, 2007) which comprises computerised and standardised measures of memory performance. There are three components for each

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of the four sections, namely verbal and visuospatial short-term memory and verbal and visuospatial working memory. The three measures for the verbal short-term memory section were digit recall, word recall and nonword recall. For each of the three tests the child heard an item sequence, that is digits, one-syllable words and one-syllable nonwords and then the requirement was for recall of the sequence in the correct order. The participants with AS tended to perform poorly in this area whereas they scored within the typical range for the other three sections. The authors considered that their performances on the verbal short-term memory measures which were offered via computerised presentations might be associated with the participants not being able to utilise phono-articulatory aspects characteristic of spoken presentations. A possible connection was noted between suggested difficulties in verbal short-term memory and problems concerning language and communication necessary for participation in conversations involving social interactions.

Furthermore, in a study by De Smedt et al.(2010) the researchers investigated the possibility of a very specific relationship between phonological awareness and single-digit arithmetic with relatively small problem sizes. They highlighted support for reading and arithmetic being associated with areas of the left temporo-parietal cortex, namely the left angular gyrus and supramarginal gyri. Also, it was noted that in developmental neuroimaging research concerning reading, performances on phonological awareness tasks were associated with activation in the left angular gyrus. In their study, typically developing children aged 9-11 years were involved in tasks including an arithmetic verification task comprising addition, subtraction and multiplication items as well as tests of phonological awareness, phonological short-term memory, reading and calculation. The results from regression analyses indicated a uniquely specific relationship between phonological awareness and arithmetic exercises with small but not large problem sizes. Also, for problems where there was a high probability of solution by retrieval, but not for those usually connected with procedural problem-solving strategies, a correlation was shown with phonological awareness. This particular relationship between phonological awareness and arithmetical exercises with a small problem size and those usually associated with a retrieval strategy was indicated after controlling for phonological short-term memory and general reading ability. Hence, the quality of long-term phonological representations in children was considered specifically important in relation to the retrieval of arithmetical facts.

Although the young people who participated in my project including those discussed by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) demonstrated some facility in relation to particular questions on both sections of the WOND, some difficulties were demonstrated on both parts. They improved their performances on both WOND sections after the training sessions involving the object assembly items, human figure drawings and the dots and facial features tasks. Improvements were shown on the Recall of Digits Forward and Backward although considerable effort was apparent sometimes in the manipulation and recall of accurate information. The pupils who had been involved in studies noted above had continued with mathematics tuition at school but they had not been in receipt of specific mathematical support from myself during the period of the projects.

Holding in mind information is an aspect of working memory and particularly the central executive(Baddeley & Logie, 1999) that has been highlighted concerning

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theory of mind acquisition involving metarepresentational abilities in those with typical development or autism(Baron-Cohen et al., 2000). Results of investigations involving backwards digit span(Davis and Pratt, 1995) and counting span(Keenan et al., 1998) have given support for working memory being a factor in the development of children's theories of mind. Also, school aged children and adolescents diagnosed with autism or Asperger syndrome who performed well on theory of mind tasks tended to respond better on digit span(Dahlgren et al., 2003).

Additionally in a recent investigation by Yerys et al.(2009), mostly high functioning children and relatively younger adolescents on the autism spectrum and some with pervasive developmental disorder not otherwise specified, aged 6-13 years were matched with typically developing controls on chronological age, gender and IQ. They were assessed in relation to their performance on the Intradimensional/Extradimensional(ID/ED) Shift Test from the Cambridge Neuropsychological Test Automated Battery. The young people in the experimental group completed as many ED and reversal ED shifts as the controls but they made significantly more errors in comparison with the controls during completion of the ED reversal shifts. The Autism Diagnostic Observation Schedule(ADOS) and the Autism Diagnostic Interview or the Revised version(ADI/ADI-R) had been used in the ASD assessment. Analyses of a subset of cases indicated a significant positive correlation between ED reversal errors and restricted interest/repetitive behaviour scores on the ADI/ADI-R in the atypically developing group.

Hence, the results were given in support of a greater need for additional feedback in relation to such children and adolescents with ASD. Also, the association between set-shifting, specifically here, ED reversal shifting and restricted interest/repetitive behaviour scores, that is, the non-social aspects could be considered as a potentially informative intermediate phenotype in relation to ASD. Certainly, the young people who participated in sessions involving my specific approach highlighted here received a considerable amount of feedback. Gradually they developed a more broadly based and flexible style of functioning in relation to specific aspects concerning home, their educational environments and in their everyday lives.

Furthermore, Yerys et al.(2009) highlight a functional magnetic resonance imaging(fMRI) investigation by Shafritz et al.(2008). Adults on the autism spectrum who were high-functioning(HFA) were compared with chronological and IQ matched neurotypical controls. Participants were involved with a target detection task which had been designed to distinguish between response and cognitive set shifts. The individuals with HFA displayed lower accuracy on response shifting trials irrespective of whether an additional requirement of those trials was a cognitive set shift. In comparison with the control participants, for the adults with ASD there was reduced activation in the frontal, striatal and parietal areas during these trials. Additionally in relation to the ASD individuals, when considering activation in the anterior cingulate cortex(ACC) and the left intraparietal sulcus(IPS) there was a negative correlation with the severity of restricted interest/repetitive behaviour scores on the ADI-R. It was considered that the findings were in line with models suggesting that the restricted and repetitive behaviours that tended to be associated with those on the autism spectrum might be related to deficits in certain aspects of executive functioning such as cognitive flexibility and response inhibition.

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In a study by Berger et al.(2006) brain activity of infants aged 6-9 months was analysed during presentations of correct and incorrect solutions for simple arithmetical equations. Longer looking times were demonstrated by the infants for the incorrect solutions in comparison with the correct solutions. Additionally, event related potentials(ERPs) which were time-locked to the solution presentations showed greater negative activity in relation to the incorrect solution conditions. Also, spectral analysis showed a similar pattern in infants as found for adults during the observation of correct and incorrect arithmetical equations. As highlighted by the researchers, error detection and conflict resolution have been considered as indicative of the development of an executive attention network involving the ACC and other frontal regions. Extensive studies concerning brain activity in adults have indicated activity with negative polarity over middle-frontal regions during error detection. The ACC has been suggested as a possible source of this activity by source localisation and fMRI investigations.

As considered by the researchers, infants at this age are not able to regulate their own behaviour during detection of their own errors and it will take some years before they can demonstrate a more mature pattern of reaction-time adjustments after detection of an error. However, it was indicated that the basic brain circuitry involved in error detection was functional before the end of the first year of life. It was noted that this mechanism would be likely to develop further, resulting in the enablement of self-regulation of behaviour and emotion. As highlighted, self-regulation crucially impacts on social functioning with associated implications concerning the development of empathy, theory of mind and conscience. These are aspects which have been considered here in relation to the approach created by the present author to help facilitate development in individuals on the autism spectrum.

As emphasised by Klin et al.(2000) appropriate social interactions between participants require engagement in holistic processing of information that changes rapidly such as that offered by facial expressions. Also, Lindner & Rosen(2006) found that children and adolescents with Asperger syndrome experienced more difficulty than the typically developing controls when required to identify emotions whether via static facial expressions, dynamic facial expressions or prosody. They highlighted the problems associated with an over reliance on verbal cues as a compensatory approach to managing social situations. As indicated above, the young people presented by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and considered here had marked difficulties concerning social interactions and aspects relating to intuition and the recognition of emotions so they tended to resort to a verbal and analytical processing mode in some situations.

In a study by Jarrold & Russell(1997) children and adolescents with autism, aged around 6-18 years were compared with those described as having moderate learning difficulties and typically developing young people. They were matched across groups in terms of verbal mental age and they were requested to count the dots presented in canonical forms or distributed arrangements involving random dot presentations and distractor stimuli. A tendency towards an analytical processing style was suggested for the participants with autism. However, although the groups differed in relation to counting speed measurements, there was not a significant difference in the number of children demonstrating global or analytical processing across the groups. The investigation by Jarrold & Russell(1997) has been discussed by Gagnon et al.(2004)

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and some controversial aspects highlighted, namely the request to count stimuli and the use of distractor stimuli.

Gagnon et al.(2004) considered the quantification abilities of individual males with high functioning autism(HFA) in comparison with typically developing young people(TD) matched on gender, chronological age and full-scale IQ. The participants, aged 10-21 years were asked to quantify as accurately and as fast as possible, the numerosities associated with the number of squares, ranging from 2-9 and displayed in random configurations. Also, the visual angles of the presented stimuli were manipulated to create a local bias, using a large visual angle and a global bias, with a small visual angle in relation to the quantification performances, specifically concerning accuracy and naming times of the young people. An effect in relation to a local and global bias associated with the stimuli presentations was not indicated by the performances of both participant groups. Also, the consideration of superior abilities in quantification for the HFA individuals was not apparent. Additionally in relation to the HFA participants, analyses of the naming time slopes for identification of small consecutive numerosities, specifically 2-5, suggested the use of counting as opposed to subitizing as indicated in the TD individuals.

In relation to the numerical aspects of the studies by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and discussed here, subitizing or ‘global counting’(Jarrold & Russell, 1997) were the processes indicated usually concerning the participants’ responses to the dot stimuli and the facial features but some ‘local counting’ occurred and slightly more so for the facial features. As they practised these tasks which included various arrangements of dots as well as facial features varying in amount but in their usual positions within schematic faces, the apparent tendency was towards more global counting and this included items beyond the expected subitizing range.

4.4 Intuition, Systemizing, Certainty, Uncertainty, Equilibrium, Symmetry, Mathematical Abilities and ASD

As highlighted by Laughlin(1997) with reference to Bastick(1982) intuition is characterised by various qualities including its non-analytic and gestalt aspects as well as affective and specifically empathic associations. Additionally, a more recent contribution noting the properties attributed to intuition by Bastick(1982) has been given by Claxton(2003). Also, in a discussion concerning beliefs described as intuitive or reflective, Sperber(1997) emphasises the representational and metarepresentational abilities of human individuals and the possible reciprocal movement between concepts of an intuitive or reflective nature in concept revision. Mental flexibility which has been noted earlier in the presentation here is a requirement for this aspect of development.

For a recent and comprehensive discussion with consideration given to information from social cognitive neuroscience in relation to intuition reference could be made to Hodgkinson et al.(2008). Specifically, definitions are discussed and one highlighted particularly in a review concerning intuition in the context of management by Dane & Pratt(2007). They consider intuitions as judgements driven by affect that emerge from associations that are fast, non-conscious and holistic. In the discussion by Hodgkinson and colleagues somatic, affective and cognitive aspects are considered as well as associated contributions in relation to intuitive judgements involving implicit

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learning, tacit knowledge, recognition of patterns and expertise. Additionally, for other recent and detailed discussions concerning intuition reference could be made to Plessner et al.(2008) and Sadler-Smith(2008). Also of relevance here is the contribution by Gillard et al.(2009) concerning intuitive/heuristic and analytic processes and their integration in relation to cognitive psychology and the psychology of mathematics education. As indicated in the present discussion, intuition is being considered within particular contexts and linking across a variety of specific domains.

In “The Value of Science”(1913) by Henri Poincaré and presented in the series edited by Gould(2001), Poincaré considers two types of individuals within the mathematical field. One group he terms logicians and analysts and those with a different sort of mathematical mind he refers to as intuitionalists and geometers. The analysts are informed and guided by the intuition of pure number, the intuition of pure logical forms. Their perceptions encapsulate the overall plan of a logical structure without apparent interference from the senses. Although Poincaré considers that there will be some inventors amongst the analysts it is not expected that there will be many within this category. He emphasises how what he terms sensible intuition in mathematics is the most common form in relation to invention with the imagination making a major contribution.

In Poincaré’s comments on his conversations with the mathematician Charles Hermite his perception concerning Hermite’s thinking was that the most abstract entities were experienced by him as living beings. Also, Hermite did not elicit sensuous images but he perceived that these abstract entities had some principle of internal unity and this was considered by Poincaré as a form of intuition.

It might be that what Poincaré refers to as sensible intuition is what is absent or at least present to a lesser degree or only in specific contexts in those with autism spectrum dispositions(ASD). Individuals with Asperger syndrome(AS) tend to be some of the relatively more able on the autism spectrum and some may have exceptional abilities in specific areas accompanied by considerable difficulties in others.

As discussed by Pring et al.(1995) in the context of savants and autism, a marked segmentation ability might characterise particularly individuals with a talent for art. Additionally, Drake et al.(2010) investigated whether typically developing children with a talent for drawing realistically demonstrated a local processing bias suggested in individuals with ASD. The participants, aged 6-12 years, were required to produce a drawing after observing a still life model and their depictions were scored for level of realism. Also, they completed three tasks to assess local processing and the parents completed the Childhood Asperger Syndrome Test(CAST). The results indicated that drawing score was predictive of local processing performance on all of the tasks and it was independent of verbal IQ, age and the number of years of art lessons experienced by the participants. Also, the scores for the observational drawings predicted more frequent repetitive behaviours as indicated by the CAST assessment. Hence, it was concluded that a skill concerning realistic drawing was related to a strong bias in local processing and repetitive behaviour tendencies. Some characteristics suggested in individuals with ASD, with or without artistic talent seemed to be apparent in typically developing children who were gifted artistically and selected here for their skill in producing realistic drawings.

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Furthermore, a facility for seeing wholes in terms of their parts might be associated with high abilities in other areas such as mathematics. Higher level functioning requires mental flexibility in relation to this mode and the ability to integrate perceptual and conceptual aspects into meaningful and coherent wholes. Also in this context, hypothetical thinking and the intuitive process are salient in the development of mature intellectual functioning and specifically in the studies described by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) concerning mathematics and art.

Additionally, it is interesting to note a case study described by Wallace et al.(2009) concerning a man who had been diagnosed as an adult with Asperger syndrome. His presentation included savant abilities in calendrical calculation which had become more apparent in his adult years as well as art, predominantly drawing with the topics being scenes, buildings and objects and some painting as a young adult. He demonstrated good memory, superior mental calculation and strong visuopsatial skills. Also, he showed marked and seemingly implicit knowledge of calculation structures and a cognitive style which indicated a focus on detail. When a comparison was made with the mean cortical thickness of the neurotypical controls, he was shown to have a thicker cortical area in the bilateral segment of the superior parietal lobe which the investigators highlight in association with drawing and other visuospatial functions and calculation skills. In contrast, thinner cortical areas were indicated in regions such as the superior and medial prefrontal, middle temporal and motor cortices which they note in connection with social cognition and other aspects of concern for those on the autism spectrum.

In his discussion concerning invention in mathematics Hadamard(1996) considers that unconscious phenomena which are most likely to become conscious are those which affect us profoundly in an emotional sense. This idea is associated with feelings of mathematical beauty as seen in the harmony concerning numbers and forms. He emphasises how significant it is to see a mathematical argument as a unique phenomenon as in grasping the physiognomy of a face and this is true in relation to inventions in other areas such as music or art. Also, with reference to Poincaré imagery is considered significant in bringing together and holding links in a mathematical argument with the synthesis giving the problem its overall structure.

Complex information managed at the unconscious level becomes simplified as the solution to a problem presents itself in consciousness. It is the flexibility of thought that leads eventually to the formation of solutions that emerge in conscious experience. Generally, intuitive leaps made by individuals are accompanied by surges of positive emotion as problem solutions are brought into consciousness. It is the emotional charge that encapsulates the essence of an idea or an experience on bringing it into consciousness. Emotion is crucial in the unification of the self.

Some individuals of high ability in mathematics but also perhaps those in other areas such as music or art might have similar experiences to those noted above in relation to abstract entities being perceived as animate phenomena. It might be that some of those individuals would not need or at least to a lesser extent relationships with other human beings because their experiences involving mathematics, music or art would be sufficient emotionally for them. Those who are very able with ASD might find considerable satisfaction in pursuing specific areas of interest as indicated above. The

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interest and relationships they form with abstract entities might be quite intense and obsessive as some relationships with people are for others. Individuals with ASD might form intense attachments for specific people but they tend to be on their terms. In the context of these aspects reference could be made to Attwood(2006) for examples of individuals with AS.

Additionally, Mercier et al.(2000) discussed positive experiences associated with restricted interests in those with high-functioning autism or Asperger syndrome. Also, Mottron et al.(2009) noted several references to highlight the indication of positive emotions in relation to performances concerning savant abilities. Furthermore, these researchers refer to a study by Grelotti et al.(2005) involving a boy with autism and a special interest in particular cartoon characters. He was aged 11 years when assessed initially and he reached 12 years of age when followed up. There were two controls, an adolescent, aged 17 years with autism but no interest or experience with these cartoon characters and a typically developing(TD) boy, aged 10 years with above average intelligence and an enthusiasm for these cartoon characters. The boy with autism and the special interest individuated the cartoon characters faster than familiar faces and common nonface objects but he did not individuate familiar faces any faster than these objects. The TD control with the special interest performed at a similar speed for the individuation of familiar faces and cartoon characters but he was faster at individuating these faces and characters in comparison with the objects and characters. Additionally with the use of fMRI, for the boy with autism and the special interest there was activation in the amygdala and fusiform gyrus in relation to perceptual discriminations involving the cartoon characters but not in association with the familiar or unfamiliar faces. This activation pattern was not apparent in the TD individual with the same special interest and it was not indicated in the control participant with autism but not the special interest.

Furthermore, in a recent study by Greimel et al.(2010) 15 adolescent males, aged 13-17 years and diagnosed with Asperger syndrome or high-functioning autism, the ASD group, were compared with typically developing(TD) controls. The groups were similar in relation to chronological age, full-scale and verbal IQ but the performance IQs of those in the ASD group were lower in comparison with the TD individuals. Also, some fathers of the ASD adolescents were compared with a selection of fathers from related to the TD young people. The individuals in both groups were comparable in terms of chronological age and full-scale IQ. Using fMRI, the participants were investigated during their involvement with a task designed to assess empathy. Happy, sad and neutral faces were selected as stimuli because congruent empathic reactions had been shown to be evoked by such items. The stimuli were presented to the participants and they had to judge the emotional states from the faces, the other-task or to assess their own emotional responses to the faces, the self-task.

For the attribution of emotional states in both the self and other conditions, the ASD individuals displayed reduced activation in the fusiform gyrus in comparison with the TD controls. Also, there was an inverse relationship between neural activity in the fusiform gyrus and social deficits in those with ASD. When ASD participants assessed their own emotional responses to faces, less congruent reactions were presented and decreased activation in the inferior frontal gyrus. The fathers of the ASD adolescents scored higher on a self-rating scale assessing symptoms associated with autism, the Autism-Spectrum Quotient or AQ as presented by Baron-Cohen et al.

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(2001) in comparison with the fathers in the control group but there was no indication of impairment in relation to their performances on the empathy task. However, when considering the neural aspects, fathers of the ASD participants showed diminished activation in the fusiform gyrus when judging the emotions of others. For the ASD group, reduced activation in the amygdala was apparent only at an uncorrected threshold but there was stronger evidence for reduced amygdala activation in fathers of the adolescents with ASD in comparison with control fathers when determining the emotions of others from weak cues. The authors discussed these results in the context of controversial issues and findings from other studies concerning amygdala activation and ASD. Also, they considered the possibility of compensatory strategies being developed and implemented by relatives of those with ASD in relation to any dysfunction in the fusiform gyrus and amygdala. Certainly in relation to individuals with ASD discussed here and some highlighted elsewhere, compensatory strategies have been developed by many of such a disposition to help them manage their lives. Also, others might not have presented with problems associated with ASD as they had been able to develop adequate strategies or find a niche in life in terms of appropriate careers for themselves, possibly partners and sometimes children.

Additionally, the researchers noted that empathy scores in the TD adolescents when assessing the emotions of others from weak cues showed a positive correlation with activity in the left insula. Furthermore, when considering the fathers across both groups, a positive relationship was demonstrated between their empathy scores and activation in the left insula during the self-task and in the right insula during the other-task. The authors referred to several studies that had indicated a role for the anterior insula in relation to empathy. Also, this region has been noted recently in the context of an investigation concerning neural representations of self and other and highlighting atypicalities in autism spectrum conditions by Lombardo et al.(2010).

In discussing his life in association with autism Edgar Schneider(1999) highlighted his problems with relationships. When considering the term love he indicated that his experience would be in relation to assessing and valuing an individual intellectually as opposed to interacting in a direct and emotional mode. Any experience of sexual arousal would be through fantasy. In response to being questioned about his greatest fear Edgar Schneider indicated that it was uncertainty. He needed a plan and he could manage change if he had a plan from which he could develop an alternative as necessary. Individuals develop plans in order to attain specific goals. For those on the autism spectrum, having a goal could be considered particularly within a facilitative context in relation to the development and maintenance of a sense of identity, unity and self-worth. The importance of certainty and uncertainty in the lives of those with AS has been highlighted by Attwood(2006).

Allman et al.(2005) have considered that Von Economo neurons(VENs) might be involved in the rapid intuitive apprehension of complex situations. They have suggested that the VENs are involved in relaying output from the fronto-insular(FI) and anterior cingulate cortex(ACC) to regions of the frontal and temporal cortex related to theory of mind and where quick intuitive judgements are connected with slower more reasoned judgements or deliberations. They highlight how research indicates that activation of the FI and ACC increases with the amount of uncertainty(Critchley et al., 2001) and these areas are involved in the adaptation of decisions and cognitive flexibility(O’Doherty et al., 2003). They emphasise how

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judgements of emotional value influence intuition and deliberation and suggest that the VEN system concerned with fast intuitive responses and a considerable degree of uncertainty in some conditions is impaired for those on the autism spectrum. An intention fundamental to the approach described by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) was to enhance cognitive flexibility by facilitating the management of uncertainty and consequently reducing anxiety via the promotion of intuitive modes of functioning and particularly across different areas of cognition.

In a related context Huettel(2006) highlights a distinction between behavioural risk, which concerns decisions and uncertainty associated with necessary action and reward risk, which concerns decisions involving uncertainty relating to possible outcomes. In their fMRI studies, young healthy adult participants viewed shapes with well learned response-reward contingencies. In one condition the size of the monetary reward was held constant and in the other experiment the expected value was kept constant. In line with earlier studies, when behavioural risk was absent activation was evoked over a wide range of brain areas. However, the presence of behavioural risk resulted in modulated activation in regions of the prefrontal, parietal and insular cortices with reward risk not eliciting such observations. Reward delivery as opposed to omission evoked an increase in activity relating to the ventromedial prefrontal cortical region and nucleus accumbens. Hence, it was concluded that distinct brain systems were involved with decisions concerning different types of risk and as the areas involved with the effects of behavioural risk were not under the influence of reward risk they were not sensitive to generalised anxiety.

Additionally of relevance here is the discussion concerning social influences in relation to perceptual decision making by Mojzisch & Krug(2008). They note the suggestive role of frontal and reward circuits in the emotional evaluation of social influences. This is in contrast to the consideration of the occipital and/or parietal lobes being involved in the integration of the opinions given by other individuals during the decision making process. Reference is made to Deutsch & Gerard(1955) who use the term ‘normative influence’ which concerns conformity in people because of a desire for acceptance and social approval. Also, ‘informational influence’ refers to conformity in individuals associated with a need to determine the correctness of their perceptions. It is noted that informational influence may manifest itself if there is a motivation for accuracy and uncertainty is present as in the case of stimulus ambiguity.

When considering ASD, individuals might be very aware that they are different in specific ways but attempts at behaving in a socially acceptable manner tend to be difficult as often, social signals are ambiguous and confusing for those of such a disposition. The anxiety experienced by these individuals might to be quite specific and very intense within contexts such as social situations where there are numerous uncertainties associated with decisions about how to respond appropriately in relation to fast changing interactions. Learning strategies may help to some extent but the resulting behavioural response may not be fast enough and integrated sufficiently into their repertoire to produce a natural presentation. The individual with ASD is confronted with a considerable variation in the range of predictability of responses and consequently, courses of action. Hence, feeling positive and confident about any involvement in such situations is especially problematic for those on the autism spectrum.

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It would seem that there are some individuals with ASD who are able to function as mathematicians in the style of analysts as described above and they are able to deal with uncertainty in this mode. However, as suggested earlier and emphasised by Byers(2007) creative mathematical ideas are non-algorithmic in origin. As individuals including those with ASD mentioned above develop a sense of certainty in specific contexts, emotional satisfaction is experienced with the formation of mathematical ideas and the solutions to mathematical problems. Byers(2007) has given a detailed discussion concerning the sense of certainty originating in, and emerging from mathematical activity. He highlighted certainty as being subjectively the correlate specifically of truth and there being no doubt in the sense of the mathematical truth experienced by the individual. Those with ASD tend to not need or do so in a different form, require to a lesser extent or are unable to avail themselves of emotional satisfaction experienced by others usually in a direct mode via human relationships but as emphasised here, they might find it elsewhere.

As highlighted by Poincaré, from a philosophical perspective it would be an illusion to deny that any of our reasoning would be void of intuition. A dependence on pure logic would lead only to tautologies and the absence of creative innovations. The analysts as described by Poincaré might to be some of the high systemizers referred to by Baron-Cohen(2006) as some of the individuals within this category would have a facility for managing abstract systems such as mathematics. Also, some of these very able individuals might present with dispositions associated with the autism spectrum as suggested by Baron-Cohen et al.(2007). However, as indicated above relying on systemizing would not be enough for intellectual progress. Mathematicians are able to reach high levels of achievement only with the possession of a specific intuitive ability. Those systemizers who do not possess this facility in relation to intuition and mathematics might manage the system in this area to a certain degree but they would be limited in their levels of attainment. Others might excel with other systems where the level of abstract thinking and intuition concerning mathematics is not a requirement.

As noted by Steinsaltz(2009), mathematical precision is not the same as accuracy but it is easily confused with the latter. This precision in mathematics may be fundamental to the strong affinity shown in relation to the subject by some very able individuals on the autism spectrum. The significance of precision may influence their approaches to situations in other aspects of life but there may be inappropriate applications with a lack of achievement of the expected results. Their expectations of outcomes would be inaccurate in this context.

The intuitionalists and geometers referred to by Poincaré would be approaching mathematical problems from a different perspective in comparison with the analysts and logicians. Specifically they would be using visualisation involving spatial and mental rotation skills. They would be accessing systems in particular ways but their primary sources of inspiration and solutions to mathematical problems would be via visualisation. Some individuals with ASD could function in this mode as they might visualise patterns and the intricate relationships of components within specific contexts as well as being able to rotate shapes. Also, geometric insights by a variety of outstanding mathematicians have been highlighted by Ronan(2006) in his discussion relating to the mathematics of symmetry.

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As highlighted by Maor(1991) the artist, Maurits Cornelis Escher and the musician, Johann Sebastian Bach appeared to share a similar mathematical intuition. In these individuals an acute sense was apparent relating to pattern, rhythm and regularity. The latter was temporal for Bach and spatial for Escher. The notion of symmetry is fundamental to the compositions of Bach as well as to the drawings of Escher. In mathematics, the definition of symmetry concerns the idea of invariance as noted by Zee(2007). The term symmetric is used in relation to a geometrical figure which remains unchanged under specific operations. Also, reference could be made to Darvas(2007) for a comprehensive discussion concerning symmetry in a variety of contexts.

The suggested relationship with systems as highlighted earlier and the inability of some individuals with ASD to avail themselves of intuitive abilities in connection with certain specific systems could be considered in association with the difficulty that these individuals tend to experience in altering mental set. The lack of intuitive abilities in specific contexts and for some excellent intuitive abilities in certain areas suggests why some individuals with ASD do not progress past a certain level in some spheres or they excel in selected domains. The reasons for their presentations including their particular strengths and weaknesses suggest the importance of explanations that consider intuition as well as remedial approaches that emphasise attempts to enhance intuition. It would appear that some individuals might hyper-systemize(Baron-Cohen, 2003) by default as they are unable to access the intuitive route easily to help them function more naturally in some situations or to find alternative pathways which will assist problem solutions and interactions. As discussed by Gallese(2001, 2006) and Gallese et al.(2007) explicit theorising appears to be the only available compensatory mechanism for those with ASD as they seem unable to experience people via a direct route in comparison with others of a more typical cognitive and emotional disposition.

In a study by Southgate et al.(2007) involving an eye-tracking task spontaneous mentalizing, the attribution of mental states was suggested in typically developing infants. Recently, the same task was used in an investigation by Senju et al.(2009). As indicated with these very young individuals, the eye movements of neurotypical adults were indicated as being anticipatory in relation to the behaviour of an adult based on her false belief. This was not so for the participants with Asperger syndrome. These individuals did not attribute mental states spontaneously but it was considered that they might be able to do so in explicit tasks via compensatory learning. Specifically, verbally mediated reasoning could be used with prompting via the structure of an explicit task and instructions.

In the biography of the mathematician, John Nash by Nasar(1998) an individual is described with quite an unusual presentation from a young age. Terms such as aloof, isolated and introverted are used in relation to his presentation and overall characteristics are noted concerning difficulties involving social interactions. Comments have referred to an apparent lack of affect or disconnection from his own emotions and those of other individuals. Reports indicated an absence of close friends but as a young person he seemed to experience enjoyment performing for other children. He could talk incessantly and he might dominate the class discussion. He was described as a bright child with a sense of curiosity and he enjoyed reading and

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learning alone. His father bought him science books, he enjoyed carrying out experiments and he developed his own approaches to solving mathematical problems. A comment was made that he tended to daydream but he might have been working something out in his own idiosyncratic way. This apparent need for originality continued into his adult life and it has been noted as quite an obsessional characteristic as part of his disposition. This search for originality is demonstrated in the way that he developed a new approach to a longstanding problem in economics, namely bargaining.

As highlighted by Camerer(2003) in his discussion on game theory, John Nash made a proposal as to how rational players would play and this became termed the Nash equilibrium. The notion which was founded on the idea of equilibrium in a physical system was that players would adjust their strategies until no benefit could be gained by any of the participants from a change of strategy. Then all of the players would be selecting action plans that were best, that is utility maximizing responses to all of the other participants’ strategies. Fundamentally, John Nash had a novel perception of a deal as the outcome of a negotiation process or strategizing independently by each individual in the pursuit of self-interest.

For specific details concerning the work of John Nash reference could be made to Kuhn & Nasar(2002). As noted in this text the distinction between cooperative games where binding agreements are possible and where they are not as in non-cooperative games was introduced by John Nash. His equilibrium concept, referred to later as the Nash equilibrium as noted above related to non-cooperative games.

Camerer(2003) describes the Nash equilibrium as a “hyperresponsive” Quantal Response Equilibrium(QRE). In a QRE the players do not select the best response with a probability of one. Camerer refers to the term “better respond” to describe how the players choose responses with higher expected payoffs with higher probability. Also, it was noted that in relation to game theory more recently proposed learning models did not assume necessarily that all players had absolute knowledge of all possible payoffs. In many situations that occurred naturally the individuals concerned might not be well informed about payoffs. Hence, uncertainties and accompanying anxieties would be experienced by those within such contexts until a sense of balance could be achieved through a resolution of the issues.

A series of lectures entitled “Symmetry”(1951) was given by Hermann Weyl and presented more recently in the Princeton Science Library series(Weyl, 1989). He discusses how the term symmetric concerns notions of being correctly proportioned or balanced. Symmetry refers to the harmonious formation of several parts integrating into a whole. Also, Weyl considers symmetry in relation to the image of the balance, specifically bilateral symmetry which is a precise geometrical concept that makes reference to operations such as reflections or rotations. Weyl emphasises how beauty is intertwined with symmetry and mathematics forms the basis of symmetry. Symmetry has been a notion which has been used in efforts at an understanding and the creation of order or structure concomitant with perfection and beauty.

For individuals on the autism spectrum a desire for symmetry would appear to be intricately related to a desire for beauty and harmony. A sense of beauty and a state of harmony are so difficult apparently for those of such a disposition to experience in

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terms of their relationships with people. Baron-Cohen(2006) highlighted the “need for sameness” with reference to Kanner(1943) in addition to the social deficit as central to his hyper-systemizing theory of autism. However, an emphasis on a desire for symmetry or balance would seem a more fundamentally appropriate way of describing a characteristic pertinent to those on the autism spectrum. Aspects of symmetry in relation to the perspectives of those with AS have been noted by Attwood(2006).

During the course of my clinical work I have become very aware of a keen sense of justice expressed by individuals with AS. If they feel wronged themselves or they witness an act of injustice in relation to someone else it is crucial for them to see that the offender is reprimanded as soon as possible. Also, it is essential that the punishment is seen by them as very specifically appropriate to the offence and this applies also if they are the offenders. If the punishment is not perceived as being meaningful and justice is not seen to be done quickly, anxiety rises to a considerable degree in the person with AS and it does not recede until the balance is reset through the acknowledgement and appropriate redress concerning the offence and the perpetrator.

As highlighted by Stewart(2007) symmetry is a particular sort of transformation or a way of moving an object. If the object appears the same after a transformation then the latter is a symmetry. A mathematician, Évariste Galois used algebra in a novel approach for studying symmetry and founded an area of mathematics termed group theory as discussed in specifically relevant texts by Ronan(2006) and Stewart(2007).

As emphasised by Reid & Szendroi(2005) every group is a transformation group. The sole purpose of a group concerns its action in space. As discussed by Weyl(1989) a particular transformation called an automorphism does not alter the structure of space. Avoiding more formal mathematical definitions, an understanding can be extracted from an example of an automorphism such as a permutation which is the ordered arrangement of a select number of items from a set or a specific mode of rearrangement concerning the elements in a list. The term symmetric group refers to the group which consists of all permutations of a given set. In relation to individuals with ASD they may go through some or all possible permutations within a specific context in trying to understand and negotiate situations, with those of a social nature being particularly demanding.

It would seem no coincidence that in relation to his disposition John Nash as a mathematician with high ability developed his ideas within the context of rational players and equilibrium concerning non-cooperative games. Individuals with ASD tend to be searching constantly for stability via verbal negotiations if they possess the ability to function at this level. Reaching any sort of agreement is very much in relation to their terms and if it is broken the result is very distressing for them as they find themselves again facing uncertainty to an intolerable degree. They would like a situation where all of the participants including themselves are aware of what happens in relation to specific decisions and actions but unfortunately, as noted above in many naturally occurring contexts this is not so.

As discussed by Nasar(1998) the mathematician Paul Halmos described two kinds of geniuses, those who were like others in the general population but more so and those

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with a rather mysterious quality associated usually with music or art. John Nash appeared to be of the rather mysterious type. In line with other significant mathematical intuitionalists such as Riemann, Poincaré and Ramanujan his intuitions in mathematics were non-rational. He would visualise solutions to problems and then construct the proofs. As highlighted by Nasar(1998) and Kuhn & Nasar(2002) John Nash had a clear, logical mind but also he had exceptional visualisation abilities which resulted in the creation of original mathematical ideas. Also, he was engaged in a variety of mathematical spheres and in Poincaré’s terms his presentation was indicative of a logician and analyst as well as an intuitionalist and geometer. Both algorithmic and non-algorithmic aspects in relation to creativity and mathematics have been considered in a comprehensive discussion by Byers(2007).

4.5 Cognitive Flexibility, Self-Unification, Mathematical Abilities and ASD

As highlighted by Phillips et al.(2002) with reference to Ashby et al.(1999) and Bodenhausen et al.(1994), positive mood tends to enhance cognitive flexibility and facilitate performance on intrinsically motivating tasks involving creative problem solving. Additionally, in a recent presentation by Subramaniam et al.(2009) a detailed discussion is given concerning positive mood in relation to insight and creative problem solving. In their research involving fMRI, adult participants with higher positive mood solved more verbal problems and particularly more with insight in comparison with other participants who presented with lower positive mood. Positive mood was shown to be associated with alterations in brain activity during a preparatory interval prior to problem solution. Sensitivity to mood and insight was demonstrated in relation to the anterior cingulate cortex(ACC) with positive mood being shown to change preparatory activity concerning the ACC and the participating individuals being biased to involvement with problem processing conducive to solution with insight. Hence, it was suggested that positive mood might be facilitative in relation to insight partly by modulating attention and cognitive control mechanisms via activity in the ACC and the possible increased sensitivity to the detection of competing solutions. The considered more global, as discussed by Gasper & Clore(2002) or broader attentional focus associated with enhanced insight or creative problem solving, with reference to Ansburg & Hill(2003) and Rowe et al.(2007) could be noted particularly, in association with those on the autism spectrum.

Additionally, as highlighted by Förster(2009) with reference to Markman & Gentner(2005), there are various motivational, cognitive and affective aspects to consider in relation to the search by individuals for similarities or dissimilarities when comparing two groups of stimuli. In the research presented by Förster(2009) involving adult participants, a bidirectional and automatic association was suggested between a global processing mode and the generation of similarities and in contrast, between a local style of processing and the production of dissimilarities. Reference was made to the study with adults by Macrae & Lewis(2002) in which it was suggested that recognition of faces could be disrupted by a task activating a local processing mode. In contrast, the activation of a global style of processing could enhance recognition memory.

As noted in the present discussion, often some of the characteristics highlighted in relation to individuals on the autism spectrum concern their apparent ease in processing specific details in certain situations and particularly, a facility for attending

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to the more unusual aspects as opposed to the similarities between stimuli. Although these are very useful attributes in certain contexts, at other times an emphasis on more holistic processing and an appreciation of similarities is not only preferable but very significant, for example, in relation to appropriate social functioning. When considering the young people discussed by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) more positive emotions were shown as they continued with the training sessions. These more positive emotional experiences were demonstrated in connection with the specific tasks and reflected later as they chose to do activities in art as well as other areas including organised group activities and everyday social situations. Certainly they demonstrated more facility in terms of organising ideas in various ways and spontaneously taking different cognitive perspectives. It was suggested by the present author that particular approaches which promote abilities in certain areas might contribute to enhancing development in other spheres. Hence, the integration and transference of skills might be facilitated and the generalisation of concepts.

As highlighted by Downing et al.(2004), the findings from their investigation with typically developing adults suggested that the human body, similarly to the face, might be given prioritisation in relation to attentional selection. Usually we know our own bodies immediately as we look at our body parts and we distinguish our bodies from those of other people. As indicated in the approach described by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) the young people with ASD were encouraged to think about body parts and to unify them in the formation of human cardboard characters or more complex aspects of the body as well as in human figure drawings. Specifically, they were helped to think about themselves and their own bodies as distinct from others and their bodies. Although the participants might have used some facial characteristics and cues to help them recognise individuals and understand their emotional presentations, they indicated that attending to bodily aspects was facilitative particularly in relation to functioning within social contexts. The subitizing tasks required them to apprehend immediately the numerosities associated with dots and with different groups of schematic facial features. Specifically, the non-algorithmic mode of functioning which is so crucial in many ways to human development and particularly in relation to social situations is an aspect that the author has aimed to facilitate in those individuals of such a disposition discussed in the studies mentioned here.

As indicated in these investigations and elsewhere, numerical associations have been made in various ways with body parts and some aspects particularly such as facial features and the fingers. The parietal lobe has been highlighted as being prominent particularly in relation to number processing including certain aspects associated with fingers as discussed in my own studies and by others as well as specifically in a review by Dehaene et al.(2003). Also, reference could be made to a fairly recent discussion concerning number sense and aspects relating to dyscalculia including developmental and acquired considerations by Wilson & Dehaene(2007). The significance of the angular gyrus is highlighted and a suggested impairment involving this area and associated with difficulties in learning and retrieving arithmetical facts, especially concerning multiplication. The angular gyrus, noted earlier and again here, is located within the inferior parietal lobule and specifically, at the junctions of the temporal, parietal and occipital lobes.

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Also of relevance are various discussions relating to mathematical learning difficulties and disabilities in the book edited by Berch & Mazzocco(2007). In particular, Simon & Rivera(2007) emphasise caution when considering the findings of neuroanatomical correlates concerning numerical cognition in neuroimaging studies involving adults and interpretations concerning children and adolescents as differences in neural activity might be detected in young people with typical and atypical presentations at a variety of stages in their development. Also, published neuroimaging investigations associated with numerical development involving children and adolescents are relatively limited in number at present. Additionally, recent discussions by Ansari et al.(2008), Kaufmann(2008), Kucian et al.(2008), Lawson(2008b, 2010) and Rotzer et al.(2008, 2009) are of relevance here. Also, reference could be made to recent contributions by Hubbard et al.(2009) and Knops et al.(2009) concerning the parietal cortex in relation to numerical cognition and spatial processing. In addition, various articles in a special journal issue edited by Dowker & Kaufmann(2009) concern numerical cognition with an emphasis on atypical development.

In the context of their investigation concerning meditation and the self, Lou & Kjaer(2005) highlight a crucial role in relation to self-representation for the medial parietal region connecting the right and also, the left lateral inferior parietal cortex with the medial prefrontal cortex known for its essential role in this respect. In relation to various studies, the authors note the abundance of anatomical connections between the medial parietal/posterior cingulate and the medial prefrontal/anterior cingulate areas in respect of their integrative function concerning reflective self-awareness and the resting state of consciousness. They emphasise how these medial anatomical features integrate the anterior and posterior areas of the brain and also, the left and right hemispheres as well as the limbic and neocortical aspects and act as gateways for the dissemination of information in the brain from lateral cortical areas. With the possibility of the self acting as a core feature in unifying conscious experience a proposed role was indicated for the involvement of these medial areas in this unification.

In a fairly recent review concerning the medial section of the parietal lobe, the precuneus, Cavanna & Trimble(2006) discuss results from functional imaging studies suggesting a major role for the precuneus in very integrated tasks. These include visuo-spatial imagery, episodic memory retrieval and operations concerning self-processing, specifically first-person perspective taking and an experience of agency. Additionally, the precuneus and surrounding posteromedial regions are amongst the brain structures showing the highest resting metabolic rates. Also, they present characteristics of transient decreases in the tonic activity during engagement in actions which are non-self-referential and goal-directed. This is the default mode concerning brain function. In relation to these aspects, there has been a proposition suggesting involvement of the precuneus in the network concerning the neural correlates of self-consciousness engaged in self-related mental representations during rest. This hypothesis shows consistency with the selective hypometabolism in the posteromedial cortex which has been noted in a broad range of altered states of consciousness such as sleep, drug induced anaesthesia and vegetative conditions.

The review concerned information that related to anatomical aspects of the precuneus and its broadly spread connections to cortical and subcortical structures as indicated in nonhuman primates in association with behavioural correlates. Precuneus activation

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patterns associated with responses to a variety of mental activities were considered in the context of a conceptual framework for linking the functional imaging results to the implicated higher level cognitive functions associated with this structure. In particular, there was an apparent convergence between patterns of activity relating to the precuneus and information concerning the anatomical and connectivity aspects with the consideration of a functional subdivision within the precuneus. There was a consideration for an anterior region in this structure being involved in strategies relating to self-centred mental imagery and a posterior area being associated with episodic memory retrieval.

Additionally, in a recent fMRI training study by Lyons & Ansari(2009) the researchers investigated the cerebral basis of mapping nonsymbolic numerical quantities onto abstract symbols. Adult participants were involved in training to associate novel symbols with nonsymbolic numerical magnitudes, that is, dot arrays. The neural correlates of numerical comparison in contrast to recognition of the novel symbols after each of two training stages were investigated via the use of fMRI. A left-lateralised fronto-parietal network which included the precuneus and the dorsal prefrontal cortex displayed more activation during numerical comparison than perceptual recognition. Contrasting with this result was the finding that a network including bilateral temporal-occipital regions showed more activity during perceptual recognition than numerical comparison. Also, those participants who achieved higher scores on a postscan numerical task, which measured their understanding of the global numerical organisation of the novel symbols, showed increasing separation between the two activities in the bilateral intraparietal sulci as a function of increased training.

Furthermore, there was a systematic relation between activity in the left intraparietal sulcus and the effect of numerical distance on accuracy. The data were offered as evidence that parietal and left prefrontal cortices were involved in learning to map numerical quantities onto visual symbols. Only the parietal cortex appeared related systematically, to the extent to which the participants learned an association between novel symbols and their numerical referents. It was concluded that the left parietal cortex, specifically might play a central role in relation to imbuing visual symbols with numerical meaning.

Also, Franklin & Jonides(2009) noted that neuroimaging studies involving the judgement of magnitude and/or order resulted in a behavioural distance effect, the finding that the comparison of stimuli was easier when the items were further apart. In their fMRI study, for both the magnitude and order tasks involving visually presented Arabic numerals comprised of two digits, activation concerning the intraparietal sulcus(IPS) was indicated in relation to the adult participants strategies rather than the distance between the numbers. The researchers concluded that a mental number line was represented in relation to the IPS and access to this mental number line could result in distance effects for magnitude comparisons and reverse-distance effects when order was considered by the participants.

In a study by Lyons & Beilock(2009) it was indicated that individual differences in working memory(WM) capacity predicted the tendency of adult participants to do more than make simple and direct associations and to form inferences concerning deeper ordinal relationships among symbolic numerical stimuli. In the first experiment, it was considered whether this tendency was apparent in a learning

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situation involving the mapping of novel symbols to quantities. Adult participants were trained to make associations between dot-quantities and novel symbols and they had to infer the overall relative order of these novel symbolic items. Individuals who demonstrated relatively higher working memory capacity(HWMs) learned ordinal information concerning the symbols and this was not so for those with lower working memory capacity(LWMs). In the second experiment, WM was considered in terms of whether it related to the performances of participants given explicit instructions to make numerical order judgements relating to particularly enculturated numerical symbols. The participants were required to indicate whether sets of three Arabic numerals were in increasing order or not. Specifically the sets were termed ‘sequential’ when they contained items that were ordered as in the integer count sequence, such as 3-4-5, balanced’ or ‘non-sequential’ for sets comprising items such as 1-3-5 or ‘skewed’ for items such as 4-8-9. All of the participants gave relatively faster responses for sequential sets when they were in order in contrast to when this was not the case. Only HWMs responded relatively faster when balanced/non-sequential patterned sets were in order so it was suggested that they were accessing ordinal associations that were not accessible for the individuals with LWMs. Overall, it was considered that the findings suggested a critical role for WM in the processing of order information in relation to numerical symbols. Those with higher capacity concerning working memory tended to go beyond the quantity representation associated with numerical symbols and to concentrate on their relative numerical order.

Furthermore, an fMRI study by Fehr et al.(2010) involving a prodigious adult male mental calculator is of interest here. When he was engaged with extremely difficult exponentiation tasks, patterns of activation were indicated in areas of the brain adjacent to those regions where activity was shown for tasks requiring moderate calculations when performed by himself as well as the typical control participants. These brain regions included the left precuneus, lingual and fusiform gyrus as well as the right cerebellum. It was concluded that exceptional performance in arithmetical calculations might result from changes in the brain associated with extensive daily practice over many years in combination with excellent abilities concerning working memory.

Additionally, Booth & Siegler(2008) found that for children aged around 7 years, the linearity of their number line estimates showed a positive correlation with their existing knowledge concerning addition. Also, their pretest numerical magnitude representations were found to be predictive of their learning of solutions to unfamiliar addition exercises. This aspect concerning the learning of novel addition problems was apparent after controlling for previous arithmetical knowledge, short-term memory for numbers and scores relating to achievement in mathematics. Also, young participants who were exposed to accurate visual representations relating to the magnitudes of addends and sums increased their learning of the solutions to the novel addition exercises above the level achieved via the simple presentation of problems and answers. Hence, numerical magnitude representations were considered to have a correlational and causal relationship with arithmetical learning.

Also, in an investigation using fMRI Cantlon et al.(2009b) studied children aged 6-7 years and adults while they performed tasks comprising numerical comparisons involving nonsymbolic and symbolic items, dot arrays and Arabic numerals

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respectively, which were presented visually. The participants were required to choose the larger item for each of the dot array pairs of stimuli and the Arabic numeral pairs of items. The children and adults engaged a common cortical network which consisted of the occipito-temporal, parietal and precentral regions for judgements of comparisons concerning both the dot arrays and the Arabic numerals. In contrast to the adults, the children engaged the inferior frontal gyrus to a much greater extent during both types of numerical activities. The authors suggested that in relation to the findings of several studies it was indicated that the inferior frontal cortex was engaged more by children than adults in the coordination and direction of information concerning abstract task goals.

Furthermore, these researchers refer to another study by Libertus et al.(2009) involving infants aged 7 months. They were presented with dot stimuli associated with familiar and novel numerosities and electroencephalogram recordings were made of their brain activity. The findings offered convergent evidence for the detection of numerical novelty in these infants. Both the alpha-band and theta-band oscillations differed for the familiar as well as the novel numerosity presentations. The spectral power in the alpha-band over midline and right posterior scalp areas was shown to be modulated by the ratio between the familiar and novel numerosities. Hence, it was indicated in these infants that numerical discrimination was ratio dependent and followed Weber’s Law. Support was given for the use of an analogue magnitude system for approximate numerosity representation by these infants and indicated in older children as well as adults and nonhuman animals. Also, the findings were supportive of the notion that frontal and parietal cortical networks were involved with ratio-dependent number discrimination during the first year of infancy and in line with neuroimaging results concerning children in older age groups and adult individuals.

Additionally, Holloway & Ansari(in press) investigated the development of brain areas in relation to representations of numerical magnitude independent of format. In their study, children aged around 7-9 years and relatively young adults were engaged in numerical comparison tasks with symbolic, that is, Hindu-Arabic numerals and nonsymbolc items, namely, arrays of squares. Also, there were two control tasks and during their involvement with all of the activities the participants had their brains scanned with the use of fMRI. The conjunction was calculated between symbolic and nonsymbolic numerical comparison and then, regions of the brain were considered in which this conjunction was different for the children and adults. A large network was indicated which involved visual and parietal areas with greater activation for the adult participants relative to the children. An examination of age-related differences in the conjunction of symbolic and nonsymbolic comparison, after subtraction of the contribution from the control tasks revealed a more restricted group of brain regions including the right inferior parietal lobe near the intraparietal sulcus(IPS). In addition to displaying an increase in activation in relation to symbolic and nonsymbolic magnitudes, after accounting for activation associated with response selection, age-related differences in the distance effect were indicated in this area.

The authors presented a detailed discussion involving various controversial issues including the extent to which numerical representation was lateralised. Reference was made to a number of studies and some aspects highlighted particularly concerning the investigation by Cantlon et al.(2009) noted above. Also, some consideration was given to research with adults by Cappelletti et al.(2010) in which the importance was

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emphasised of controlling for the effects of task and response time when investigating particularly, effects that were specific to number. Additionally, Holloway & Ansari(in press) highlighted the significance of using appropriate control tasks in conducting developmental neuroimaging studies.

Furthermore, in a study by Cohen Kadosh et al.(2010) transcranial magmetic stimulation was combined with an adaptation paradigm to investigate whether in the adult human intraparietal sulcus(IPS) there were number-sensitive neurons that coded numbers in a mode that was format-independent or format-dependent. Also, the researchers considered whether in the adult human IPS there were neurons which showed more preference for a particular numerical quantity but not the associated number word. The stimuli which were Hindu-Arabic numerals and verbal numerals were presented visually on a monitor. The results indicated that for stimulation of the right parietal lobe, there was a dissociation between digits and number words in the right IPS. In relation to the left parietal lobe, a double dissociation was apparent for the different formats in the left IPS. The findings were presented as a demonstration that in both parietal lobes, there were notation-dependent neurons capable of encoding quantity.

Also, in another fMRI investigation by Holloway et al.(2010) adult humans were involved in a task which required them to compare the relative numerical magnitude of symbolic, specifically, Hindu-Arabic numerals and nonsymbolic items, that is, arrays of squares which were the stimuli used in the study described above by Holloway & Ansari(in press). The initial conjunction analysis indicated significant activation in the right inferior parietal lobule for the symbolic and nonsymbolic numerical magnitude judgements. Both the left angular and superior temporal gyri showed greater activation for the symbolic in contrast to the nonsymbolic numerical magnitude judgements. Several areas including the right posterior superior parietal lobe displayed more activation in relation to the nonsymbolic compared to the symbolic judgements of numerical magnitude. Hence, it was considered that the processing of numerical stimuli in formats that were general or specific had been identified in the adult human brain.

In the investigation described earlier in the current discussion by Belmonte et al.(2010), reference was made to a study by Belmonte & Yurgelun-Todd(2003). It concerned adult participants with ASD as well as typically developed controls and they were involved with fMRI while they performed a bilateral visual spatial attention task. It was suggested that for those with ASD, distractor suppression might evoke atypically heightened activation in posterior intraparietal sulcus.

In numerical, arithmetical and other areas of mathematical processing it is essential to be able to ignore irrelevant information as quickly as possible and to direct attention to the relevant aspects of the task so that they can be integrated in the creation of a solution. As noted, the activities which I used in the specific approach highlighted here involved the fast processing of dots and facial features associated with small numerosities as well as the formation of human characteristics and parts of the body via the manipulation of cardboard components and the drawing of human figures. Overall, the aim was to help the promotion of cognitive development in the young participants with ASD through the coordination of ideas and to facilitate mental functioning at a higher level and in relation to themselves and others.

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In a discussion concerning the mind, the brain and consciousness by Mittelstrass(2008) the difference is highlighted between the construction of scientific knowledge about oneself and the construction of understanding concerning the self by the individual. Also the contribution of the latter construction is emphasised in relation to the meaning of consciousness. Individuals with sufficient ability on the autism spectrum may be able to construct scientific knowledge about themselves but understanding themselves is more problematic. The ultimate aim of the approach presented by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) was to make a contribution to self-understanding and self-unification with the associated concern to promote the development of human relationships. Often because of poor social and communication skills and an unusual presentation young people with ASD may experience social isolation, discrimination or bullying.

4.6 Social Competence, Self-Perception, Positive Disposition, Mathematical Abilities and ASD

As highlighted by Harris & Fiske(2006) the stereotype content model(SCM) predicts variation in prejudice with only extreme out-groups being stereotypically both hostile and incompetent, that is low on the warmth and competence dimensions. As indicated above and in other studies the medial prefrontal cortex(mPFC) is significant in relation to social cognition. In the investigation by Harris & Fiske(2006) mPFC activation was shown in connection with all social groups except extreme, that is low-low out-groups who activated particularly the insula and amygdala. This pattern is compatible with disgust which is the predictable emotion in relation to the SCM. Although objects were assigned the same emotions, activation of the mPFC was not apparent. Hence, neural evidence was given in support of the prediction that extreme out-groups might be perceived as less than human or dehumanized.

Individuals with ASD tend to be seen as low in warmth and low in social competence. They may be competent and very highly so in some areas but their cognitive profiles are likely to be uneven. Hence, it seemed poignant specifically to develop ways of helping individuals with ASD to function in a more unified mode in order to prevent prejudice. Those with ASD have been considered often as somewhat unusual in their presentation as they tend to centre on themselves and to lack the intuitive ability necessary for responding quickly and appropriately in social situations. The exceptional abilities of some individuals such as savants on the autism spectrum tend to be seen in the context of their perceived disabilities and contrasted with them.

As highlighted in a review by Fenske & Raymond(2006) the results from a number of studies suggest a negative affective impact for attention in relation to relatively neutral visual stimuli such as abstract patterns or unfamiliar faces where the requirement is for them to be ignored or inhibited during the performance of an activity. Some individuals such as those on the autism spectrum might not attend to specific stimuli such as the faces of unfamiliar people. Hence, it is possible that those with ASD might associate negative emotions with some people and consequently, they might experience further problems socially in addition to their intrinsic difficulties. Generally there might be a tendency for people to be perceived negatively and this might influence further expectations and interactions including negative

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affective responses from others. Hence, a cycle of negative interactions might evolve between those with and without ASD.In relation to specific abstract patterns, some individuals with ASD might find them particularly meaningful and consequently associated with positive emotional experiences. In his discussion concerning mathematical thinking Byers(2007) considers how the production or recognition of patterns appears to be fundamental to intelligence, meaning mathematical ideas. Mathematics is referred to as ‘intelligence in action’. From this perspective an emphasis is placed on mathematical comprehension in relation to individuals understanding themselves and their environment.

Additionally, Lakoff & Núñez(2000), Núñez & Lakoff(2005) and Núñez(2008) emphasise how mathematics is a natural component of humans in their discussions of the embodied mind and mathematics. The importance of the fingers and the hands has been given some consideration by Lawson(2008b, 2010) and reference has been made to Carlson et al.(2007). Their discussion highlights the significance of the hands not only for their representational role concerning the attentional and declarative aspects relating to cognitive activities but in terms of their supportive role within a dynamic context concerning the procedural aspects associated with these activities. In particular, these researchers considered the use of hands in relation to elementary arithmetical items and emphasised the importance of investigating the embodiment of cognition. Additionally, the significance of gesture in relation to cognition and specifically in the context of mathematics has been discussed by Núñez(2008). Also within a mathematical context, conceptual metaphors have been given consideration with an emphasis on their dynamic and holistic aspects by Lakoff & Núñez(2000), Núñez & Lakoff(2005) and Núñez(2008).

Shepard(2001) highlights the significance of reflection and symmetry in scientific creativity and emphasises these aspects in relation to the development of a science concerning the mind. In an associated context, Dehaene(2007) discusses numerical cognition and notes specifically how the psychology of arithmetic leads to a reconsideration of the laws relating to cognitive psychology. It is noted how human mental activity produces mathematics that assists in the formulation of its laws.

Additionally, Sfard(2008) highlights mathematics from the perspective of it being considered an autopoietic system, that is, one which is self-producing. In such a system, the components interact with each other in productive processes to maintain these same components and the relationships between them. For detailed discussions concerning autopoietic systems reference could be made to Maturana & Varela(1980, 1998) and Mingers(1995). In relation to this aspect, some of those with ASD might experience a particular inclination towards mathematics. Autopoiesis, which is a distinctive feature and consequential in relation to autonomy and self-reference concerns a process of self-creation. The term ‘structural coupling’ relates to the notion of adaptation, except that the adaptive changes that occur are not determined by the environment. Their occurrence ensures maintenance of autopoiesis and the lack of it results in the disintegration of the system. The self-generated, self-styled functioning of those on the autism spectrum is reflective of adaptations within themselves that have formed in order for them to experience a meaningful world and to maintain and promote further self-development. It is apparent for individuals with ASD that considerable effort is required for the maintenance of themselves and for some, the

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self which is at least not completely integrated becomes more segmented or fragmented and in certain cases, eventually reaches a state of complete disintegration.In order to achieve success with anything at a high level it is necessary to centre the mind intensively on the issue under consideration. Individuals on the autism spectrum appear to have a particular facility in this respect and for those who are particularly able in a specific sphere this can be markedly advantageous. The effort required may be extremely intensive to the extent that the person becomes somewhat detached from him/herself such that self-centred functioning becomes increasingly selfless. Then, as noted earlier in relation to the solution of mathematical problems there is a positive release of emotion which contributes to self-unification. Alongside these aspects is the experience of certainty developing from uncertainty and the essence of love. Hence, the functioning of an individual which may seem egoistic and sometimes, extremely so may be perceived within a more altruistic context in terms of outward manifestations being of notable value to others and recognised as such by the person concerned as well as the possibility of further developments.

In ‘No Man is an Island’, with reference to a recent edition, namely Merton(2005), Thomas Merton discusses the aesthetic experience in relation to the creation or contemplation of artistic works. He considers how art in its various forms makes it possible for us to find and lose ourselves simultaneously. The mind’s response to the intellectual and spiritual aspects found within various artistic spheres such as poetry, painting or music results in the discovery of new and spiritually uplifting experiences. Additionally, in relation to the discussion here, the suggested high level of aesthetic fulfilment in the arts is experienced in the creation of mathematical ideas and gives a particular poignancy to experiencing the self in a specific context and at an exalted level. When considering individuals of a certain disposition including some with ASD, mathematics offers a specialised medium in relation to self-understanding. Also, losing themselves in terms of not focusing on themselves facilitates directly their ability to give out and relate to others, that is to promote selflessness and therefore to develop and perceive themselves more comprehensively and realistically.

Hence, for those with sufficient ability in mathematics, the latter might offer an enhanced and specific facility as well as contribute to a particular stance concerning the apprehension of the world and its inhabitants. Consequently, for some individuals with ASD this might be an avenue to pursue in relation to promoting their development in this respect. Also, even for those who are not so able in this field some facilitation from an approach involving a specific mathematical aspect as described, for example, by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) might assist their development. Additionally, in a study by Warneken & Tomasello(2008) with participants aged 20 months it was demonstrated that altruistic tendencies appeared to be motivated intrinsically. This finding at a young age would seem to be supportive of the idea highlighted here concerning the promotion of interconnections in areas where there is an apparent intrinsic motivation or this can be created or enhanced via the facilitation of associations within a holistic context.

In the approach discussed in detail by Lawson(2008b, 2010) an emphasis was placed on merging sensual experiences to promote learning, especially in relation to the multiplication tables. In the other studies by the present author just mentioned above, symbolic experiences have been brought together with the aim not only of promoting harmony within and across the specific areas concerned but elsewhere within a social

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context. The summation of all knowledge in a symmetric and synoptic mode in relation to a central notion is fundamental to ‘The Glass Bead Game’, with reference to the recent edition, that is, Hesse(2000). The interrelationships between different spheres of knowledge as emphasised in the ‘Game’ are essential to my approach discussed here and promoted for further consideration. For those on the autism spectrum, a primary aim concerning ways of enhancing their development is to facilitate harmonious unity within the individual. Something akin to the fundamental idea in the ‘Game’ is the underlying notion associated with the approach discussed here by the present author.

In the review by Reber et al.(2004) it is noted how perceivers seem to experience more aesthetic pleasure with an increase in processing fluency of items. Specific variables that have been considered to affect aesthetic judgements including figural goodness, figure-ground contrast, stimulus repetition, symmetry and prototypicality are discussed in relation to processing fluency. Also, in a recent study by Reber et al.(2008) adult participants were involved in an arithmetical verification task comprising addition equations with dot patterns which varied in terms of their symmetrical presentation and they were correct or incorrect. The results were considered indicative of the use of heuristics in intuitive mathematical judgements and suggestive of symmetry being used as a cue for correctness. It is highlighted how beauty is correlated with processing fluency and ideas are discussed in relation to beauty and truth which have been given consideration and noted in the presentation here concerning discovery in mathematics.

Baron-Cohen(2008) using a definition of ‘truth’ as being lawful patterns in data suggests that individuals on the autism spectrum are motivated particularly to find the ‘truth’. In relation to the discussion here and some specific aspects just noted, they may be stimulated by beauty in line with others. However, for certain individuals of higher ability including some of those with ASD, their drive may be enhanced specifically in association with particular disciplines including mathematics, science, art and/or music. One noteworthy individual who would seem to reflect these characteristics is Paul Dirac whose biography has been presented recently by Farmelo(2009). In quantum mechanics he was a pioneer and he became one of the youngest theoreticians to be awarded the Nobel Prize for Physics. He was highly motivated in his search for truth and crucially related to his research style was visualisation and the notion of mathematical beauty. Challenging aspects of his disposition included extreme reticence and literal-mindedness as well as marked difficulties concerning communication and empathy. For those who are less able, they may find aesthetic pleasure at a different level in a variety of fields.

Dudley(2008) edits a collection of pieces including the work of Altshiller Court(1958) in which it is highlighted how the transmission of accumulated experience from one generation to the next is manifested particularly in mathematics. The cumulative process in relation to mathematics is associated with the notion of progress and aspects of clarity and distinctiveness. Mathematics offers intellectual beauty and promotes the desire to search for beauty in life and the creation of a more beautiful existence.

As perceptual fluency is related to positive affect, an inherent appeal would seem to be offered by involvement in tasks which those with ASD may see as media for

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experiencing these aspects. As uncertainty is replaced by certainty, anxiety is released and a state of equilibrium resulting in calmness felt by the individual. The idea fundamental to the ‘Glass Bead Game’ would seem to present an excellent opportunity for the experience of a high level of perceptual fluency. Hence, any approach that aims to facilitate such an aspect and associated phenomena is crucial in promoting holistic development within the individual and offers a specific avenue to enhance progress in those with particular presentations such as ASD.

In a review of the notion of ‘mindfulness’ Brown et al.(2007) consider a definition of the term as attention which is receptive to present events and experience as well as an awareness of them. This was noted with reference to an earlier article by Brown & Ryan(2003) and in this discussion it is noted that within traditional spiritual beliefs when the effects of mindfulness are considered there is an emphasis on mental composure and a settled state of mind. Additionally, Brown et al.(2007) highlight the contribution by Ryan & Brown(2003) who suggest that an individual whose functioning is integrated and mindful tends not to pursue self esteem but to search for action which is perceived as right.

In a review by Koole(2009) emotion regulation is considered as the group of processes by which individuals manage emotional states. It is emphasised with reference to Feldman Barrett et al.(2001) and Brown et al.(2007) that empirical findings are suggestive of individuals with competencies which are relatively strong in relation to emotion-regulation being characterised more by self-reflexivity and a deeper awareness of their emotions.

For those with ASD, often there is a tendency as indicated above for individuals of such a disposition to hold events in the mind from the past, particularly when they feel an occurrence has been managed in such a way that is perceived by them as being inappropriate or unjust and this is heightened when the situation involves them directly. Their self-esteem tends to be affected severely and they are in heightened states of arousal which do not facilitate self-reflexivity. Some people with ASD are sensitive especially to ideas concerning what is considered to be socially or morally correct. Unfortunately, there may be the development of an inappropriate and extreme association with the self. Hence, it is necessary to encourage them to be become more integrated and mindful by promoting some aspects that appear to be strengths particularly in certain individuals. In contrast, it is necessary to facilitate a decrease in the characteristics which have a negative impact and present as a source of difficulty. It would be expected that as they developed the ability to reflect more on themselves and greater emotional awareness then they would be able to regulate their emotions more easily. Hence, they should become increasingly at peace with themselves and others.

In a philosophical account relating to certainty and the foundations of mathematics, Giaquinto(2002) refers to a confession by Bertrand Russell indicating that he wanted certainty in a similar mode to how people wanted religious faith. Individuals with ASD could be considered as requiring certainty in this style. Also, Giaquinto(2002) indicates how we are not able to be certain of the reliability of all classical mathematics but we can be certain of a significant part and have confidence in the reliability of it all. For some of those with ASD, they may experience certainty to some extent and confidence in mathematical activities. These positive experiences

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may have an impact elsewhere in their lives and hence promote their development in various respects. Additionally, as noted by Giaquinto(2002), there are various mathematical approaches concerned with the refinement and abstraction from what are originally intuitions. Also, he emphasises the non-systematic nature of mathematical discovery which has been highlighted in the present discussion. Furthermore, the diversity of mathematical thinking has been discussed in detail by Giaquinto(2007) in his epistemological study of visual thinking concerning mathematics. Any dichotomies between mathematical thinking that might be termed algebraic in contrast to geometric, or symbolic as opposed to spatial are noted with caution. A preference is indicated for the consideration of a spectrum in relation to various styles of thinking in mathematics.

Additionally, as highlighted recently by Cattaneo et al.(2009) in relation to various research findings, it has been suggested that numbers and visual space have a shared underlying mental representation with the association being acquired within an active and cultural context. In an investigation by Salillas et al.(2009) single-pulse transcranial magnetic stimulation(TMS was directed at the ventral intraparietal sulcus(VIPS) to assess the performance in adults concerning tasks involving motion detection and numerical comparison. The reaction times and thresholds of the participants in relation to the perception of laterally presented coherent motion in random dot kinematograms showed a significant increase in association with stimulation of the contralateral VIPS as opposed to the interhemispheric sulcus and to the ipsilateral VIPS. In the numerical comparison activities, participants were required to compare the magnitude indicated symbolically by the laterally presented numerals 1-9 and the numeral 5. A significant increase was shown in the reaction times with the TMS application to the contralateral VIPS in contrast to the control areas. Hence, it was suggested in relation to VIPS involvement that motion and numerical comparison processes shared an association at a neural level.

Furthermore, Arzy et al.(2009) consider that when humans imagine time and their own life events as well as those of others, not only is there retrieval of events that have occurred and prediction of when they will occur but also, there is in a sense an automatic projection of themselves and different events on an imagined mental time line. They suggest in relation to their findings that the processing of these events relies logarithmically on the temporal-distance between them and the actual self-location or imagined self-location in time of the person who is experiencing the events. The researchers argue that the shared logarithmic effects concerning the mental representation of time and number are indicative of spatial mappings fundamental to cognition.

Additionally, in relation to the origins of mathematical intuitions with particular reference to arithmetic, Dehaene(2009) notes how cross-cultural investigations have indicated that approximate number is an intuition available to humans irrespective of language and education. A sense of number allows a fast evaluation of how many objects approximately are in a scene, whether this is more or less than another number and any changes in this number resulting from simple operations of addition and subtraction. In relation to this number sense three criteria are considered in the context of a definition for the term intuition, specifically that it is rapid, automatic and not accessible to introspection. A detailed discussion concerns various issues which have been highlighted in the current presentation including the importance of specific brain

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regions in relation to numerical and associated aspects as well as developmental and educational considerations.Also, in a recent discussion concerning philosophical perspectives in relation to mathematics within a human and cultural context by Ernest(2009), the tacit dimension of mathematical knowledge is highlighted in addition to the algorithmic aspects. It is noted that as well as abstract representational knowledge, mathematics concerns a wide range of human activities and knowledge-based practices. Some individuals with ASD may progress well in mathematics and for a select few, to an exceptional degree in certain mathematical specialities. However, it is likely that this success is more concerned with the ability to perceive the issue under consideration in an apparently unusual way rather than being related to a high analytical or systemizing ability which makes its own particular contribution. Hence, it is essential that those with ASD are able to consider themselves in a positive way and that others can appreciate the possibility of different modes of thinking in individuals of such a disposition. The ability to acknowledge and value a variety of perspectives is necessary in association with mathematics as well as in relation to other disciplines and aspects of life.

Attempts have been made to help facilitate the understanding of those with ASD and to create interventions with the aim of enhancing their progression throughout the lifespan. Alongside these positive moves the author would prefer the term ‘disorder’ to be eliminated from the classification of ASD with consideration being given to the alternative term ‘disposition’ as this highlights a particular style of functioning and does not centre on negative aspects. This view, in terms of overcoming difficulties and promoting positive aspects of ASD has been advocated well in the recent book by Daniel Tammet(2009). He indicates that he has been described as an individual with Asperger syndrome and a ‘prodigious savant’ which refers to someone with exceptional abilities irrespective of any developmental issues.

5. Conclusion

Specific approaches which might facilitate the promotion of abilities in some areas might be used to enhance development in other spheres. The approach which I used involving human figure drawings, facial features, small numerosities, arithmetic and other aspects of mathematics was aimed at facilitating the perception of people and numbers within a holistic context by emphasising the significance of particular and relevant details and their interconnections. As noted by Matthews(1999) the drawing process is part of the child’s complex repertoire for expression and representation. Communications are involved with associated emotions and intentions relating to real and imaginable entities. Additionally, Callaghan(2008) emphasises how symbols are intentionally communicative. Also, aspects that are fundamental to the development of pictorial symbols are applicable to other symbolic systems. For a recent discussion concerning the development of representational and expressive drawing and their relationship, reference could be made to Jolley(2010). He highlights how often, drawing is considered a solitary activity. Also, the present author notes that this is true of mathematics. However, linking the two activities as I have encouraged via the approach presented here and promoting these activities, sometimes quite specifically in associated contexts within and outside of an educational environment in group situations as well as individually might help to facilitate social and emotional development.

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As discussed by Zeki(1999), the function of vision may be considered as a search for constancies in order to acquire knowledge concerning the world. From this perspective, the brain has the task of extracting essential and permanent aspects in the visual world and discarding redundant and changing information. Similarly, the function of art may be considered as an active process with the artist being selective in relation to constant, essential and enduring attributes and discarding unwanted information. Then, the specifically acquired knowledge is available for generalisation in association with various items and situations. Grasping the essence of an idea tends to evoke a positive emotional response within the individual and this has been highlighted here particularly in the context of mathematics and art.

As highlighted by Goldstone et al.(2008), one of the most significant applications of theories associated with grounded cognition relates to science and mathematics education. Here, primarily the goal is to develop knowledge and skills that are easily transferable to novel situations. They consider knowledge as not only in the extracted verbal or formal description but concerning the perceptual interpretations and motoric interactions involved with a concrete scenario. While embodied experiences were considered to ground learning, there still remained the possibility and power of transference across contexts. Principles might be learnt in a grounded fashion that enabled their recognition in many concrete forms. It was considered that interpretations dependent on perspectives were capable of promoting transfer, where formalised strategies had been unsuccessful, by the education of flexible similarity within the individual. In this approach, transference occurred not via the application of a rule from a domain to a new one but by allowing the embodiment of the same principle to be seen in two scenarios. This notion is fundamental to the ideas developed by myself and the ensuing applications.

Certain aspects considered in the approaches used with children in earlier studies contributed to the more comprehensive approach used with the children and adolescents in the following studies and discussed here. Expressive and representational abilities might be promoted in various areas as well as the possible facilitation or enhancement of hypothetical thought, intuition and representation of mental representations. The results presented in the investigations by Lawson(2003, 2004, 2005a, b, 2008a, c, 2009) and considered here suggest that at least to some extent, positive changes in these abilities have occurred in relation to particular young people. As emphasised by Bronk(2009) in his discussion concerning romanticism and economics, imagination as well as reason are highly valued human attributes and a close association is required in relation to their functioning. Also, as noted by Glimcher(2009) in his discussion concerning neuroscience, psychology and economic behaviour, the developing field of neuroeconomics, when there is a difference between economic and psychological utility, the psychological utilities that guide choice appear to be reflected in the neural architecture.

It has been indicated here, that certain individuals on the autism spectrum may have very strong reasoning abilities within specific contexts but their tendency to lack wisdom manifests itself clearly in social situations. Hence, some of those with ASD may be the recipients of markedly positive and negative reactions from other people. In relation to my own work, an intention has been to facilitate the development and more judicious application of knowledge within an interpersonal context for those experiencing social and communication difficulties. Overall, I have tried to develop

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approaches from a specific perspective involving innovative and creative ideas as highlighted in being crucial to research in order to enhance progress concerning the autism spectrum by Rutter(2005).

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