MRES

Kenya Secondary School

students' Intelligence

Beliefs-A case study in

mathematics QR2

Herine Otieno-24040369

5/1/2015

Beliefs that students hold towards their intelligence have been shown to affect their orientation

towards learning. In situations considered challenging, those with incremental views have been

shown to exhibit adaptive motivational patterns whereas those with entity views have been shown

to exhibit maladaptive motivational patterns. This qualitative exploratory study focuses on the

extent of incremental and entity beliefs amongst a group of 26 Kenya secondary school students.

Analogical diagrams by students, written protocols and participant observations were used to

provide a contextualized perspective on predominant intelligence beliefs amongst the students as

postulated by Dweck's theory of intelligence. This research suggests that most of the students held

the theory that their intelligence for mathematics is innate and fixed.

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1.0: Introduction

Researchers and educators are increasingly paying attention on a students' learning behaviour in an effort to address concerns on students' learning and retention (Stump, Husman and Corby 2014). This interest is based on a number of factors including the understanding that students play a role in the learning process and empirical evidence from previous research that has consistently demonstrated that learning is belief driven.

In seeking to increase insight in the learning behaviour of students, there has been particular focus on examining the students' beliefs about the nature of knowledge and knowing and about the nature of their intelligence (Zhu, Valcke and Schellens 2008).

A key model in the study of students' beliefs about the nature of intelligence that has received a great deal of attention amongst researchers and educators is the Dweck's model of the implicit theories of intelligence.

Dweck contend through this model that most students hold one of two distinct conceptions of their intellectual ability; the belief that their intelligence is a fixed trait, or an entity they possess (uncontrollable trait) and the belief that their intelligence is malleable and can be incrementally increased through their own efforts to learn (Dweck 2008).

The main postulate of this model is that the implicit theories of intelligence determine the way students approach learning and achievement situations (Dupeyrat and Marine 2004); students who hold an incremental theory of intelligence tend to be oriented towards mastery approach to learning. They associate successful learning with effort and when they encounter failure, their self-efficacy, or confidence in their ability to learn and perform well in a course is not shaken (Bandura 1997). On the other hand, students holding entity beliefs are oriented towards performance approach to learning (Stump, Husman and Corby 2014; Dupeyrat and Marine 2004). They primarily focus on confirming or proving their ability relative to others, and tend to have high self-efficacy for learning and performance in a course when their studies are going well but often show debilitation when faced with a set back or difficulty(Stump, Husman and Corby 2014; Otieno 2015(b)).

Whilst this model is considered to have contributed valuable information to our understanding of students' success in their course work (Ahmavaara and Houston 2007; Otieno 2015; Dweck and Leggett 1988), the majority of the studies have emerged from a Western context and few more from the Asian context. To the best of my knowledge, there have been no studies on the nature of intelligence beliefs (especially in mathematics) amongst students from Africa continent.

The consideration of empirical evidence for nature intelligence beliefs held by students and relationship with various aspects of learning across different cultures is key since it can assist in identifying mono-cultural bias and help develop an improved understanding of different aspects of students' learning process (Zhu,Valcke and Schellens 2008; Braten and Stromso 2005). Further, such research provides opportunity to identify both uniformities and

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consistencies in learning and student beliefs, while at the same time identifying where there is systematic variation across cultural contexts (Pillay, Puride & Boulton-Lewis 2000; Purdie, Hattie and Douglas 1996).

This study seeks to extend the investigation of students' implicit theories of intelligence to the African context. Its main purpose is to explore which of the intelligence theories as proposed by Dweck's theory of implicit intelligence is predominant amongst a sample of 26 secondary school students from a secondary school in Kenya

To the best of my knowledge, this is the first kind of study focusing on the mathematics intelligence beliefs amongst Kenya secondary school students. As a pilot case study it therefore presents an initial step and possible foundation for future work in determining further generalizability of existing theoretical frameworks on students' intelligence beliefs (Hofer 2004; Braten and Stromso 2005).

1.1: The Kenyan Education Context

Kenya education culture can be considered to have dimensions of both the Confucian heritage cultures and the Western cultures: Similar to countries of the Confucian heritage cultures like china, respect for and obedience to authority are valued by Kenyan students. However unlike their Chinese students who consider effort and persistence as the key determinants of what a person achieves, Kenya culture like the western cultures stress personal abilities for achievement more than efforts (Zhu,Valcke and Schellens 2008;). In the context of mathematics education, this belief in personal ability is demonstrated in a recent policy change that saw an introduction of what has been dubbed alternative B mathematics curriculum which is considered to be a simpler version of mathematics (Kosgei 2015).

Generally, teacher -centred behaviourist teaching and learning is still the dominant in Kenyan institutions of learning and students are largely expected to remember or absorb existing knowledge. There is however a current push by the government to implement constructivist teaching and learning in the mathematics and science classrooms.

The Kenyan education system is very examination dominated and intensely competitive. The competition is basically hinged on the fact that government can only sponsor a limited number to some of the highly sought after professional courses like engineering, medicine and a select number of business courses. Further, given the high levels of poverty in most parts of the country, access to higher education is a considered by parents as a valuable means of economic opportunity and status.

2.0: Methodological framework:

The methodological framework for this research is that of an exploratory case study. As Dooely( 2002) notes, case study as a research method excels at bringing understanding of a complex issue and is particularly appropriate for testing or building theory. This is because case study as a methodology generally allows for holistic and in-depth investigation focusing on one or two issues that are fundamental to understanding the system being examined (Tellis

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1997). This case study draws on data from analogical diagrams drawn by the participants, written protocols by the participants during a mathematical exercise and observations made by me during a mathematics problem solving activity. The use of different sources of data is particularly valuable in ensuring triangulation of data. The need for triangulation arises from the ethical need to ensure construct validity of the study or what has also been referred in qualitative research as the confirmability of the study( Gibbert, Ruigrok and Wicki 2008; Riege 2005;).

Given the fact that case studies allow for multiple research methods, it is possible for a researcher to embrace different research paradigms at different stages depending on the research method that is being put in use. The strict use of different qualitative methods in this study underscores the fact that the intention of this study was to develop an interpretative understanding (Renganathan 2009) of the extent of incremental and entity beliefs amongst the participating students (Hofer 2004). This sets this study apart from a majority studies on implicit theories which have generally used the deductive approach largely using survey as their core method of research. In choosing the constructive approach, I seek to avoid noted shortcomings of survey approach including the tendency of some of the students to agree with statements in the questionnaires either because of social desirability or because they truly believe that they are using some of the strategies linked to either of the theories when in real learning situations they actually use different types of strategies (Dupeyrat and Marine 2004). Further the methods used in this approach, unlike the survey method do provide opportunity for dynamic, in-depth views of intelligence beliefs and their relations to other constructs (Braten and Stromso 2005)

The central focus of analysis is considered an important aspect of the design of every case study. This particular case study can be best understood as a single case design(Baxter and Jack 2008) in that the focus is the analysis is the extent of incremental and entity beliefs amongst secondary school students of a single community secondary school in Kenya. The choice of the single case study was informed in part by the understanding that previous research has shown that single-case studies are not only suitable for confirming or challenging a theory but are also ideal for revelatory cases where an observer may have access to a phenomenon that was previously inaccessible(Tellis 1997).

2.1: Participants and school context:

26 students participated in the study; 7 of the participants were form ones, 10 were form twos, 4 were from threes and 5 were form fours. The participants, 12 of whom were females were of mixed ability. The school from which the participants were drawn was private community based secondary school in Kenya that admitted students from a network of relating churches across the country. Most of the teachers that taught in this school were also drawn from the church network. As such the school functioned as a family with a strong focus on shaping a biblical value based philosophy amongst its members, key amongst them being entrenching collaboration instead of competition as a way of life. I am a member of the founding community and was a physics teacher in the school until 2014 when I left to pursue my PhD studies.

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2.2: Procedure:

The permission and support of the school director and principal to conduct the pilot study during a short visit back to Kenya. This was done first through writing, and later through a meeting where we discussed the objectives of the study. Prior to the study, I had a session of interaction with all the students at the school, to catch up with them and share with them some goodies that I had bought them on my way back. This session was attended by a number of the parents and it is during this session that I explained to them the intent of my pilot study. The study was scheduled to be carried out on the second day of their midterm break, in a church community hall which was more accessible due to its central location. Information about the study was passed on to the parents through the school. Participation in the study was voluntary and the participants were not required to write their names on any of their activity sheets. They were however required to indicate their gender and year of study.

On the day of the study, I took time to elaborate more on the objective of the study to the students who had turned up for the activity. I indicated to them that they were free to opt out of the study at any point, if they found it necessary to do so. Indeed some of them even after coming to the community hall opted to just hang around instead of participating in the activity. All the participants participated in the first activity-the drawing of the analogical diagrams. The participants were then assigned to different activities; some worked individually on a past exams mathematics question and externalised their thoughts during the process in writing and some worked in groups of three or more to discuss a set of problem based mathematical tasks(Jaquet and Grugnetti 2005) and audio recorded their discussions during the process. The groups were free to hand in their recorded work after the activity. The groups comprised of students from the same year of study.

The study lasted for three hours and was stopped at the first sign of fatigue even though by that time the students had not figured out the solutions for the problem based mathematical task. As a closing session, I built on the feedback given by the students on the lessons they had learnt from the activities seeking to orient them to more positive dispositions towards mathematics learning. I also took time to answer questions from the students especially on my studies abroad which was a subject of interest to many of them. I later gave a brief to the principal on some strategies the school could employ in helping the students to be better learners of mathematics. I did send my first draft of findings of this study to the principal and school director. I will be discussing the findings of the study and its implication with the students and parents in a visit to the school later in the year.

2.3: Designing the study protocol;

The first stage of this study entailed the development of the study protocol. This was in the form of a project approval form which was discussed with one of the course tutors. The course tutor, acted as a dependability (reliability) auditor; paying attention to the documentation of the process inquiry, examining to what extent the outlined process was theoretically driven and what mechanisms were in place to minimise researcher's bias during the study (Riege 2005; Tellis 1997). Another key consideration during this phase was the

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scope and boundaries of the research, this was particularly important in contributing to the external validity of the study, specifically in the aspect of analytical generalisation (Riege 2005).

2.4: Data collection:

2.4.1: Observations:

Having assigned different groups of students to different activities, I acted as a participant observer throughout the course of the activities. Participant observation is the process of establishing rapport within a community and learning to act in such a way as to blend into the community so that its members will act naturally then removing oneself from the setting or community to immerse oneself in the data to understand what is going on and be able to write about it (Kawulich 2005).

My blending with this group of students was not very difficult given that I was part of the bigger community that they were drawn from and had been their teacher before leaving for my studies. However their close association with me and their knowledge of my passion for mathematics and current state as a PhD student in an international university brought out the issue of power difference that could possibly interfere with their acting naturally. I sought to decentre power around me in relation to the participant by assigning them activities in groups(Vardeman-Winter 2014) and avoiding interview mode of data collection that could have tempted the participants to give me responses that they thought I wanted to hear (Tellis 1997). As such, while the general design of the research activities was motivated by a desire to investigate to what extent existing theories on epistemological beliefs and metacognition applied to the Kenyan context and would thus be taken as an etic approach, given the power difference, the data collection process was designed to be more 'bottom up' allowing the participants and data to speak to me as a researcher and for the themes, patterns and concepts to emerge (Renganathan 2009; Rabe 2003). Finally one key strategy that I employed during the data collection process to help reduce the effects of the power difference was adopting what has been described as an ethic of empathy and friendship; approaching the research as a witness to the participant's story rather than as a spectator in the process and recognizing the participants as holistic beings rather than object (Way, Zwier and Tracy 2015). Thus, even though the activities were solely participant led, I ensured that the interaction between the participants and I was characterized by a sense of honesty, fellowship, lack of manipulative intent, intensity and love (Johannessen 1971).

The environment created did indeed enhance my capacity to make observations that provided 'thick descriptions' (Geertz 1973; Ponterotto 2006) that may help convey both the participants' experiences and the interpretations that follow.

My observations centrally focused on the students' reaction and behaviour during the group discussions. I recorded the observations in writing as running field notes and later interpreted them in accordance to Dweck's model of implicit theories (Hofer 2004).

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2.4.2: Analogical/metaphoric diagrams and explanations:

Students were asked to make analogical/metaphorical drawings of what their conception of mathematics and learning mathematics was. The specific question to the students was; 'draw

a picture that best present what mathematics is and what learning mathematics is from your

experience of learning mathematics'. The interpretation of the question was left fairly open to minimise potential bias (Bagnoli 2009).

My choice of the drawing activity as the first activity of the study was based on the understanding that it's creative and fun nature would enable it to work well as openers and ice breakers for the research exercise. More importantly though, given the power difference between me and the students, I considered it an appropriate methodology since the creative dimension of drawings is known to encourage thinking in non-standard ways, making participants avoid, clichés and ready-made answers(Buckley and Waring 2013). Drawings are also known to encourage a holistic narration usually including aspects that participants may find sensitive and difficult to be related in words (Bagnoli 2009). In particular the evocative nature of diagrams can enable participants to represent concepts in a particularly condensed manner including the emotional dimension that in most cases is out of reach of text based research (Buckley and Waring 2013). Accordingly, diagrams are also considered a source of thick descriptions and are unique to the extent that generally they allow for data to emerge instead of forcing of data.

The use of analogical/metaphorical diagrams in particular is known to unleash and reveal deep meaning, multiple perspectives taking and fluidity of thought-in the processes allowing for visual representation of the otherwise invisible (Kendrick and McKay 2002;Wright 2007; Buckley and Waring 2013). This is because the process of drawing an analogical/metaphorical diagram is considered to be more reflexive and thoughtful than ordinary diagrams. This is particularly so because the underlying goal is usually to promote the understanding of abstract concepts in terms of well understood visuospatial phenomena of some kind. In other words objects employed are usually commonly encountered human-scale artefacts chosen for maximum familiarity and hence maximal explanatory power (Risch 2008).

The diagrams drawn by the students were interpreted using the Gentner structure of analogical modelling and comprehension. According to this model of analogy comprehension, the features that are preferentially selected for projection in analogical diagrams are those that express systematic relations among the relevant concepts in the source domain (Gentner 1983).

In interpreting the data I sought to identify the extent to which conceptual objects, object attributes and inter-object relations of the student diagrams and the accompanying text explanations were indicative of either the incremental or entity view as outlined in Dweck's model.

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2.4.3: Written protocol analysis

This was an adaptation of verbal protocol analysis, a qualitative research method that is frequently used in cognitive psychology and education (Branch 2000). As a research method, verbal protocol analysis is usually used to gain information about a participant's cognitive thoughts using verbal reports (Branch 2000; Nielsen, Clemmensen and Ysiing 2002). The verbal reports are classified into two: Concurrent verbal reports are done as one engages in the task and retrospective verbal reports made after the task is completed.

While there has been controversy on verbal reports relating to their accessibility, veridicality and completeness (Wilson and Clarke 2004), Ericsson and Simon (1984) contend that both methods have validity depending on the nature of the task.

For this study, I used a modified dimension of the retrospective and concurrent verbal reports; instead of audio taping their thoughts for analysis, the students were asked to write down their thoughts during or soon after the problem solving exercise. In this case their thoughts were not to be limited to those that were related to cognitive or metacognitive processes but were also include behavioural and affective aspects (Branch 2000).Two groups of students (form two and form three) that were randomly chosen from the group worked in two sets at different tables. The mathematics questions were word problems that had been picked from past national examination revision book. Though the questions could be considered challenging, they were within achievement levels of the participating students. To help orient the students to what was expected of them in externalizing their thoughts, the students were shown samples of metacognitive statements from earlier research that had been developed as cues for constructing a visual account of their thinking during a problem solving activity (Wilson and Clarke 2004). During the exercise, I did not interrupt the students unless specifically asked a question by any of the participant. The students were encouraged to write down their thoughts immediately after finishing the exercise or during the exercise-whichever they found comfortable.

Using Dweck's model, the detailed structure and content of the written thought for each student was analysed with a goal of identifying the nature of motivational patterns invoked during the exercise and the level of planning, reasoning displayed in the protocals .

3.0: Analysis and findings:

Data analysis is the process of examining, categorizing, and recombining the evidence from the gathered information to address the initial proposition of a study (Branch 2000; Tellis 1997). Given the fact that statistical analysis is not necessarily used in case studies, in analysing data collected during a case study, a researcher is usually expected to rely on experience and the literature to present the evidence in various ways, using various interpretations(Tellis 1997). In general the analysis of any case study is usually hinged on its theoretical foundation. In case the study is not founded on any theoretical position then the researcher is expected to develop a descriptive framework around which the case study can be organised.

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Either way, it has been proposed that every case study investigation should have a general analytic strategy; the possible techniques that have been proposed from earlier research include pattern-matching, explanation-building and time series. In this study, I employed largely pattern matching in the analysis of the data collected. After immersing myself in the literature around mathematical ability, epistemological beliefs and application of Dweck's model of implicit theories of intelligence in related research, I first went through the data; diagrams; written field notes and the written protocols, looking for evidence of attributes of either the incremental or entity beliefs as postulated by Dweck's theory of intelligence beliefs.

Generally given the implied connection between students' goal orientation and respective intelligence belief, attributes and systematic relations of diagrams; observations made during the group mathematical task and behavioural and affective dimensions of the students thoughts, externalized in their written protocals were analysed with a view of establishing which of the goal orientation they were indicative of.

My final methodological step was to consider issues of verification. One acceptable way of establishing credibility in a qualitative study is what has been referred to as 'member checking' which involves providing an early draft of findings with at least a small sample of the participants to discuss their perspective of the accuracy and fairness of the researchers' representation and veracity of interpretation of the data(Riege 2003: Hofer 2004 ). It was not practically possible to share my initial findings with the participants of the study. I however shared the findings via email with some of the lead teachers of the school. At the point of writing this paper I had not received feedback from them. Possibly it would be more appropriate if I had a verbal discussion with them on the findings of the study. I would argue that the verification of the data was done in part by the convergence of outcomes from the multiple sources of data used in the study(Dooley 2002; Baxter and Jack 2008 ) and peer reviewing when I made a presentation of the draft findings in a departmental seminar(Hofer 2004; Riege 2003 ).

3.1: Findings:

The analyses below are organized by goal orientation dimension (mastery and performance). The intent of the analysis was to establish the predominant intelligence belief amongst the participants. Diagrams and sections (words or phrases) of written explanations and written protocals that were deemed to be indicative of either of the entities are highlighted.

3.1.1: Focus on IQ and mind vs focus on strategy and effort:

According to Dweck's model on intelligence belief, those who hold entity beliefs, focus on supposed index intelligence like their IQ while those of incremental beliefs consider exertion of effort as a key means of becoming more intelligent (Otieno 2015).

One key feature of the diagrams drawn by the students was that they associated learning of mathematics with the brain, ideas and thus the head. In choosing to use diagrams of the head and brain as a representation of what learning mathematics was my inference was that they seem to suggest an innate dimension of intelligence. Further, the attributes of the head and

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the worried faces tend to resonate with observation by Stump Husman and Corby (2014) that when students believe their intellectual ability is innate, they worry about having enough of it.

3.1.2: Focus on ability/performance versus mastery of task.

As has already ben indicated, according to Dweck's model of intelligence theories, those with incremental beliefs tend to actively strive toward development and growth of competence while those with entity beliefs tend to focus on validating their ability or avoiding the demonstration of lack of it (Dweck and Grant). As such, those with entity beliefs emphasise outcomes (success or failure) during a task while their counterparts with incremental beliefs tend to focus on strategy and effort. The students' statements explaining the key meanings behind their diagrams tended to amplify the aspects of outcome than strategy and effort. Even when one of the student likened learning mathematics to playing chess, a game that is known to depend on strategy, the amplification was more on the winning or losing the game. The aspect of having it or not having it was further emphasised by the metaphorical use of diagram like a star or a double edge sword which in the context of the participants' cultural upbringing is associated with separating one from another. Accordingly, the two diagrams and the use of words like prestigious and sophisticated underscored the elitist view of

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mathematics as a subject by this set of students as is captured in the following statement by Povey (2010, p. 2) that…'the view that 'mathematics is difficult' helps to underpin the belief

that mathematics is an elite subject suitable for the most advantaged to study; it also helps to

maintain the role of mathematical success as a gatekeeper to privilege'

3.1.3: Motivational patterns exhibited during tasks.

The impact of intelligence beliefs on learning is seen chiefly when a high degree of challenge is present, when a task is personally important, or when the processing of complex material is necessary (Grant and Dweck 2005). In analysing the data from the diagrams and their accompanying e text explanations, both retrospective and concurrent written protocols and

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the written filed notes, it is clear that a majority of the students exhibited maladaptive motivational achievement behaviour when carrying out task that they considered challenging.

As seen in the sample of the data collected below, the words or attributes expressed in the students diagrams, were indicative of loss of self-worth captured in terms like 'I feel like a

dummy', negative affect like anger or feeling like crying, task avoidance behaviour like 'singing' and a low intrinsic motivation. These responses are indicative of entity beliefs for according to Dweck ( in Otieno 2015(b) p.12), 'a belief in fixed intelligence raises pupils

concerns about how clever they are, creates anxiety about challenges and makes failures into

a measure of intelligence that will result in defensive and helpless behaviour that worsens

performance….'

Debilitation was also observed amongst the form ones, two and threes when they engaged in the problem solving task which was considerably challenging to them. The room was full of grunts and moaning from most of the students as they attempted the questions. There were also verbal exclamations of how difficult the task was, a number of students complaining of headache and exclaiming that thinking was hard. The group work was interrupted many times by group members breaking into songs or arbitrary drumming of tables. Frustration was clearly manifest on the faces of most of the students, with some expressing open anger at the perceived difficulty in carrying out the task. The depth of the debilitation that occurred was best captured by feedback statements at the end of the task like…''

The findings from the data collected from the participants, through the diagrams and observations made during the activities, indicate that both gender predominantly held entity beliefs.

3.1.3.1: Diagrams:

note the change in the face attributes as the mathematics grow in complexity.

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3.1.3.2: Written protocol:

Concurrent: Easier task

Concurrent: More difficult task:

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Retrospective written protocol

However there was some evidence that at least two (one male and the other female) of the students seemed to be more oriented towards incremental beliefs. As seen in the written protocol below and feedback at the end of days the group open task, these students seem to extol; effort, planning and persistence in the undertaking of the tasks.

Retrospective written protocol leaning more towards mastery orientation

Feedback at the end of the problem solving group exercise:

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4.0: Discussion:

This study provides the first glimpse of Kenya secondary school students' mathematics intelligence beliefs using Dweck's theory of intelligence beliefs. Results from the study provide evidence that most of the students in the study may be holding inherent belief that their mathematics intelligence is innate and fixed. This orientation towards entity beliefs of intelligence could be attributed to amongst other things, the fact that the Kenyan education system is intensely competitive and tend to emphasize ability and performance (Stump, Husman and Corby 2014).

The emergent of the data on theories of intelligence from a study primarily designed to investigate the epistemological beliefs may add weight to Schommer-Aikins argument that the two set of beliefs are probably intimately tied to each other (Braten and Stromso 2005). The fact that the school's policy to do away with ranking at the end of the end term examinations, have not had a significant impact in reorienting the students' intelligence beliefs maybe a pointer to how impactful earlier orientations of intelligence theories may have in students but may also point out to the fact that reorientation would require more deliberate strategies than policy change. A potential area to exploit is a pedagogical shift; moving from teacher oriented to more student centred learning. Indeed the feedback from the students at the end of the group activities indicated the evolving nature of the students' intelligence beliefs with most students pointing to the fact that they had learnt that through collaboration they could actually be able to overcome the mathematical challenges.

A key strength of this study was that its interpretative nature provided for dynamic assessment for the students' implicit theories of intelligence thereby providing an opportunity for a deeper understanding of the beliefs and their relationship with other epistemological beliefs. Further, the dynamism of the methods used allowed for participant reflexivity (Yang 2015; Riach 2009).

It is must be noted though, that one of the methods used-that is the written protocols did not seem appropriate for the male students. Unlike their female counterparts who were open in writing down their thoughts during a mathematical exercise the male students seemed to shy away from revealing their thoughts possibly because they may have thought they would not be aligned to what they thought were deemed socially acceptable. The male's reluctance to share their inner thoughts and feelings may also be attributed to the predominant culture that orients the male child to be less emotionally expressive.

Another key limitation of the study is that it was based on small sample of students. To get a better grasp of the general orientation of intelligence beliefs amongst Kenya secondary school students', it would be desirable to study a larger number of students in different categories of secondary schools across the country.

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Future research should also focus on investigating the intelligence beliefs of mathematics teachers in Kenya and comparing it with the mathematics intelligence beliefs of students at the three stages of learning; primary secondary and university. Intervention studies, seeking to shape mathematics intelligence beliefs of students' should also be a key area of focus in the future.

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Appendix 1: Mathematical Questions and Problem solving tasks used during the study.

Set of activities for group tasks (Grugnetti and Jaquet 2005)

Activity one

Activity two

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Mathematics questions for the written protocol task (source: Kenya Secondary Certificate Examinations: Mathematics Revision Book)

Question solved by Form twos:

In January, Mambo donated a 1/6th of his salary to a children's home while Samba donated a 1/5th of his salary to the same children's home. Their total donation for January was 14820. In February, Mambo donated a 1/8th of his salary to the children's home while Simba donated 1/12 of his salary to the children's home. Their total donation for February was 8675. Calculate Mambo's monthly salary.

Questions solved by Form fours:

Question one:

Three business partners; Kioko, Njau and Osyako are to share 12,000/= in the ratio of 5:6:x respectively. If Kioko received 4000 determine the value of x.

Question two:

The coordinates of the points P and Q are (1, -2) and (4,10) respectively. A point T, divides the line PQ in the ratio 2:1. Determine the coordinates of T. Find the gradient of the line perpendicular to PQ hence determine the equation of the line perpendicular to PQ and passing through T.

Appendix 2: Information and Consent form to parents: Parental Permission for

Participation of a Child in a Research Study

Title of Study: Investigating Kenya Secondary school students' beliefs towards

mathematics.

Description of the research and your child’s participation

Your child is being asked to participate in a research study conducted by Herine Otieno-a PhD student in mathematics education at Sheffield Hallam University-UK. The purpose of this research is to provide preliminary information on some of the beliefs secondary schools in Kenya hold towards mathematics as a subject.

Your child’s participation will involve presenting their experience of learning mathematics in drawings and either working individually on some textbook kind of mathematics questions and recording their thoughts as they do so or working with other students in groups to solve open ended mathematics questions. The academic level of the students has been considered in

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the choice of the questions and activities. The activities will be held at the LRC hall on 30/2/2015 from 9a.m-12.00 noon.

Risks and discomforts

There are no known risks associated with this research.

Potential benefits.

At the end of the study, I will be discussing with the students possible areas and strategies that they can employ in improving their learning of mathematics. I will also be sharing with the school leadership and teachers the findings of the study with possible recommendations on how mathematics teaching and learning can be improved in the school. Finally, the findings of this research will be used in shaping my main research whose focus is developing a local framework for self-regulated learning of mathematics in Kenya.

Protection of confidentiality

This study is anonymous. We will not be collecting or retaining any information about your child’s identity. The records of this study will be kept strictly confidential. Research records will be kept in a locked file and all electronic information will be coded and secured using a password protected file. The audio recordings made during the group work will not be shared with anyone and will be appropriately erased at the end of the data analysis process.

Voluntary participation

• Participation in this research study is voluntary. You may refuse to allow your child to participate or withdraw your child from the study at any time. Your child has the right not to answer any single question, as well as to withdraw completely from the interview at any point during the process; additionally, you have the right to request that the interviewer not use any of the interview material. Your child will not be penalized in any way should you decide not to allow your child to participate or to withdraw your child from this study. There will be no payment for participating in this study.

Contact information

You have the right to ask questions about this research study and to have those questions answered by me before, during or after the research. If you have any further questions about the study, at any time feel free to contact me, Herine Otieno at Herine.Otieno@student.shu.uc.uk or by telephone at [ 0721534392(before or during the

study)or +44734889431(after study). If you like, a summary of the results of the study will be sent to you. If you have any other concerns about your rights as a research participant that have not been answered by me, you can report them my module tutor Spencer Steve at sslss@exchange.shu.ac.uk

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Consent

I have read this parental permission form and have been given the opportunity to ask

questions. I give my permission for my child to participate in this study.

Participant’s signature_______________________________ Date:_________________

Child’s Name:_______________________________________

A copy of this parental permission form should be given to you.