Precursors of early mathematics and early intervention programs

International Seminar on Mathematical Learning Difficulties

Maria Chiara Passolunghi

Helsinki, Finland6-9 November

Department of Life SciencesPsychology Unit “Gaetano Kanizsa”

University of TriesteItaly

OVERVIEW

� Possible core deficts in children with MLD

� Relation between MLD and Working Memory

� Precursors of mathematical learning

� Suggestions for early intervention programs

Question

Why children with good intelligence have mathematical

difficulties?

Important for

assessment

intervention

earli prevention

Understand the core deficitsCORE DEFICIT of MLD

MLD due on prevalence on deficits affecting working memory and executive functions (Bull & Sherif, 2001; Gathercole, Brown, & Pickering, 2003; Wilson & Swanson, 2001)

CORE DEFICITS ofMathematical Learning Disability (MLD)?

no general agreement

MLD relies essentially on deficits at number level and number module (Iuculano et al., 2008; Libertus et al., 2011; Rousselle & Noel, 2007)

Developmental Psychology Research with children with typical development and with MLD

(De Smedt et al., 2009; Friso-Van den Bos et al., 2013; Gathercole & Pickering, 2000; Geary et al., 2000; Passolunghi & Cornoldi, 2007; Passolunghi & Siegel, 2004)

Results in favor relationship WM-Math

Patient with preservedcalculation skills but severely impaired WM(Butterworth et al., 1996)

Digit Span: 3 cifreMental calculation: OK +, -

Temple and Sherwood (2002) Children with MLD vs controlNo differences in STM(digit span, Corsi forward)

Results NOT in favorrelationship WM-Math

Why this lack of agreement?

� Patients and adults vs children WM dysfunction (strategies)

� Lack of distinction of different aspects of WM

� Complexity of MLD(Mathematical Learning Disability)

Mathematical Learning Disability

MLD

Dyscalculia…

WIDE VARIETY of MLD

Rubinsten and Henik (2009) 3 Subtypes/Profile

� DD Developmental dyscalculia – very rare deficit intra-parietal sulcus Reduced gray matter volume in the IPS.

� MLD Mathematical Learning Disabilityheterogeneous disorderDeficit in WM, inhibitory processFRONTAL LOBES very important in learning and development

� Comorbidity

Developmental Dyscalculia (DD)

From Piazza et al., 2010

Appoximate Number System (ANS)

9 6

Numerical magnitude processing

Non-symbolic comparison

Symbolic comparison

ANS predicts success mathematic learning (Halberda et al., 2008; Libertus et al., 2011, 2012)

Low ANS in dyscalculic children (Piazza et al., 2010)

Enhancement of ANS improve the ability of arithmetic calculation(Park et al., 2014; Hyde et al., 2014)

� Fias W, Menon V e Szucz D. (2013), Multiple components …., Trends in Neuroscience and Education.

Multiple components and causes

Influence of Working Memoryon Math learning ?

� QUESTIONS

� There is a relation between WM and mathematical learning?

� Children with MLD have a deficit in WM?

� - What are the processes of WM impaired in children with MLD?

Influence of Working Memoryon Math learning

� What is WM ?

WM abilities

` WM = has been described as an active information process responsable for STORING and PROCESSINGinfomation for a short time

(Baddeley, 1986; Baddeley & Hitch, 1974)

Math learning

Working memory

• Main role of Central Executive

Modified from Baddeley, 2003

“active” working memory (WM)

“passive” short-term memory

(STM)

MLD

Matched

Age School level GenderReading comprehensionIQ

TD

sequ. CR tot. intr. 0

10

20 MLD

TD

Working Memory

Passolunghi, Cornoldi , & DeLiberto (1999) M&CPassolunghi & Siegel (2001,2004) JECPD’Amico & Passolunghi (2009) LID

MLD

9Lower recall of relevant information

9Higher recall of irrelevant information

Persistent deficit (even one/two years later)

9Difficulties in inhibitory mechanisms

of working memory

9Overload of memory system

INIBITION

This difficulty in basic memory processes affects more complex

tasks (high level)?

Recall the relevant information for the solution

PROBLEMThis summer, that was very hot, Mary helped her parents to clean the house and received 50 Euro as a reward. With this money she decided to buy a hat that costs 30.50 Euros. Mary, who is very greedy, with the money left, decided to buy some special cakes with almonds, which cost 1.50 Euro each. How many cakes will be able to buy Mary with the money left?

Recall the relevant information

PROBLEMThis summer, that was very hot, Mary helped her parents to clean the house and received 50 Euro as a reward. With this money she decided to buy a hat that costs 30.50 Euros. Mary, who is very greedy, with the money left, decided to buy some special cakes with almonds, which cost 1.50 Euro each. How many cakes will be able to buy Mary with the money left?

irrelevant

PROBLEMThis summer, that was very hot, Mary helped her parents to clean the house and received 50 Euro as a reward. With this money she decided to buy a hat that costs 30.50 Euros. Mary, who is very greedy, with the money left, decided to buy somespecial cakes with almonds, which cost 1.50 Euro each. How many cakes will be able to buy Mary with the money left?

MLD

9Lower recall of relevant information

9Higher recall of irrelevant information

We need to verify:

Are they able to distinguish the relevant information in a text of a problem?

Written problem

9To underline only the relevant information

9 to write "data" under the problem

this test showed

NO SIGNIFICANT DIFFERENCE

between MLD vs TD

The children with MLD were able to identify the DATA in the text problem,however,These children did not use these elements in order to built the representation of the problem

9This difficulty in basic memory processes spreads to more complex tasks (high level) such as

understanding and solving a text of a problem

9 This difficulty affects the way in which children control the information contained in the text of the

problem and then the mental model and the representation that they formed of the problem

Intervention

Passolunghi et al.Erickson Press

Precursors of early mathematics

� Working memory is a basic skill relevant in mathematical tasks

� Working memory is also a main precursor of mathematical abilities at the beginning of school education?

� Abilities hypothesized as possible precursors in the literature (IQ, phonology, counting, numerical competence, processing speed….)

Precursors of early mathematics

¾ ANS

- Approximate quantity comparison

- Non symbolic appoximate addition

¾ EARLY NUMERACY

- Counting

- One to one correspondence

- Symbolic number line

Domain specificabilities

¾ Processing Speed

¾ Intelligence

¾ Working memory

.....

Domain generalabilities

Precursors of early mathematics

Passolunghi et al., 2007 Cognitive Dev. First graders

Precursors of early mathematics

Passolunghi & Lanfranchi, 2012 Kindergarten to first grade

Precursors of early mathematics

Passolunghi et al., 2014 BJEP first graders

Early training on WM and numerical competences

� Development of training programs

�Working Memory

�Specific Abilities

Enhancement of:

- Counting- One to one correspondence- Quantity comparison- Number comprehension- ....

(Arnold, Fisher, Doctoroff, & Dobbs, 2002;Butterworth & Laurilliard, 2010; Greenes, Ginsburg, & Balfanz, 2004; Kroesbergenet al., 2012; Starkey, Klein, & Wakeley, 2004; Young-Loveridge, 2004).

Early numeracy training

Working memory trainingThe debate is still open:

• Some studies show positive effects of WM training (Holmes, et.al; 2009; Kuhn & Holling, 2014; Witt, 2011)

• Only a few studies have explored the possibility of

enhancing working memory abilities in kindergartners (Dowsett & Livesey, 2000; Kroesbergen, et al., 2012)

• Other authors questioned the effectiveness of WM(Melby-Lervåg & Hulme,2013)

AIMS• Comparisons of the effects of the two types of

training on early numerical abilities in mainstream preschool children

• Hypothesis:

1) WM training Æ improve not only working memory but will also produce a transfer effect on early numeracy

2) Early numeracy training Æ have a more specific and limited effect on early numeracy abilities

(Passolunghi & Costa, 2014 Child Neurops.)

Method• Preschool children (5-year-old)

• 15 children (7F): WM training • 15 children (6F): early numeracy training • 18 children (9F): control group

• 5 weeks, 2 times per week (1 hour)

• Both training were adaptive

• Implemented in small groups

MBT VERBAL MBT�VISUOSPATIAL WORKING�MEMORYEARLY�MATHEMATICAL�

ABILITIES

Word Span�forward

(Passolunghi&Siegel�2001)

pathway�recall(Lanfranchi et�al.,�

2004)�

verbal double task(Lanfranchi et al.,2004)

ENT�ͲEarly�Numeracy�Test�(Van�Luit,�Van�de�Rijt,�e�Pennings,�1994)

Doppio�compito�visuoͲspaziale(Lanfranchi�et�al.,�2004)

Pre- and Post -training Assessments

(Passolunghi & Costa, 2014 Child Neurops.)

Working MemoryTraining

• Activities that promote the storage and manipulation of information visuo-spatial or verbal

• Enhancement of all three components of the working memory(Baddeley, 1986)

ACTIVITIES ENHANCED ABILITIES

e.g. Line of Words STM verbal games

e.g. Farmers STM visuo-spatial games

e.g. Animals’ Home WM verbal games

e.g. Jellyfishes WM visuo-spatial games

WM training

• Required the temporary storage and manipulation of sequences of spoken verbal items

• Children were presented with lists of words and have to memorize the first word of a list

• When they heard the name of an animal, they together had to make its noise and had to keep in mind the first word of the list

Apple – sun- head- cow - hand

RECALL

ACTIVITIES ENHANCED ABILITIES

e.g. number doggerel Counting

e.g. Number Path Linear representation of numbers

e.g. Tombola Relationships between numbers and quantities

e.g. Cats and Mice Comparison of quantities

Early Numeracytraining

Number Rhyme

Results: WM Visuo-spatial

**

*

F=�10.46,�p <�.001,�Kp2 =�.32,

*

Results: WM Verbal

*

*

F =�7.62,�p =�.001,�Kp2 =�.25

*

*

*

*

Results: Early Numeracy

F =�17.96,�p <�.001,�Kp2 =�.45

* *

* *

NO SIGNIFICANT EFFECT of training on

ÆSTM verbal

ÆSTM visuospatial

Memory educational Lab

Early numeracy educational Lab

SUMMARY• Possibility to improve cognitive functioning, with

interventions designed to boost domain-general or domain-specific precursors

At early age

• WM training di MDL Æ improve not only working memory but will also produce a transfer effect on early numeracy

• Early numeracy Training Æ more specific and limited effect on early numeracy abilities

• early prevention of learning disabilities in preschool children – well-being

Thank you!�

passolu@units.it