dr. daniel ansari's presentation (pdf)

Building blocks of mathematical competence: evidence from brain & behaviour

Daniel AnsariNumerical Cognition Laboratory

Department of Psychology & Brain and Mind InstituteUniversity of Western Ontario

Neuroplasticity & Education: Strengthening the Connection, Vancouver, October 23rd 2015

How important is numeracy?

• Low numeracy associated with unemployment, physical illness, depression & incarceration (Bynner & Parsons 2005)

• Improvements in mathematical competence are related to economic growth (OECD, 2010)

• Low$numeracy$costs$UK$Government$~$£2.4$Billion$per$year$(KPMG$Report)$

• Ability of patients & health professionals to use health-care information - Health Numeracy (Golbeck et al., 2005)

How important are early numerical skills?

School entry skills predicting later math

School entry skills predicting later reading

Implication: Spending time on

numeracy early may have benefits later not only for math but also reading achievement

So what should time be spent on?

Conceptualization of learning math

Arithmetic is not the starting point of math

learning

Foundational competencies

• What are the early foundations?

• What is scaffolding in early development?

Foundational competencies

• Analogy: phonological awareness

• Awareness that language decomposes into units of sounds

• Foundational competence

• Readiness skill

Foundational competencies

So what do we know about the foundational

competencies underlying math

Infants have a sense of quantity

Infants have a sense of quantity

8 vs 16

8 vs 12

X

e.g. Xu & Spelke (2000)

8 vs 16

8 vs 12

X

We share a sense of quantity with other

animals

Animal Number

Cantlon & Brannon (2005)

A brain system for numerosity

Libertus & Brannon (2009)

We are born with a sense of non-symbolic quantity that we share

with other species

Numerical Symbols Human invention

Making symbols meaningful

DEVELOPMENT

A growing body of research shows that children’s early

understanding of numerical symbols is a

critical scaffold

Informal Formal

Mediators

Building connections symbolic - non-symbolic

connections• Talk about number & numerical relations

• Engage students with symbolic and non-symbolic representations of number

• Counting, naming, comparing, ordering, matching

• Use of number lines to understand numerical relations

Using number symbols in the context of

play-based learning

How to assess foundational

competencies?

Number comparison• Correlations with math performance in

multiple studies across the globe

A simple 2 minute testNadia Nosworthy

Nosworthy et al. (2013, PLoS ONE)

SymbolicNon-symbolic 56 items/condition1 minute/condition

160, 1st-3rd graders

Also tested on: WJ Math fluency

WJ Calculation Skills

Does this 2-minute magnitude processing

test correlate with math achievement?

Correlation with Math Fluency

Nosworthy et al. (2013; PLoS ONE)

Symbolic counts!

• Both symbolic & non-symbolic correlate

• But:

• Only symbolic accounts for unique variance in arithmetic

• over and above working memory, intelligence and reading ability

• Processing of number symbols critical

• Deficits arise in connecting symbolic with intuitive system ?

Does performance on this test predict

performance over time?

Predictive measure?

• 268 children tested in senior kindergarten on paper and pencil test

• In collaboration with Toronto District School Board

• School board permitted access to Grade 1 grades

Predictive Measure?

Number Sense Measurement GeometryData

Management

Symbolic(Kindergarten) ✔ ✔ ✔ ✔

Non-symbolic(Kindergarten) ✔ ✔

✔ indicates significant correlation, p<.05

Unpublished Data

www.numeracyscreener.org

Useable tool

How does symbolic number processing in

the brain relate to math achievement?

?

Brain-Behaviour relationship

• 17 children

• 7-9 years

• Math & Reading skills

1 9

* 8 9

* 3 7

Time

Stephanie Bugden

Which brain regions activated during symbolic number

processing correlate with children’s

arithmetic skills?

Brain behavior-relationship

Left Intraparietal SulcusNo correlations with reading

R L

p<.05, correctedLeft IPS Activation

Mat

h Fl

uenc

y

Developmental Dyscalculia

Developmental Dyscalculia

• Persistent difficulties in math

• Below other competencies (reading, IQ)

• Prevalence ~ 5%

• Prevalence comparable to dyslexia

Developmental Dyscalculia

Ratio of publications on Dyslexia : Dyscalculia

14:1

Berch & Mazzocco (2007)

What underlies Developmental

Dyscalculia?

Symptoms and causes

Geary (1993)

What about number-specific processes?

Focus on basic number processing

• Landerl, Bevan & Butterworth (2004)

• Comparison of:

• Dyscalculics

• Dyslexics

• Double Deficit

• Typically developing

Focus on basic number processing

Number comparison- which is numerically larger?Size comparison - which is physically larger?

1 9 8 2

Landerl, Bevan & Butterworth (2004)

Basic number processing

0

200

400

600

800

1000

1200

1400

1600

Controls

Dyslex

ics

Dysca

lculic

s

Dyslex

ic/Dys

calcu

lics

Size Comparison

Number Comparison

Basic number processing

• Findings suggest that:

• Dyscalculia = deficit to represent and process numerical magnitude in a typical way

Basic number processing

Lack of understanding

numerical magnitude

Difficulties in learning

numerical expressions and maintaining them

in memory

Developmental time

No single cause!

Math as multicompentialSpatial Cognition

Working memory

Executive functionsBasic number processing

Phonological Awareness

MathEmotional Factors

Math Anxiety

DEVELOPMENT

TeachersLanguage

Neuroplasticity and Education

• Education changes the brain

• Experience-dependent plasticity

• Teachers as ‘Orchestrators of neuronal plasticity’

• Understanding the brain - changes in practice?

• Understanding how education changes the brain can inform neuroscience

Need for caution

• Lots of products marketed as ‘brain-based’

• Fascination with brain can be exploited

• Is there a peer-reviewed study proving efficacy?

• How valid are claims that are being made?

Neuromyths

What is the risk of neuromyths?

• Time spent on activities that are not beneficial

• Wrong use of instructional time

• Wrong characterization of learners

• How transferrable are trained skills?

Thank you for your attention!

Website: www.numericalcognition.orgTwitter: @numcog

E-mail: daniel.ansari@uwo.ca