dr. daniel ansari's presentation (pdf)
TRANSCRIPT
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
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: [email protected]