SLIDE 1 What scaffolds the early development of numerical and mathematical competencies?
Daniel Ansari Numerical Cognition Laboratory Department of Psychology & Brain and Mind Institute University of Western Ontario
A Forum For Action, Effective Practices in Mathematics Education, Toronto, December 11th 2013
SLIDE 2 Foundational competencies
- What are the early foundations?
- What is scaffolding in early development?
- Analogy: phonological awareness
- Cumulative effect
SLIDE 3
Foundational competencies
Stanovich (1986)
SLIDE 4
So what might be foundational competencies for numeracy?
SLIDE 5
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Foundational system
SLIDE 11 Foundational system
- Sensitivity to numerical magnitude
SLIDE 12 Foundational system
- Sensitivity to numerical magnitude
- Non-symbolic
SLIDE 13 Foundational system
- Sensitivity to numerical magnitude
- Non-symbolic
- From infancy onwards
SLIDE 14 Foundational system
- Sensitivity to numerical magnitude
- Non-symbolic
- From infancy onwards
- Measurable in other species
SLIDE 15 Foundational system
- Sensitivity to numerical magnitude
- Non-symbolic
- From infancy onwards
- Measurable in other species
- Brain systems
SLIDE 16
Human development
3
Non-symbolic Iconic Symbolic non-iconic Mapping between intuitive and cultural system
SLIDE 17 Does it matter?
- Are the intuitive skills related to children’s
math learning?
- What is the role of integrating symbolic
with intuitive (non-symbolic systems)?
?
SLIDE 18 Does it matter?
56 items/condition 1 minute/condition 160, 1st-3rd graders Also tested on: WJ Math fluency WJ Calculation Skils
Nadia Nosworthy
Nosworthy et al. (2013, PLoS ONE) Symbolic Non-symbolic
SLIDE 19
Does this 2-minute magnitude processing test correlate with math achievement?
SLIDE 20
Correlation with WJ Math Fluency
Nosworthy et al. (2013; PLoS ONE)
SLIDE 21
Correlation with WJ Calculation
Nosworthy et al. (2013; PLoS ONE)
SLIDE 22 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 ?
SLIDE 23
Does performance on this test predict performance over time?
SLIDE 24
Predictive measure?
SLIDE 25 Predictive measure?
- 268 children tested in senior kindergarten
- n paper and pencil test
SLIDE 26 Predictive measure?
- 268 children tested in senior kindergarten
- n paper and pencil test
- from
TDSB NW1 FoS
SLIDE 27 Predictive measure?
- 268 children tested in senior kindergarten
- n paper and pencil test
- from
TDSB NW1 FoS
- School board permitted access to Grade 1:
SLIDE 28 Predictive measure?
- 268 children tested in senior kindergarten
- n paper and pencil test
- from
TDSB NW1 FoS
- School board permitted access to Grade 1:
- First progress reports
SLIDE 29 Predictive measure?
- 268 children tested in senior kindergarten
- n paper and pencil test
- from
TDSB NW1 FoS
- School board permitted access to Grade 1:
- First progress reports
- 2nd term grades
SLIDE 30
Does performance in SK predict 1st grade teacher-rated performance?
SLIDE 31 Predictive measure?
Progressing with difficulty Progressing well Progressing very well
Progress Report
Progressing well
Unpublished Data
SLIDE 32 Predictive Measure?
Number Sense Measurement Geometry Data Management Symbolic
✔ ✔ ✔ ✔
Non-symbolic
✔ ✔
1st term grades
✔ indicates significant correlation, p<.05 Unpublished Data
SLIDE 33 Evidence supports notion of ‘scaffolding’
Numerical Magnitude Processing
Arithmetic
Algebra
Trigonometry Calculus
SLIDE 34
A developmental perspective
SLIDE 35
A developmental perspective
Lack of understanding numerical magnitude
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A developmental perspective
Lack of understanding numerical magnitude
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A developmental perspective
Lack of understanding numerical magnitude Difficulties in learning numerical expressions and maintaining them in memory
SLIDE 38
A developmental perspective
Lack of understanding numerical magnitude Difficulties in learning numerical expressions and maintaining them in memory Developmental time
SLIDE 39
Website with test & norms forthcoming in Spring 2014
SLIDE 40
Summary and Conclusions
SLIDE 41 Summary and Conclusions
- Basic numerical magnitude processing
SLIDE 42 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
SLIDE 43 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
- Provides an important scaffold
SLIDE 44 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
- Provides an important scaffold
- By no means the only - one of many
SLIDE 45 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
- Provides an important scaffold
- By no means the only - one of many
- Related to arithmetic skills
SLIDE 46 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
- Provides an important scaffold
- By no means the only - one of many
- Related to arithmetic skills
- Particularly symbolic skills
SLIDE 47 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
- Provides an important scaffold
- By no means the only - one of many
- Related to arithmetic skills
- Particularly symbolic skills
- Intuitive-cultural mapping
SLIDE 48 Summary and Conclusions
- Basic numerical magnitude processing
- Evolutionary history / early development
- Provides an important scaffold
- By no means the only - one of many
- Related to arithmetic skills
- Particularly symbolic skills
- Intuitive-cultural mapping
- Strengthening numerical magnitude
processing early to enhance dev. trajectory
SLIDE 49 Thank you for your attention!
Funding: Students and collaborators on these projects:
Lisa Archibald Annie Appleby (TDSB) Samuel Zheng (TDSB) Stephanie Bugden Bea Goffin Ian Holloway Nadia Nosworthy Gavin Price
www.numericalcognition.org
