What scaffolds the early development of numerical and mathematical - PowerPoint PPT Presentation

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

Foundational competencies • What are the early foundations? • What is scaffolding in early development? • Analogy: phonological awareness • Cumulative effect

Foundational competencies Stanovich (1986)

So what might be foundational competencies for numeracy?

Foundational system

Foundational system • Sensitivity to numerical magnitude

Foundational system • Sensitivity to numerical magnitude • Non-symbolic

Foundational system • Sensitivity to numerical magnitude • Non-symbolic • From infancy onwards

Foundational system • Sensitivity to numerical magnitude • Non-symbolic • From infancy onwards • Measurable in other species

Foundational system • Sensitivity to numerical magnitude • Non-symbolic • From infancy onwards • Measurable in other species • Brain systems

Human development 3 Non-symbolic Symbolic non-iconic Iconic Mapping between intuitive and cultural system

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)?

Does it matter? Nadia Nosworthy Symbolic Non-symbolic 56 items/condition 1 minute/condition 160, 1st-3rd graders Also tested on: WJ Math fluency WJ Calculation Skils Nosworthy et al. (2013, PLoS ONE )

Does this 2-minute magnitude processing test correlate with math achievement?

Correlation with WJ Math Fluency Nosworthy et al. (2013; PLoS ONE)

Correlation with WJ Calculation 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?

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

Predictive measure? • 268 children tested in senior kindergarten on paper and pencil test • from TDSB NW1 FoS

Predictive measure? • 268 children tested in senior kindergarten on paper and pencil test • from TDSB NW1 FoS • School board permitted access to Grade 1:

Predictive measure? • 268 children tested in senior kindergarten on paper and pencil test • from TDSB NW1 FoS • School board permitted access to Grade 1: • First progress reports

Predictive measure? • 268 children tested in senior kindergarten on paper and pencil test • from TDSB NW1 FoS • School board permitted access to Grade 1: • First progress reports • 2nd term grades

Does performance in SK predict 1st grade teacher-rated performance?

Predictive measure? Progress Report Progressing with difficulty Progressing well Progressing very well Unpublished Data Progressing well

Predictive Measure? 1st term grades Data Number Sense Measurement Geometry Management Symbolic ✔ ✔ ✔ ✔ ✔ ✔ Non-symbolic ✔ indicates significant correlation, p<.05 Unpublished Data

Evidence supports notion of ‘scaffolding’ Calculus Trigonometry Algebra Arithmetic Numerical Magnitude Processing

A developmental perspective

A developmental perspective Lack of understanding numerical magnitude

A developmental perspective Lack of understanding numerical magnitude

A developmental perspective Difficulties in Lack of learning understanding numerical numerical expressions and magnitude maintaining them in memory

A developmental perspective Difficulties in Lack of learning understanding numerical numerical expressions and magnitude maintaining them in memory Developmental time

Website with test & norms forthcoming in Spring 2014

Summary and Conclusions

Summary and Conclusions • Basic numerical magnitude processing

Summary and Conclusions • Basic numerical magnitude processing • Evolutionary history / early development

Summary and Conclusions • Basic numerical magnitude processing • Evolutionary history / early development • Provides an important scaffold

Summary and Conclusions • Basic numerical magnitude processing • Evolutionary history / early development • Provides an important scaffold • By no means the only - one of many

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

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

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

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

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