What Counts?Cognitive Factors that Predict Children’s

Mathematical Learning

Jo-Anne LeFevreProfessor of Psychology and Cognitive Science

Carleton UniversityOttawa, Canada

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Investigators: Jeff Bisanz, Sheri-Lynn Skwarchuk, Brenda Smith-Chant, Deepthi Kamawar

Research Coordinator: Lisa Fast

Graduate students: Marcie Penner-Wilger, Tina Shanahan, Wendy Ann Deslauriers, Becky Watchorn, Marilyn Smith

Undergraduate researchers in Ottawa, Winnipeg, and Peterborough

PARTICIPANTS: Students, Teachers, Schools

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What is numeracy?

• “…an ‘at-homeness’ with numbers and an ability to cope with the mathematical demands of everyday life…”

• Cockcroft Report 1982

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1 Develop measures to predict numeracy acquisition

2 Collect longitudinal data

3 Develop a model of how children acquire numeracy

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Do early numeracy skills predict mathematical learning?

• Yes (preschool to Grade 2)

• Children with higher levels of skill remain high

• Some children improve

• Others do not -- why?

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Are there cognitive precursors that predict the acquisition of numeracy?

• Linguistic

• Quantitative

• Attentional

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Why these three pathways?

• Literature review

• Examination of early numeracy skills

• Neuropsychological evidence related to processing numbers (vs. words)

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Quantitative pathway

• Neuropsychology - humans have a brain-based quantitative capacity (approximate or small-number exact?)

• We chose to assess small-number exact

• Support from research with dyscalculia

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Linguistic pathway

• Number system knowledge is a language

• Grammar, syntax, vocabulary

• Symbolic representations

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Attentional pathway

• Working memory is central to various math tasks

• WM (executive? Phonological? VSSP? Depends on task)

• ADHD co-morbidities

• Math tasks require attention

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Hypotheses

• These three cognitive precursor “pathways” contribute independently to numeracy development

• The relative contribution of each pathway depends on the mathematical ‘outcome’

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What is a mathematical ‘outcome’• In contrast to reading, performance in

mathematics is diverse• Measurement of performance

– Curricular [NCTM] guidelines; number & operations, geometry, probability & data analysis, algebra, measurement, problem solving

– standardized measures have multiple subtests [e.g., numeration, geometry, calculation]

– Experimental tasks: number comparison, estimation, calculation

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Current data

• N = 182 children tested at age 4 or 5 (preschool or kindergarten)– Cognitive precursors– Early numeracy skills

• N=122 children retested 2 years later (Gr 1 or 2)– Mathematical outcomes

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Current analysis

• Outcomes– Standardized tests (general, global

measures)– Measures of underlying numerical

representations

• Evidence for pathways if predictors are differentially related to outcomes

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Longitudinal patterns

• Assess cognitive abilities early (in each pathway)

• Assess early numeracy skills (which should mediate cognitive abilities)

• Determine relative contributions of early skills (age 4 to 5) to various outcomes (age 6 to 7; Year 2 or 3)

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Cognitive Measures

• Linguistic– vocabulary & phonological awareness

• Attention – spatial span

• Quantitative -- subitizing speed

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Spatial span

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Subitizing

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Early Numeracy Measures

• Symbolic numeracy:– Number naming (1, 3, 7, 12, 17, 24…)

• Nonsymbolic numeracy:– Nonsymbolic/nonlinguistic quantity

transformations

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Cognitive Precursors and Early Numeracy Skills

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Pathways - regression coefficients

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Model to predict outcomes

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Mathematical Outcomes

• Numeration

• Calculation (written)

• Measurement

KeyMath Numeration Example

4,837 4,759 4,832

Read these three numbers to me, starting with the smallest number and ending with the largest.

Item 14: Mean raw score for Grade 2 is 13.79 (SD 3.3)

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Numeration

Calculation

Mean raw score for grade 2 in 2007 was 11.6(N=112, S.D. 2.9)

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Calculation

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Measurement

• KeyMath Measurement subtest

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Measurement

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Summary: Pathways

• Linguistic --> Number system knowledge

• Quantitative --> quantity representations and transformations

• Attention --> more general and diffuse relation to skills

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Connections among pathways

• Ansari 2008 (also Rouselle & Noel, 2007): connections between the quantitative and the symbolic systems are the source of math difficulties

• Could be one source; but weakness in any or all of the pathways could implicate math difficulties

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Conclusions/Suggestions:

• Researchers should pay more attention to outcomes; different math tasks are likely to implicate different underlying skills and different knowledge sets

• Patterns of relations among skills and tasks may change with time

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Implications

• Useful framework for understanding– Developmental trajectories (across children)– Potential for designing remediation– Early instruction (curricula); what children

know vs. what they need to learn– What kinds of early experiences are

important for numeracy acquisition

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Thank you!

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Number Line Estimation

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Estimation

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Lobes of the Brain

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Neuropsychological support

• Description of brain regions that support numeracy - Dehaene et al. (2005)

• Three parietal circuits– Horizontal segment of the intraparietal sulcus

(HIPS) = quantity– Left angular gyrus (AG) = verbal– Posterior superior parietal lobule (PSPL) =

spatial attention

• All three contribute to numerical development

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Brain Pathways for Numeracy

Angular gyrus

Intraparietal sulcus

Posterior superior parietal lobule

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Magnitude Comparison

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Magnitude Comparison

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Why do we need a model?

• Prediction of numeracy acquisition

• Early Numeracy skills --> 1, 2, or more years later

• What should be in the model?– Precursors (cognitive)– Experiences (home, preschool)– Experiences (during school)