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What Counts? Cognitive Factors that Predict Childrens Mathematical Learning Jo-Anne LeFevre Professor of Psychology and Cognitive Science Carleton University Ottawa, Canada

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Count Me In Count Me In Team 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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Count Me In 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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1Develop measures to predict numeracy acquisition 2Collect longitudinal data 3Develop a model of how children acquire numeracy

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Count Me In 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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Count Me In 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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Count Me In 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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Count Me In Linguistic pathway Number system knowledge is a language Grammar, syntax, vocabulary Symbolic representations

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Count Me In 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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Count Me In 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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Count Me In 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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Count Me In 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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Count Me In 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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Count Me In Spatial span

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Count Me In 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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Count Me In Cognitive Precursors and Early Numeracy Skills

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Count Me In Pathways - regression coefficients

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Count Me In Model to predict outcomes

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Count Me In Mathematical Outcomes Numeration Calculation (written) Measurement

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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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Count Me In Numeration

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

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Count Me In Calculation

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Count Me In Measurement KeyMath Measurement subtest

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Count Me In 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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Count Me In 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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Count Me In 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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Count Me In 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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Count Me In Thank you!

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Count Me In Number Line Estimation

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Count Me In Estimation

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Count Me In Lobes of the Brain

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Count Me In 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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Count Me In Brain Pathways for Numeracy Angular gyrus Intraparietal sulcus Posterior superior parietal lobule

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Count Me In Magnitude Comparison

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Count Me In Magnitude Comparison

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Count Me In 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)

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