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

2. 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

3. 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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5. 1Develop measures to predict numeracy acquisition 2Collect longitudinal data 3Develop a model of how children acquire numeracy

6. 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?

7. Count Me In Are there cognitive precursors that predict the acquisition of numeracy? Linguistic Quantitative Attentional

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9. Why these three pathways? Literature review Examination of early numeracy skills Neuropsychological evidence related to processing numbers (vs. words)

10. 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

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

12. 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

13. 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

14. 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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17. 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

18. 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

19. 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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21. Cognitive Measures Linguistic– vocabulary & phonological awareness Attention – spatial span Quantitative -- subitizing speed

22. Count Me In Spatial span

23. Count Me In Subitizing

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25. Early Numeracy Measures Symbolic numeracy: –Number naming (1, 3, 7, 12, 17, 24…) Nonsymbolic numeracy: –Nonsymbolic/nonlinguistic quantity transformations

26. Count Me In Cognitive Precursors and Early Numeracy Skills

27. Count Me In Pathways - regression coefficients

28. Count Me In Model to predict outcomes

29. Count Me In Mathematical Outcomes Numeration Calculation (written) Measurement

30. 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)

31. Count Me In Numeration

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

33. Count Me In Calculation

34. Count Me In Measurement KeyMath Measurement subtest

36. Count Me In Measurement

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38. Summary: Pathways Linguistic --> Number system knowledge Quantitative --> quantity representations and transformations Attention --> more general and diffuse relation to skills

39. 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

40. 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

41. 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

42. Count Me In Thank you!

43. Count Me In Number Line Estimation

44. Count Me In Estimation

45. Count Me In Lobes of the Brain

46. 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

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

48. Count Me In Magnitude Comparison

49. Count Me In Magnitude Comparison

50. 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)