What Counts?

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

2. 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. What is numeracy? • “…an ‘at-homeness’ with numbers and an ability to cope with the mathematical demands of everyday life…” • Cockcroft Report 1982

5. Count Me In • Develop measures to predict numeracy acquisition • Collect longitudinal data • Develop a model of how children acquire numeracy

6. 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. Are there cognitive precursors that predict the acquisition of numeracy? • Linguistic • Quantitative • Attentional

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

10. 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. Linguistic pathway • Number system knowledge is a language • Grammar, syntax, vocabulary • Symbolic representations

12. 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. Hypotheses • These three cognitive precursor “pathways” contribute independently to numeracy development • The relative contribution of each pathway depends on the mathematical ‘outcome’

14. 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

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. Current analysis • Outcomes • Standardized tests (general, global measures) • Measures of underlying numerical representations • Evidence for pathways if predictors are differentially related to outcomes

19. 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)

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

22. Spatial span

23. Subitizing

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

26. Cognitive Precursors and Early Numeracy Skills

27. Pathways - regression coefficients

28. Model to predict outcomes

29. Mathematical Outcomes • Numeration • Calculation (written) • Measurement

30. KeyMath Numeration Example 4,837 4,832 4,759 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. Numeration

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

33. Calculation

34. Measurement • KeyMath Measurement subtest

36. Measurement

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

39. 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. 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. 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. Thank you!

43. Number Line Estimation

44. Estimation

45. Lobes of the Brain

46. 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. Brain Pathways for Numeracy Posterior superior parietal lobule Intraparietal sulcus Angular gyrus

48. Magnitude Comparison

49. Magnitude Comparison

50. 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)