1. Charting the Role of Spatial Abilities in Mathematical Development Jo-Anne LeFevre Sheri-Lynn Skwarchuk, Jeffrey Bisanz, Brenda Smith-Chant, Deepthi Kamawar

2. Count Me In Pathways Model Cognitive skills that predict early mathematics –Spatial ”attention” –Verbal –Quantitative Relative contribution depends on the outcome measure LeFevre et al. (2010). Child Development.

3. Count Me In Question How do spatial abilities relate to mathematical skills? Gunderson et al. (2012): “little work has investigated the various underlying pathways by which spatial skill can improve mathematics early in development”.

4. Count Me In Hypothesis Gunderson et al.: We hypothesized that spatial skill plays a crucial role in the development of numerical reasoning by helping children to create a spatially meaningful, powerful numerical representation: the linear number line.”

5. Count Me In Data: Count Me In Data: three- or four- year longitudinal sample of > 500 children (www.carleton.ca/cmi) Initial testing: preschool to Grade 2 (Grade 1 to Grade 5) Many measures; focus here on the number line task, arithmetic, and number knowledge 101 children in grades 2, 3, and 4, 1 year follow-up

6. Count Me In Number Line Task Given a number and a line with marked endpoints, place the number on the line

7. Count Me In What does the number line task measure? Reflection of children’s internal mental representation of number/quantity (Siegler, Booth, Opfer) –Logarithmic vs. linear Reflection of children’s knowledge of the number system + proportional reasoning (Barth; Moeller; Bouwmeester)

8. Count Me In Linear

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12. Why do children’s number lines become more linear? Because children’s internal representations become more linear (Siegler) Because children gain more knowledge of the number system (in the appropriate range) Because their spatial processes and number system knowledge improve

13. Count Me In Arithmetic -multi-digit addition, subtraction -Single-digit multiplication

14. Count Me In Number knowledge Naming and Ordering large numbers Place value

15. Count Me In Research Questions Is spatial ability related to mathematical task performance? Does spatial ability contribute to growth of number line performance? Is the number line on the “causal pathway” between spatial abilities and later mathematical performance?

16. Count Me In Correlations? Is spatial ability correlated with math measures? Spatial measured 1 year earlier

17. Count Me In Partial Correlations (Year 1) Spatial Ability Number Line Number Knowledge Number Line.27** Number Knowledge.39**.25** Arithmetic.38**.31**.42** Note: Controlling for grade, gender, vocabulary

18. Count Me In Is spatial ability related to mathematical task performance?

19. Count Me In Does spatial ability contribute to growth of number line performance?

20. Count Me In Hypothesis Gunderson et al.: We hypothesized that spatial skill plays a crucial role in the development of numerical reasoning by helping children to create a spatially meaningful, powerful numerical representation: the linear number line.”

21. Count Me In Is number line performance the link between spatial ability and other math performance?

22. Count Me In What else predicts number line growth?

23. Count Me In Summary Spatial ability is correlated to many mathematical measures Spatial ability is related to growth in a task (number line) that has clear spatial requirements However, spatial ability doesn’t predict growth in other math measures

24. Count Me In More Summary… And, number line performance is not causally related to arithmetic or number system knowledge

25. Count Me In Tentative conclusions? Need to explore in more depth the role for spatial processes in number-based mathematical measures Most important skill (these data) is learning how the number system works Number system knowledge is causally predictive of number line performance

26. Count Me In Cautionary Tale Correlations do not mean causation Need more research on links between spatial ability and mathematical performance

27. Count Me In Thanks! Support by SSHRC, my collaborators, and many many helpful students over the years.