Charting the Role of Spatial Abilities in Mathematical Development

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

2. 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. 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. 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. 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. Number Line Task • Given a number and a line with marked endpoints, place the number on the line

7. 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. Linear

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. Arithmetic • multi-digit addition, subtraction • Single-digit multiplication

14. Number knowledge • Naming and Ordering large numbers • Place value

15. 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. Correlations? • Is spatial ability correlated with math measures? • Spatial measured 1 year earlier

17. Partial Correlations (Year 1) Note: Controlling for grade, gender, vocabulary

18. Is spatial ability related to mathematical task performance?

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

20. 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. Is number line performance the link between spatial ability and other math performance?

22. What else predicts number line growth?

23. 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. More Summary… • And, number line performance is not causally related to arithmetic or number system knowledge

25. 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. Cautionary Tale • Correlations do not mean causation • Need more research on links between spatial ability and mathematical performance

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