Charting the Role of Spatial Abilities in Mathematical

Development

Jo-Anne LeFevreSheri-Lynn Skwarchuk, Jeffrey Bisanz, Brenda

Smith-Chant, Deepthi Kamawar

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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.

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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”.

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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.”

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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

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Number Line Task

• Given a number and a line with marked endpoints, place the number on the line

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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)

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Linear

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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

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Arithmetic

- multi-digit addition, subtraction

- Single-digit multiplication

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Number knowledge

• Naming and Ordering large numbers

• Place value

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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?

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Correlations?

• Is spatial ability correlated with math measures?

• Spatial measured 1 year earlier

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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

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Is spatial ability related to mathematical task performance?

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Does spatial ability contribute to growth of number line performance?

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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.”

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

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What else predicts number line growth?

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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

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More Summary…

• And, number line performance is not causally related to arithmetic or number system knowledge

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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

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Cautionary Tale

• Correlations do not mean causation

• Need more research on links between spatial ability and mathematical performance

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Thanks!

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