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Charting the Role of Spatial Abilities in Mathematical Development. Jo-Anne LeFevre Sheri-Lynn Skwarchuk, Jeffrey Bisanz, Brenda Smith-Chant, Deepthi Kamawar. Pathways Model. Cognitive skills that predict early mathematics Spatial ”attention” Verbal Quantitative - PowerPoint PPT Presentation
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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.