CogDev2007

# CogDev2007 - When it pays to compare Benefits of comparison...

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When it pays to compare: Benefits of comparison in mathematics classrooms Bethany Rittle-Johnson Jon R. Star

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Common Ground: Comparison Cognitive Science: A fundamental learning mechanism This symposium! Mathematics Education: A key component of expert teaching
Comparison in Mathematics Education Compare solution methods “You can learn more from solving one problem in many different ways than you can from solving many different problems, each in only one way” (Silver, Ghousseini, Gosen, Charalambous, & Strawhun, p. 288)

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Compare Solution Methods Expert teachers do it (e.g. Lampert, 1990) Reform curriculum advocate for it (e.g. Teachers in higher performing countries help students do it (Richland, Zur & Holyoak, 2007)
Does comparison support mathematics learning? Experimental studies on comparison in K-12 academic domains and settings largely absent Goals of initial work Investigate whether comparing solution methods facilitates learning in middle-school classrooms 7th graders learning to solve equations 5th graders learning about computational estimation

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Compare condition: Compare and contrast alternative solution methods vs. Sequential condition: Study same solution methods sequentially facilitate conceptual and procedural knowledge? An experimental study  on learning to solve equations.  Journal of Educational Psychology .
Compare Condition Equation Solving

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Sequential Condition n e x t p a g
Predicted Outcomes Students in compare condition will make greater gains in: Procedural knowledge, including Success on novel problems Flexibility of procedures (e.g. select efficient procedures; evaluate when to use a procedure) Conceptual knowledge (e.g. equivalence)

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Study 1 Method Participants: 70 7th-grade students and their math teacher Design: Pretest - Intervention - Posttest
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CogDev2007 - When it pays to compare Benefits of comparison...

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