Cogsci07

Cogsci07 - Compared to What? How Different Types of...

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Compared to What? How Different Types of Comparison Affect Transfer in Mathematics Bethany Rittle-Johnson Jon Star
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What is Transfer? Transfer “Ability to extend what has been learned in one context to new contexts” In mathematics, transfer facilitated by flexible procedural knowledge and conceptual knowledge Two types of knowledge needed in mathematics Procedural knowledge: actions for solving problems Knowledge of multiple procedures and when to apply them (Flexibility) Extend procedures to a variety of problem types (Procedural transfer) Conceptual knowledge: principles and concepts of a domain
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How to Support Transfer: Comparison Cognitive Science: A fundamental learning mechanism Mathematics Education: A key component of expert teaching
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Comparison in Cognitive Science Identifying similarities and differences in multiple examples is a critical pathway to flexible, transferable knowledge Analogy stories in adults ( Gick & Holyoak, 1983; Catrambone & Holyoak, 1989) Perceptual Learning in adults (Gibson & Gibson, 1955) Negotiation Principles in adults (Gentner, Loewenstein & Thompson, 2003) Cognitive Principles in adults Category Learning and Language in preschoolers (Namy & Gentner, 2002) Spatial Mapping in preschoolers Spatial Categories in infants (Oakes & Ribar, 2005)
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Comparison in Mathematics Education “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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Methods Expert teachers do it (e.g. Lampert, 1990) Reform curriculum advocate for it (e.g.
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This note was uploaded on 11/11/2011 for the course MATH 110 taught by Professor Staff during the Winter '08 term at BYU.

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Cogsci07 - Compared to What? How Different Types of...

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