Calculus Expertise and Strategy Use when Comparing Multiple Representations

Julie BoothTemple University, Philadelphia, PA, United States
Briana ChangTemple University, Philadelphia, PA, United States
Jennifer CromleyTemple University, Philadelphia, PA, United States
Thomas ShipleyTemple University, Philadelphia, PA, United States
Theodore WillsTemple University, Philadelphia, PA, United States

Abstract

Expertise affords individuals a variety of advantages for learning and for problem solving, including competing advantages such as using automatic strategies vs. using sophisticated strategies. In the present study, high school students with varying levels of calculus expertise completed measures of conceptual understanding and skill with external representations before a task in which they were asked to coordinate between multiple representations (CMR) and determine whether they represented the same mathematical function. Strategy use during the CMR task was coded based on think-aloud data. Results indicate that students with more expertise tended to use automatic strategies when completing the task, and, surprisingly, used fewer sophisticated strategies than more novice peers.

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