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http://dx.doi.org/10.7468/jksmee.2022.36.1.39

A Case Study on the Relationship between Indefinite Integral and Definite Integral according to the AiC Perspective  

Park, Minkyu (Seoul National University Graduate School)
Lee, Kyeong-Hwa (Seoul National University)
Publication Information
Communications of Mathematical Education / v.36, no.1, 2022 , pp. 39-57 More about this Journal
Abstract
This study aims to design an integral instruction method that follows the Abstraction in Context (AiC) framework proposed by Hershkowitz, Schwarz, and Dreyfus to help students in acquiring in-depth understanding of the relationship between indefinite integrals and definite integrals and to analyze how the students' understanding improved as a result. To this end, we implemented lessons according to the integral instruction method designed for eight 11th grade students in a science high school. We recorded and analyzed data from graded student worksheets and transcripts of classroom recordings. Results show that students comprehend three knowledge elements regarding relationship between indefinite integral and definite integral: the instantaneous rate of change of accumulation function, the calculation of a definite integral through an indefinite integral, and The determination of indefinite integral by the accumulation function. The findings suggest that the AiC framework is useful for designing didactical activities for conceptual learning, and the accumulation function can serve as a basis for teaching the three knowledge elements regarding relationship between indefinite integral and definite integral.
Keywords
AiC; indefinite integral; definite integral; accumulation function; context;
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