Treffer: Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the Maple computer algebra system. Students worked in pairs utilizing the pair-programming model of collaboration. Four groups of student pairs from one intact class programmed their own computational tools and subsequently used them to explore the limit and derivative concepts. Four additional pairs of students from an additional intact class were provided with similar pre-constructed computational tools and asked to perform identical explorations. A multiple embedded case design was utilized to explore ways students in the two classes, programming class, P, and non-programming class, N, constructed understandings focusing upon their interactions with each other and with the computational tools. The Action-Process-Object-Schema (APOS) conceptual model and Constructionist framework guided design and construction of the tools, outlined developmental goals and milestones, and provided interpretive context for analysis. The results provided insights into the effective design and use of computational tools in fostering conceptual understanding. The study found learning programming was challenging and overburdened students in class P in ways that misdirected students' attention away from the intended mathematical concept of limit. Students in class P tended to see the limit as an unreachable boundary whereas students in class N, using pre-constructed exploratory tools, tended to see the limit in its proper formal form. The study additionally found, however, that pre-constructed tools could effectively promote conceptual understanding of the limit concept when coupled with a mature conceptual model of development. Four themes influencing development of these understandings emerged: An instructional focus on skills over concepts, the instructional sequence, the willingness and ability of students to adopt and utilize computational tools, and the ways cognitive conflict was mediated. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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