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Sequence limits in calculus: using design research and building on intuition to support instruction

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Abstract

This article is based on research completed within an ongoing project to develop a calculus course which serves as the foundation for the mathematical education of undergraduate students who are training to become elementary teachers. Several research-based activities have been developed, tested, and refined. In this paper we discuss how the design research approach was used to create and implement an instructional task that introduces the concept of limit of a sequence using popular characters from a children’s television show. We present the intuition that students brought to the instructional sequence, the development of the tasks based on the instructional design theory of Realistic Mathematics Education, and the evolution of the intuition that students displayed after instruction. Results include the instructional task developed and student work which reveals that students use context, informal notions of limit, and the notion of “arbitrarily close” to write about their limit understandings.

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Authors and Affiliations

  1. North Carolina State University, PO Box 7801, Raleigh, NC, 27695, USA

    Karen Allen Keene, William Hall & Alina Duca

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  1. Karen Allen Keene
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  2. William Hall
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  3. Alina Duca
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Correspondence to Karen Allen Keene.

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Keene, K.A., Hall, W. & Duca, A. Sequence limits in calculus: using design research and building on intuition to support instruction. ZDM Mathematics Education 46, 561–574 (2014). https://doi.org/10.1007/s11858-014-0597-8

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