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Mathematics Education Research Journal

, Volume 27, Issue 2, pp 183–200 | Cite as

Graphical construction of a local perspective on differentiation and integration

  • Ye Yoon Hong
  • Michael O. J. Thomas
Original Article
First Online:

Abstract

Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually established through the school curriculum to a view of function that includes a local, or interval, perspective. This is necessary for study of concepts such as continuity and limit that underpin calculus and analysis at university. In this study, a first-year university calculus course in Korea was constructed that integrated use of digital technology and considered the epistemic value of the associated techniques. The aim was to encourage versatile thinking about functions, especially in relation to properties arising from a graphical investigation of differentiation and integration. In this paper, the results of this approach for the learning of derivative and antiderivative, based on integrated technology use, are presented. They show the persistence of what Tall (Mathematics Education Research Journal, 20(2), 5–24, 2008) describes as symbolic world algebraic thinking on the part of a significant minority of students, who feel the need to introduce algebraic methods, in spite of its disadvantages, even when no explicit algebra is provided. However, the results also demonstrate the ability of many of the students to use technology mediation to build local or interval conceptual thinking about derivative and antiderivative functions.

Keywords

Graphical Derivative Antiderivative Pointwise Local Versatile 
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Notes

Acknowledgments

This paper builds on ideas published in the 2013 proceedings of the conference for the International Group for the Psychology of Mathematics Education (IGPME) held in Kiel, Germany.

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Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2014

Authors and Affiliations

  1. 1.Yonsei UniversitySeoulSouth Korea
  2. 2.The University of AucklandAucklandNew Zealand

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