A detailed look at continuity in Calculus textbooks

• Andrijana Burazin ^[1] ; Veselin Jungić ^[2] ; Miroslav Lovrić ^[3]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
  2. [2] Simon Fraser University

     Simon Fraser University

     Canadá

     
  3. [3] McMaster University

     McMaster University

     Canadá

     

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• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 9, 2025, págs. 1631-1647
• Idioma: inglés
• DOI: 10.1080/0020739X.2024.2337943
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• Resumen

  • The aim of this paper is to contribute to the ongoing discussion about the role of intuition and ambiguity in doing, teaching and learning mathematics. We start by discussing the ways in which limits and continuity are presented in Calculus textbooks, to illustrate some of the ambiguities, and to contrast them with precise and rigorous definitions and statements. Next, we offer a brief overview of the topological terms necessary to introduce the notion of a continuous function in the topological setting. We conclude by suggesting a way of presenting the concept of a continuous function appropriate for Calculus instruction, while still staying true to its topological roots. This paper is also a suggestion to mathematics instructors to consider modifying the way they introduce limits and continuity in their classrooms, by creating a balance (appropriate for their students!) between rigour on the one side and intuition and ambiguity on the other.

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