A Comparison of Rigour and Intuition in Illustrations in Calculus and Analysis Textbooks
Harsh Harsh K. Mishra (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M. Dhume – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M. Skrodzki – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
R.R. Venkatesha Prasad – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
In this paper, illustrations in both computation-based calculus and proof-based analysis textbooks are analysed, with particular attention to differences in their roles. Using a thematic analysis approach, we examine how visualisations of continuity, differentiability, and integration function within a corpus of three textbooks.
Our analysis identifies the juxtaposition of rigor and intuition as a central theme. The coded illustrations reveal differences that support this distinction and are divided into three subthemes: definitions, examples, and proofs. For definitions, analysis textbooks appear to use illustrations related to more formal definitions, whereas calculus textbooks more frequently use illustrations tied to informal definitions and introductions to definitions. Examples show a similar distinction between analysis and calculus textbooks: counterexamples and examples that build intuition versus exercises and confirming examples. For proofs, this study shows how illustrations are adapted such that the same illustration serves a different role depending on the textbook: either as a substitute for the proof or as a general outline of the proof.