Journal of Research in Science, Mathematics and Technology Education

A Comparative Analysis of Classical and Contemporary Approaches to the Calculus of Tangents: A Conceptual Perspective

Tirivanhu Muchuweni 1 * ,
Benjamin Tatira 2,
Zingiswa Jojo 1
1 Rhodes University2 Walter Sisulu University* Corresponding Author
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Journal of Research in Science, Mathematics and Technology Education, Volume 9, Issue 3, September 2026, pp. 83-103
OPEN ACCESS VIEWS: 31 DOWNLOADS: 19 Publication date: 15 Sep 2026
ABSTRACT
This study examines how the concept of a tangent line has been understood in classical and contemporary mathematics. Classical approaches interpret tangents through approximation, algebraic reasoning, geometry, and infinitesimals, while contemporary calculus defines them using derivatives and limits. This study uses a qualitative conceptual and historical analysis to examine how tangents are understood across these approaches. The analysis focuses on key ideas such as slope, change, approximation, and formal definition, and compares how these ideas are represented in classical and contemporary mathematics. The findings show that classical approaches emphasize intuitive and conceptual reasoning, while contemporary approaches emphasize formal definitions and symbolic procedures. The findings also indicate that these approaches provide complementary forms of mathematical thinking. The study concludes that understanding tangents requires connections between intuitive meaning and formal reasoning. The study contributes to mathematics education by highlighting the importance of integrating classical and contemporary perspectives to support deeper conceptual understanding of tangents.
KEYWORDS
Calculus, Conceptual understanding, Derivatives, Historical approaches, Mathematical proficiency, Tangent line.
CITATION (APA)
Muchuweni, T., Tatira, B., & Jojo, Z. (2026). A Comparative Analysis of Classical and Contemporary Approaches to the Calculus of Tangents: A Conceptual Perspective. Journal of Research in Science, Mathematics and Technology Education, 9(3), 83-103. https://doi.org/10.31756/jrsmte.935
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