THE PROBLEM OF TANGENT, MAXIMA AND MINIMA: A HISTORICAL APPROACH TO ITS TEACHING
THE PROBLEM OF TANGENT, MAXIMA AND MINIMA: A HISTORICAL APPROACH TO ITS TEACHING

Summary/Abstract: As it is generally taught in upper secondary and technical schools, mathematical analysis often presents fewer initial procedural difficulties for students than Euclidean synthetic geometry. Textbooks typically introduce the fundamental concepts of this branch—function, limit, derivative, and integral—in an intuitive manner, before moving abruptly toward a rigorous formalization in terms of ε-δ language. Furthermore, there is arguably an excessive pedagogical emphasis on certain dry, introductory topics. For instance, a considerable amount of instructional time is spent on determining the domain of a function, a task which essentially reduces to solving systems of equations or inequalities, offering little conceptual richness.

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