15 - History in a Competence Based Mathematics Education: A Means for the Learning of Differential Equations

Summary

Introduction

In a series of papers, Michael N. Fried has discussed a dilemma in historical approaches to mathematics education arising because “mathematics educators are committed to teaching modern mathematics …” and he continues “However, when history is being used to justify, enhance, explain, and encourage distinctly modern subjects and practices, it inevitably becomes what is “anachronical” […] or “Whig” history” [6, p. 395, italics in the original].Whig history refers to the kind of history that is written from the present, i.e., a reading of the past in which one tries to find the present. On account of the mathematics teacher, Fried phrased the dilemma as follows:

if one is a mathematics educator, one must choose: either (1) remain true to one's commitment to modern mathematics and modern techniques and risk being Whiggish, i.e., unhistorical in one's approach, or, at best, trivializing history, or (2) take a genuinely historical approach to the history of mathematics and risk spending time on things irrelevant to the mathematics one has to teach. [6, p. 398].

In Fried [7, p. 203], he emphasizes that this should not be understood as if history has no place or role to play in mathematics education, but was meant to point out “that a dilemma arises when the traditional commitments of mathematics education are assumed.”

The purpose of the present paper is to argue that this dilemma can be resolved by adopting both (1) a competence based view of mathematics education, and (2) a multiple-perspective approach to the history of the practice of mathematics.