On Picard's iteration method to solve differential equations and a pedagogical space for otherness

Abstract

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving differential equations. In this article, we respond to Robin's work by subjecting these claims, methods and applications to closer scrutiny. By outlining the historical development of Picard's iterative method for differential equations and drawing on relevant literature, we show that the iterative scheme of Robin has been known for some time. We introduce the need for a 'space for otherness' in mathematics education, by drawing on Foucault and posit alternative pedagogical approaches as heterotopias. We open a space for otherness and make it concrete by considering alternative perspectives to Robin's work. On a practical note, we see the importance of history and theory to be part of the pedagogical conversation when teaching and learning iterative methods; and provide a set of Maple code with which students and teachers can experiment, explore and learn. We also advocate more broadly for educators to open a space for otherness in their own pedagogical practice.