On resolving the tension between visiting mathematical works and questioning the quantum world

Abstract

For the past 40 years, researchers in didactics of mathematics have developed and utilised didactic engineering as a methodology for design-based research. In this article we discuss its second step, the so-called a priori analysis. In the framework of the Anthropological Theory of the Didactic, engineering is in the form of the implementation of a study and research path (SRP), an inquiry-based course. SRPs may be either finalised, that is aimed at the teaching of a particular piece of knowledge, or rather open, that is solely aimed at answering a given question. This tension between sometimes competing goals especially shows in the a priori analysis of SRPs, a phenomenon we address in this paper. Our study is based on pieces of evidence collected by setting up an SRP two years in a row at the interface between mathematics and quantum mechanics, in third year of bachelor's degree. We take a particular care in explicating the rationale behind the a priori analysis and its connection with the preliminary analysis. We bring out the significance of spelling out one's epistemological stance, as didactic engineer, emphasising the value of the notion of reference epistemological models to do so.

Keywords:

• Didactic engineering
• anthropological theory of the didactic
• paradigm of questioning the world
• interface between mathematics and physics
• quantum computing

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 In physics, a well is a region of space where the graph of the potential energy has a convex shape. In quantum mechanics such a well may be idealised as a rectangular hole, sometimes having ‘infinite’ walls (see Figure 6).

2 In the didactical meaning of the word. See for instance Chevallard (1989, p. 8).