What does it mean to solve an equation?


Carl Winsløw, IND


Equations are used and solved everywhere in mathematics, both at secondary school and in university studies and research. At the same time, the notions of equation, and of solving an equation, are not explicitly defined. Equations and the act of solving them are, therefore, not mathematical notions, but paramathematical ones (in the sense of ATD).

In this lecture, we present a theoretical and observation-based proposal on how mathematics students can achieve a more explicit and adequate knowledge of what equations are, and especially about what it means and takes to solve them.  Students will draw on knowledge they have acquired in fragmented and often partial forms while taking undergraduate courses on abstract algebra and real analysis. We formulate the general hypothesis that Klein's Plan B should be invested in task design for capstone courses aiming at improving students' relationship with paramathematical notions.