Paramathematical notions and Klein's Plan B: the case of equations

Undergraduate students of mathematics continue to solve equations in virtually any course they attend, just as they did in secondary school -- yet what do they learn about equations and their solutions at university? Are they capable to combine elements of abstract algebra and real analysis to assess what it means to solve an equation, in particular, what it means for an equation to be solvable -- or not? In this paper, we present a mathematical and didactical analysis of these questions, illustrated by examples from a capstone course for future Danish high school teachers.
Comment: To be submitted for the 2024 congrees of INDRUM (International Network for Didactical Research on University Mathematics). Preliminary version, comments welcome