Addressing pre-service teachers’ mathematical reasoning through reverse engineering

In this Note from the Field, I show how undergraduate pre-service teachers exercised mathematical reasoning when they were required to find the rules determining their score in successive rounds of an iterative game. The rules were hidden from them, and therefore they needed to use mathematical reasoning to reverse engineer the rules based on their scores. The teachers generated similar conjectures as they worked to decipher the rules, even as, with each iteration of the game, pre-service teachers learned the rules to maximize their scores. Reverse engineering, as a pedagogical strategy, would seem to offer a promising avenue for teaching mathematical reasoning in teachers — who can then teach their students.