Proof-scripts as a lens for exploring students’ understanding of odd/even functions

•Proof-scripts used to study understanding of odd/even function.•Adds to the literature regarding proof-script methodology.•Participants had limited understanding of non-monomial cases.•Participants conflated particular odd/even functions with the general case.

A group of prospective mathematics teachers was asked to imagine a conversation with a student centered on a particular proof regarding odd/even functions and produce a script of this imagined dialog. These scripts provided insights into the script-writers’ mathematical knowledge as well as insights into what they perceive as potential difficulties for their students. The paper focuses on the script-writers’ understandings of derivative and of even/odd functions.