Reforms to the teaching of mathematics encourage teachers to support students both in making conjectures and refuting those that are false using counterexamples. This study reports on the counterexamples provided by 17 preservice elementary teachers when asked to refute students' false conjectures about fractions. The analysis drew upon existing frameworks to distinguish the pedagogical power and accessibility of counterexamples. Findings indicate that preservice elementary teachers’ counterexamples lacked pedagogical power. Additionally, counterexamples that lacked pedagogical power also varied in terms of: (a) their mathematical complexity and (b) their ability to mirror the reasoning used by the student who authored the false conjecture being refuted. Future work may examine how counterexamples displaying a range of mathematical complexity and mirroring ability support students in abandoning their false conjectures.

Session Type: Brief Research Report