Proof schemes of pre-service middle and secondary mathematics teachers

ABSTRACT

This article reports proof schemes used by pre-service mathematics teachers enrolled in third- and fourth-year mathematics education courses at a Midwestern university. Six pre-service teachers constructed proofs for mathematical conjectures and were subsequently interviewed. Using Harel and Sowder’s (1998) proof schemes theoretical framework, the study found that there exists variation in the proof schemes used by pre-service teachers, depending on their grade-level certification. Middle school pre-service teachers, pursuing a grades 5–9 certification, predominantly used external proof schemes, while dual (middle and secondary) certification pre-service teachers primarily used empirical proof schemes. However, secondary pre-service mathematics teachers, pursing a grades 9–12 certification used a variety of proof schemes. This study has implications for teacher preparation programs and the need to develop pre-service teachers’ proof skills, considering that pre-service teachers’ proof schemes provide insights into their perspectives of mathematics and way of thinking. For instance, pre-service teachers who exhibited external conviction proof schemes perceived mathematics as a collection of truths provided by their teachers, textbooks and other entities, rather than as a product of their social norms and practices.

KEYWORDS:

• Proof
• proof schemes
• pre-service teachers