Investigation of Prospective Mathematics Teachers' Proof Completion Processes Supported By Key Ideas

The aim of this research was to examine prospective mathematics teachers' completion processes of mathematical proofs supported by key ideas in the field of abstract algebra. Prospective teachers were asked to complete the parts of a proof left incomplete using those key ideas. It was decided, together with three academics who are experts in the field of algebra, which theorems to use and which proof sections to leave missing in the proof completion form. The proof completion form consisted of five proofs and was applied to five participants. The participants' processes for completing the proofs were evaluated in semi-structured interviews supported by the think-aloud method. Interviews were recorded on video and transcribed, and descriptive analysis was performed. The findings obtained were analyzed with think-aloud protocols. According to the results, key ideas can be said to play an active role in the proof process and the teaching of proof. In addition, developing activities consisting of proofs supported by key ideas can contribute to prospective teachers' abilities to prove without memorization and internalize proof processes.