Higher order reasoning produced in proof construction: how well do secondary school students explain and write mathematical proofs?

摘要

The culture of mathematical explanations and writings based on conceptual understanding in proof construction is on the focus of the paper. We explore students’ attempts to explain construction of mathematical proofs after reading them and write mathematical proofs after working out their own constructions. Two examples of proofs, by induction and by contradiction, are discussed in detail to highlight students’ difficulties in proving and possible ways for their resolving.