This professional practice paper is underpinned philosophically by the indisputable centrality of proof to the discipline of mathematics. Proof offers students the opportunity to deepen their own understanding of mathematical ideas, to construct and defend logical arguments, and to think critically about the veracity of mathematical statements. Such opportunities afford students key skills required for further study, and arguably for a myriad of careers. Proof by contradiction is a particular mathematical technique taught in Australian senior secondary classrooms (ACMSM025, ACMSM063) which will be explored in this paper. In particular, several worked examples will be outlined alongside implications for best instructional practice within the context of the secondary mathematics classroom.


mathematics, senior secondary schools, Australia, proof

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