Towards a comprehensive knowledge package for teaching proof: A focus on the misconception that empirical arguments are proofs

Abstract

The concept of proof is central to meaningful learning of mathematics, but is hard for students to learn. A serious misconception dominant amongst students at all levels of schooling is that empirical arguments are proofs. An important question, then, is the following: What knowledge might enable teachers to help students overcome this misconception? Earlier research led to construction of a significant but rather incomplete ‘knowledge package’ for teaching in this area. Major elements of this knowledge package are summarised and its further development is contributed to by discussing a research-based instructional intervention found to be effective in helping secondary students begin to overcome the misconception that empirical arguments are proofs. Implications for mathematics teacher education are considered.