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

Note: This article is a substantially revised version of the author’s plenary lecture at the 15th Annual Congress of the Association for Mathematics Education of South Africa (AMESA), which appeared in the proceedings of the congress (Stylianides, 2009b). 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.