Original Research

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

Andreas J. Stylianides
Pythagoras | Vol 32, No 1 | a14 | DOI: https://doi.org/10.4102/pythagoras.v32i1.14 | © 2011 Andreas J. Stylianides | This work is licensed under CC Attribution 4.0
Submitted: 08 July 2011 | Published: 03 August 2011

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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.


classroom teaching; mathematical reasoning; proof; mathematics teacher education; teacher knowledge


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