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

About the author(s)

Andreas J. Stylianides, Faculty of Education, University of Cambridge, United Kingdom


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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