Formal Proof And Exploratory Experimentation:A Lakatosian View On The Interplay Between Examples And Deductive Proof Practices In Upper- Secondary School

This paper investigates conceptions of mathematical investigation and proof inupper-secondary students. The focus of the paper is an intervention that scaffolds theinteraction between open explorative activities and the development of proof sketchesthrough explorations of lattice polygons, aiming at proving Pick’s theorem. In theprocess we investigate whether and how the conceptions of proofs and explanationsin mathematics change. We work with the hypothesis that the problem of supportingthe transition to deductive proofs in upper-secondary school students can at leastpartly be explained as a problem of bringing their empirical investigations into thedeductive proof process in relevant and productive ways. Through our analyses of theportfolios and deliberations of the students, we are able to assess their performanceof proofs and the conceptions of mathematical methodology before and after theintervention