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 in
upper-secondary students. The focus of the paper is an intervention that scaffolds the
interaction between open explorative activities and the development of proof sketches
through explorations of lattice polygons, aiming at proving Pick’s theorem. In the
process we investigate whether and how the conceptions of proofs and explanations
in mathematics change. We work with the hypothesis that the problem of supporting
the transition to deductive proofs in upper-secondary school students can at least
partly be explained as a problem of bringing their empirical investigations into the
deductive proof process in relevant and productive ways. Through our analyses of the
portfolios and deliberations of the students, we are able to assess their performance
of proofs and the conceptions of mathematical methodology before and after the
intervention.