Proving Tasks Involving Multiple but Finitely Many Cases
Andreas J. Stylianides · Oxford University Press eBooks · 2016
This chapter reports an investigation of proving tasks that call for consideration of all (finitely many) cases involved in a situation. Specifically, it discusses combination, permutation, and Cartesian product tasks, all infused with the requirement for a proof. The emphasis is on the proving activity that these tasks can help generate in the elementary classroom and on the teacher’s role while implementing the tasks. The investigation is situated in the context of two classroom episodes with 8–9-year-olds from England and the United States that raise complementary issues pertaining to the use of these tasks. This chapter describes and discusses each episode separately and concludes with a general discussion. A key issue concerns the representational complexity that might arise for elementary students in considering all cases involved in a situation, with implications drawn for the teacher’s role in helping students develop more efficient representational tools as they engage with proof.