Using Examples of Unsuccessful Arguments to Facilitate Students’ Reflection on Their Processes of Proving

Proving is an essential component in mathematical activities, but a difficult one for many students. We assume that one reason for this might be that Unsuccessful arguments unsuccessful arguments made during the process of planning a proof do not appear in the completed proof, and therefore students cannot see how those arguments influenced the proof. If students could reflect on such arguments, they would be able to learn about proving and effective ways to derive a proof. Previous studies have provided worked examples showing successful ways of deriving a proof to enhance students’ understanding of proving. However, such examples do not include unsuccessful arguments. This chapter examines how examples of unsuccessful arguments can facilitate students’ reflection on their process of planning a proof by designing, implementing, and analyzing an eighth-grade geometry lesson. It was found that an example of unsuccessful arguments enabled the students to comprehend why the unsuccessful arguments failed and why the successful ones worked.