Investigating grade-6 students’ justifications during mathematical problem solving in small group interaction

In this study, we focused on grade-6 students’ justifications during mathematical problem solving in small group interaction. Video recordings from two classrooms were analyzed, using Harel and Sowder’s (2007) taxonomy of proof schemes as a tool to categorize students’ justifications, which showed that the frequency of various types of justifications corresponded to previous studies of adult students’ demonstrations of proof schemes. Results also showed that both Non-referential Symbolic and Transformational justifications contributed to students’ formulations of general arguments. In addition, agreements between proximately located justifications based on examples and calculations supported students’ improvements of solutions. However, in cases of disagreements, justifications based on calculations often had most influence on the proving process even when the calculation was incorrect. Our results imply that teachers should emphasize the importance of agreement between calculations and empirical examples, as well as the significance of counterexamples, as a support to students’ progression towards mathematical proving.