Eighth-grade Students’ Use of Communal Criteria for Collaborative Proving

ABSTRACT This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students’ abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal criteria for proof and subsequently worked in small groups to collaboratively construct arguments which attempted to meet the communally-negotiated criteria. The findings revealed there was no significant correlation between the number of times a group appealed to communal criteria and the quality of their argument. However, the qualitative analysis revealed groups who created valid arguments utilized communal criteria in productive ways, while groups who created invalid arguments superficially engaged with communal criteria or exhibited fundamental misunderstandings of some criteria. These findings imply developing and utilizing communal criteria is a promising support for improving school-aged students’ proving capacities, but further theoretical and empirical research is needed to determine how to develop communal criteria in ways that all students within a classroom community can meaningfully utilize the criteria to mediate their abilities to create arguments.