How elementary and collegiate instructors envision tasks as supportive of mathematical argumentation: A comparison of instructors’ task constructions

Abstract

We examine how instructors at different grade levels proposed mathematical tasks to support students’ engagement in constructing viable arguments and critiquing others’ reasoning. During small group interviews with pairs of practicing elementary and collegiate mathematics instructors, they created tasks intended to support students’ ability to create and critique mathematical arguments. From the anslysis of their written and verbal work, we found that although all instructors requested explanations in their created tasks, there were key differences in the nature of reasoning-and-proving expected. Grade 1 instructors tended to focus on empirical justifications and procedural explanation; Grade 3 and 4 instructors included similar requirements, but had more emphasis on soliciting rationales; and college instructors required students to ultimately develop more formalized arguments, consistently including requests for conjectures and generalizations. The findings provide evidence for key differences in argumentation norms at specific levels in schooling, and implications for research, teaching, and curricular design.