Students need opportunities to construct definitions in mathematics. We describe a sorting activity that can help students construct and refine definitions through discussion and argumentation. We include examples from our own work of planning and implementing this sorting activity to support constructing a definition of linear function.
Erin E. Baldinger, Matthew P. Campbell, and Foster Graif
Rebecca Vinsonhaler and Alison G. Lynch
This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.