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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.

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Anne Quinn

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

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Gabriel Matney, Julia Porcella and Shannon Gladieux

This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.