Sophia Kovalevsky's story

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### George J. Roy, Jessica S. Allen and Kelly Thacker

In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

### Tim Erickson

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.

### Erin E. Baldinger, Matthew P. Campbell and Foster Graif

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.

### 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.

### 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.