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Providing preservice teachers with opportunities to engage with parents and begin to see them as collaborators in their children's education is a persistent challenge in mathematics methods courses and teacher preparation programs more broadly. We describe the use of family mathematics nights as a model for engaging parents and preservice teachers. These events helped preservice teachers feel more comfortable in working with parents, while also giving them a friendly space for learning more about parents, the ways they work with their children, and activities they do with their children. Incorporating surveys about parents' needs and suggestions for preservice teachers allowed us to use the results as a catalyst for fostering discussions around parent engagement later in the methods course.

We have used letter writing as a means for preservice teachers (PSTs) to develop ability to design effective tasks, in terms of eliciting high levels of cognitive activity from students. Studies on student-dependent task analyses, by assessing the levels of cognitive demand indicated in students' responses, have demonstrated significant growth among PSTs over the course of letter-writing exchanges. We examine growth with a qualitative analysis of two PSTs who became effective at designing tasks that elicited high levels of cognitive activity. In particular, we examine how those PSTs accounted for tasks that did not elicit the kinds of activity they expected and how they adjusted their tasks to elicit higher levels of activity. We found disparity between the two PSTs' apparently successful approaches: one that fit the larger goals of the project and one that fit only the descriptions specified in the project rubric. The study affirms the potential value of letterwriting projects while introducing a concern that has implications for all professional development projects.

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