# Learning to pose cognitively demanding tasks through letter writing

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## Abstract

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 letter-writing projects while introducing a concern that has implications for all professional development projects.

## Keywords

Mathematical tasks Preservice teachers Professional development Students’ mathematical thinking Task design Task posing## Notes

### Acknowledgments

We thank the Indiana Mathematics Initiative, Zachary Rutledge, and Kareston Hall for their support on the underlying project.

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