# Snapshots of mathematics teacher noticing during task design

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## Abstract

Designing a mathematically worthwhile task is critical for promoting students’ reasoning. To improve task design skills, teachers often engage in collaborative lesson planning activities such as lesson study. However, to learn from the process of lesson study, it is important for teachers to notice productively the concepts, students’ confusion and the design of the task. But what researchers mean by productive noticing varies. In this article, I present the FOCUS Framework which highlights two characteristics of productive noticing: having an explicit focus for noticing and focusing noticing through pedagogical reasoning. Using these two characteristics, I develop snapshots of noticing as a representation of practice to present a fine-grained analysis of teacher noticing. Through vignettes of teachers discussing the design of a task to teach fractions, I illustrate how two teachers’ noticing can be analysed and represented using snapshots of noticing. To conclude, I highlight what snapshots of noticing tell us about a teacher’s noticing and suggest ways to use these snapshots in future studies of noticing.

## Keywords

Mathematics teacher noticing Productive teaching practices Task design Representations of practice Fractions## Notes

### Acknowledgments

I would like to express my heartfelt thanks to my PhD supervisors, Professors Mike Thomas and Caroline Yoon, for their advice and suggestions regarding the initial drafts. I would also like to thank the reviewers for their insightful comments which were helpful for my revision of the draft. Last but not least, I would like to thank Ms. Amy Soh for helping me with the proofreading. This article is an extended version of an earlier paper presented at the Psychology of Mathematics Education Conference in 2014.

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