# Uses of video in understanding and improving mathematical thinking and teaching

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## Abstract

This article characterizes my use of video as a tool for research, design and development. I argue that videos, while a potentially overwhelming source of data, provide the kind of large bandwidth that enables one to capture phenomena that one might otherwise miss; and that although the act of taping is in itself an act of selection, there is typically enough shown in a video that it rewards multiple watching and supports the kinds of arguments over data that are essential for theory testing and replication. In pragmatic terms, video presents phenomena in ways that have an immediacy that is tremendously valuable. I discuss ways in which videos help students and teachers focus on phenomena that might otherwise be very hard to grapple with. This article begins with a brief review of my uses of video, almost 40 years ago, for research and development in problem solving. It then moves to the discussion of very fine-grained research on learning and decision making. The bulk of the article is devoted to a discussion of the teaching for robust understanding (TRU) framework, which was derived in large measure from the extensive review of classroom videotapes, and which serves as the basis for an extensive program of pre-service and in-service professional development. The professional development relies heavily on the use of videos to convey the key ideas in TRU, and to help teachers plan and review instruction.

## Keywords

Video Professional development Mathematics teaching Mathematics learning Teaching for robust understanding## Notes

### Acknowledgements

This research reported in this paper was partially supported by funding for The Algebra Teaching Study (US National Science Foundation Grant DRL-0909815 to PI Alan Schoenfeld, U.C. Berkeley, and US National Science Foundation Grant DRL-0909851 to PI Robert Floden, Michigan State University), and of The Mathematics Assessment Project (Bill and Melinda Gates Foundation Grant OPP53342 to PIs Alan Schoenfeld, U. C Berkeley, and Hugh Burkhardt and Malcolm Swan, The University of Nottingham).

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