Our goal in sharing the cases that follow is to make available a set of videos and related materials that we have used repeatedly with pre-service and in-service teachers to discuss the teaching and learning of mathematics, and of algebra in particular. In using these materials, our primary purpose has been to help teachers learn to notice students' mathematical thinking — that is, to identify interesting ideas that students share, try to understand the meaning of students' ideas and questions, and explore how students' comments and methods relate to the mathematics under discussion. The ability to attend to and make sense of classroom interactions in the moments of instruction has been found to be a valuable component of teaching expertise (Sherin et al., 2011); yet because of the complexity of classroom environments, doing so can be challenging. Watching and discussing video, with the ability to slow down classroom interactions, has been shown to be a productive context for developing one's noticing (van Es & Sherin, 2008).

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What is in the cases: At the center of each case is a short video clip, along with a transcript and brief case overview with background and questions to consider about student thinking. In addition, for each case we provide links to explore the mathematics involved, explore themes in student thinking, and dive deeper with a segmented video analysis guide with key questions regarding the ideas that students raise.

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How you might use the cases: The materials can be used in a variety of ways.

• We have most often used the materials with groups of teachers in a university setting, with a course instructor serving as the discussion facilitator using the video analysis guide. While the guide provides suggested evidence to highlight, it is simply meant as a resource to facilitate a productive discussion.

• We have also seen the cases used in non-university settings, among teachers who self-organize to explore the teaching of algebra. In this context, at times one person might serve as facilitator using the video analysis guide, or all participants might have access to the guide during discussion.

• Individual teachers might also find the materials useful as a way to deeply explore classroom discussion excerpts.

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Background and acknowledgments: These videos were collected as part of a series of projects that spanned ten years beginning in 1996. Given advancements in the recording and production of video during that time and since, you may notice that the video and audio quality is not the same as today's standards. Still, we anticipate that the videos and corresponding support materials can serve as a valuable resource.

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Many people were involved in the creation of these materials, most notably the teachers and students whose lessons, ideas, and images are represented in these cases. We thank them for their generosity. We also thank Jen Richards for her assistance in making these materials available for public use, and the Arthur Vining Davis Foundations for funding support.

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Miriam Gamoran Sherin; Alice Gabrielle Twight Professor of Learning Sciences; Northwestern University

Rosemary R. Russ; Associate Professor, Curriculum and Instruction; University of Wisconsin, Madison

Janet Walkoe; Associate Professor, College of Education; University of Maryland

Elizabeth Dyer; Assistant Professor, Curriculum and Instruction; University of Illinois, Urbana-Champaign

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November 2023

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To cite: Sherin, M. G., Russ, R. R., Walkoe, J., & Dyer, E. (2023). Algebra classroom video cases. Freezing Time Research Group. https://www.freezingtime.sesp.northwestern.edu/videocases. © 2023. Licensed under Creative Commons Attribution-NonCommercialShareAlike 4.0 International.

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We'd love to hear how you use the cases!  Feel free to "Contact Us" to share!

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