Motivations for VCAST

• Research suggests that in order to significantly advance student understanding of mathematics, educators must pay careful attention to students’ mathematical ideas (c.f. Stein & Smith, 2011). Expert teachers, however, recognize that it is not enough to simply pay attention to students’ mathematical ideas; instead, teachers must learn to respond to students in ways that enable students to move forward without removing ownership and authority for doing mathematics from students (Ball, Thames, & Phelps, 2008). Learning to attend and respond to students’ mathematical ideas in this way requires a specialized knowledge of mathematics that includes knowing how mathematical ideas are related, how to represent mathematical ideas in meaningful ways, and how students might develop certain mathematical ideas over time (Ball, Thames, & Phelps, 2008). Consequently, we set forth to investigate ways to support secondary mathematics teacher candidates’ development of this specialized knowledge. We were specifically interested in how video clips of secondary students might support candidates in their ability to recognize, describe, and make connections between students’ mathematical ideas. Building upon research on the use of video cases (Llinares & Valls, 2009; Sherin & van Es, 2005) and what teachers notice about student thinking (Jacobs, Lamb, & Philipp, 2010), we began developing video-based modules to engage teacher candidates in investigating students’ functional reasoning.
• Successful instructional interventions are developed over time through a series of iterative improvements. Thus, the goal of this National Science Foundation (NSF) funded design and development project is to use design-based research to iteratively develop and revise four video-based modules via implementation in authentic secondary mathematics teacher preparation settings. The first two years of the VCAST project are focused on developing the module curriculum materials and testing them at Boise State University and the last two years are focused on implementing the curriculum materials at other institutions.

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