9731339 Branca This four-year project creates K-12 mathematics professional curriculum materials based on classroom videos. The materials consist of a series of professional development sessions based on video cases from grades K-12 and include such features as: videoclips, student work samples, teacher and mathematician commentaries, and facilitation guides that allow materials to be used flexibly in many settings and with a variety of audiences from K-12. Mathematicians explicate the mathematical content in the video lessons through analyses and discussions. Their resulting commentaries and videotaped discussions provide a perspective to enrich case discussions about the mathematics situated in practice, enhancing opportunities for increased mathematical content knowledge. Building on the methodology and technology of the TIMSS Video Study, the technological tools provide efficient and flexible access to the features of the video cases. The tools that accompany each case permit educators to engage in face-to-face and Internet conversations about the video cases, enhancing analysis opportunities and extending professional development opportunities beyond the "workshop" door. The facilitation guides will provide strategies to engage participants in critical discussions aimed at improving mathematics teaching practices K-12. The proposed modules are: (1) "Algebraic Thinking as Generalized Arithmetic," which will examine how algebraic ideas at the secondary level are developed from elementary work with number; (2) "Algebraic Thinking from a Geometry Perspective," which will examine lessons from middle and high school classrooms and highlight instances of algebraic reasoning from geometric models; (3) "Modeling," which will provide opportunities to develop a language to discuss and support a robust understanding of the role of modeling in mathematics; and, if a fourth module is possible, (4) "Language and Representation," a K-12 examination of changes in levels of sophistication o f mathematical language from elementary through high school. Project evaluation is focused around three key questions: * What are the effects, if any, of using these video cases in professional development on teachers' knowledge of mathematical content and the theories of teaching? * What are the effects, if any, of using these video cases in professional development on teachers' instructional decision-making and classroom practice? * What are the effects, if any, of using these video cases in professional development on student learning? The project will work closely with the Mathematics Renaissance K-12, Local Systemic Change projects, and other Teacher Enhancement projects, using the video cases as part of the professional development program with nearly 4000 teachers. Cost sharing, derived primarily from the San Diego State University Foundation, is approximately 43% of the NSF request.
