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Ian Whitacre and Susan D. Nickerson

This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of partial products and to reason flexibly about products. We document how the class overcame the challenge of accounting for partial products in multidigit multiplication, including particular activities and ways of reasoning that facilitated progress. The results provide insights into how prospective elementary teachers' understanding of multidigit multiplication can develop during a content course and how a sequence of instructional activities and practices can productively leverage the resources that they bring in support of that development.

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Susan D. Nickerson, Cherie Nydam and Janet S. Bowers

Current trends in middle school curricula highlight the importance of integrating algebraic reasoning throughout the middle grades. The use of innovative technologies offers one exciting way to engage students in algebraic problem-solving activities. In this article, we report on our efforts to design for seventh graders a computer-based instructional unit that would not only address state standards but, we hoped, also lay the groundwork for the students' subsequent formal study of algebra. The software we chose, SimCalc MathWorlds, is available free of charge via the World Wide Web at www.simcalc. Look on the first page of this site. With this program, students can animate characters on the screen by creating graphs of position and velocity.