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Bilge Yurekli, Mary Kay Stein, Richard Correnti and Zahid Kisa

A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.

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Mary Kay Stein and Jane W. Bovalino

Getting students to think about mathematics in ways that go beyond using procedures to solve routine problems is an important goal of mathematics reform. Manipulatives can be important tools in helping students to think and reason in more meaningful ways. By giving students concrete ways to compare and operate on quantities, such manipulatives as pattern blocks, tiles, and cubes can contribute to the development of well-grounded, interconnected understandings of mathematical ideas.

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Margaret S. Smith, Elizabeth K. Hughes, Randi A. Engle and Mary Kay Stein

Five practices constitute a model for effectively using student responses in whole-class discussions that can potentially make teaching with high-level tasks more manageable for teachers.