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Keith R. Leatham, Blake E. Peterson, Shari L. Stockero, and Laura R. Van Zoest

The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical opportunities—what we call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. We analyze dialogue to illustrate a process for determining whether a classroom instance offers such an opportunity and to demonstrate the usefulness of the construct in examining classroom discourse. This construct contributes to research and professional development related to teachers' mathematically productive use of student thinking by providing a lens and generating a common language for recognizing and agreeing on a critical core of student mathematical thinking that researchers can attend to as they study classroom practice and that teachers can aspire to notice and build upon when it occurs in their classrooms.

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Victoria Hand and Tamsin Meaney

Our connected world is exploding with images and sounds of cultural hybridity and fluidity. Mathematics classrooms, however, remain frozen in time. One consequence of this inertia is that mathematics education, rather than being a way to provide opportunities that lead to better lives for students, continues to limit those opportunities by reproducing existing societal inequities (Ernest, 2009). The inertia continues despite Herculean efforts by a range of stakeholders in mathematics education to broaden and diversify the voices participating in classroom mathematical conversations. What does the contrast between the increasingly dynamic and “flattened” (Friedman, 2005) nature of our global culture and the static and hierarchical nature of the mathematics classroom have to do with a book about classroom mathematical discourse and issues of equity?

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Hala Ghousseini, Sarah Lord, and Aimee Cardon

mathematics discourse and studying teaching and teacher learning. Sarah Lord , , is a doctoral student in mathematics education at the University of Wisconsin. She studies children’s mathematical development in number and operations and

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Eric Cordero-Siy and Hala Ghousseini

their classrooms. Hala Ghousseini , , is a teacher educator and the John G. Harvey Professor of Mathematics Education at the University of Wisconsin. She is interested in classroom mathematics discourse and studying teaching and

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Allyson Hallman-Thrasher, Susanne Strachota, and Jennifer Thompson

associate professor of mathematics education at Ohio University, Athens. Her research ranges from teachers’ learning to facilitating to classroom mathematics discourse and the preparation of K–12 mathematics teachers. Susanne Strachota , susanne