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Ksenija Simic-Muller, Erin E. Turner and Maura C. Varley

An after-school mathematics program for Latino students focuses on field trips to explore the mathematical practices of the community's businesses.

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Erin E. Turner and Beatriz T. Font Strawhun

Angel and Naisha, two sixth-graders in Ms. Font's mathematics class, had the following conversation as they reflected on their experience with posing and investigating problems related to overcrowding at their school.

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Tonya Bartell, Erin E. Turner, Julia Marie Aguirre, Corey Drake, Mary Q. Foote and Amy Roth McDuffie

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

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Erin E. Turner, Debra L. Junk and Susan B. Empson

Building understanding of multiplicative relationships is a key goal of mathematics instruction in the upper elementary and middle grades. Multiplicative thinking includes comparing numbers through many processes: multiplication and division (rather than addition and subtraction), ratio, proportions, stretching and shrinking, magnification, scaling, and splitting. Research has shown that multiplicative thinking develops slowly in children, over long periods of time (Clark and Kamii 1996; Vergnaud 1988). Initially, children tend to reason additively about multiplicative situations, and this additive thinking is often resistant to change (Hart 1984). Students need practice with tasks that help develop multiplicative thinking—in particular, tasks that help them recognize and reason about multiplicative relationships.

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Alfinio Flores, Erin E. Turner and Renee C. Bachman

Several scholars (e.g., Brown and Walter 1990; English 1997; Silver 1994) have highlighted the benefits of students posing mathematical problems (for example, students become better problem solvers). Posing mathematical problems can also help teachers develop their own mathematical knowledge and understanding. Teachers who learned mathematics mostly as “rules without reasons” now must learn how to teach for conceptual understanding. This article describes how two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students. Each teacher taught a combined fourth-fifth grade in an urban school. The problems that the teachers posed and solved were collected during an initial session and from the draft of an article they wrote. Additional insights and information were obtained from interviews.

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Corey Drake, Tonia J. Land, Tonya Gau Bartell, Julia M. Aguirre, Mary Q. Foote, Amy Roth McDuffie and Erin E. Turner

Make these small adjustments to your syllabus and watch spaces open to connect to children's multiple mathematical knowledge bases.

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Julia M. Aguirre, Cynthia O. Anhalt, Ricardo Cortez, Erin E. Turner and Ksenija Simic-Muller

Two major challenges in mathematics teacher education are developing teacher understanding of (a) culturally responsive, social justice–oriented mathematics pedagogies and (b) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teachergenerated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci–by using mathematical modeling to investigate and analyze important social justice issues–can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed.