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Dan Battey, Rebecca A. Neal and Jessica Hunsdon

How we handle classroom relationships between teachers and students plays an important role in how all students experience mathematics.

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Tonya Bartell, Anita Wager, Ann Edwards, Dan Battey, Mary Foote and Joi Spencer

The Common Core State Standards for Mathematics (CCSSM) do not make any promises about the teaching practices that should be used to support students' enactment of the standards. Thus, equity gets framed as achievable through making the standards a goal for all students. We know from research on past reform efforts that standards without explicit (or companion) teaching practices, and teaching practices without explicit attention to equity, will inevitably result in the failure of the standards to achieve goals for students. This commentary provides a framework for future research that hypothesizes research-based equitable mathematics teaching practices in support of the CCSSM's Standards for Mathematical Practice, connecting research, policy, and practice in order to realize the equity potential of the CCSSM.

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Victoria R. Jacobs, Megan Loef Franke, Thomas P. Carpenter, Linda Levi and Dan Battey

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with teachers in Grades 1–5. Participating teachers generated a wider variety of student strategies, including more strategies that reflected the use of relational thinking, than did nonparticipating teachers. Students in participating classes showed significantly better understanding of the equal sign and used significantly more strategies reflecting relational thinking during interviews than did students in classes of nonparticipating teachers.