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P. Holt Wilson, Marrielle Myers, Cyndi Edgington and Jere Confrey

Teaching young children to create equal-size groups is your treasure map for building students' flexible, connected understanding of and reasoning about ratios, fractions, and multiplicative operations.

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P. Holt Wilson, Cynthia P. Edgington, Kenny H. Nguyen, Ryan C. Pescosolido and Jere Confrey

Develop and strengthen students' rational number sense with problems that emphasize equipartitioning.

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Cyndi Edgington, P. Holt Wilson, Paola Sztajn and Jared Webb

Mathematics teacher educators play a critical role in translating research findings into frameworks that are useful for mathematics teachers in their daily practice. In this article, we describe the development of a representation that brings together four research-based learning trajectories on number and operations. We detail our design process, present the ways in which we shared this representation with teachers during a professional development project, and provide evidence of the ways teachers used this translation of research into a pedagogical tool to make sense of students' mathematics. We conclude with revisions to the representation based on our analysis and discuss the role of mathematics teacher educators in translating research findings into useful tools for teachers.

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P. Holt Wilson, Hollylynne Stohl Lee and Karen F. Hollebrands

This study investigated the processes used by prospective mathematics teachers as they examined middle-school students' work solving statistical problems using a computer software program. Students' work on the tasks was captured in a videocase used by prospective teachers enrolled in a mathematics education course focused on teaching secondary mathematics with technology. The researchers developed a model for characterizing prospective teachers' attention to students' work and actions and interpretations of students' mathematical thinking. The model facilitated the identification of four categories: describing, comparing, inferring, and restructuring. Ways in which the model may be used by other researchers and implications for the design of pedagogical tasks for prospective teachers are discussed.