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Keri D. Valentine and Johnna Bolyard

Past experiences as mathematics learners play a critical role in the way mathematics teachers consider what it means to know, do, and teach mathematics. Thus, understanding past experiences and ways to work with them in teacher education is a critical concern. Using phenomenological inquiry, we investigated moments of shift that occur along one's mathematics journey. The study draws on 30 prospective teachers' experiences in the form of lived-experience writing and interview data. Findings show that prospective teachers' shifts manifest in relations with others, across different time frames, and through material relations with mathematics. Most salient was the tentative and mutable nature of shifts, showing that shift might be better viewed as a possibility rather than a single event.

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Sararose D. Lynch and Johnna J. Bolyard

A problem-solving pen pal project between preservice teachers and sixth graders presented a lens through which a teacher could view students' work and her instruction.

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Sarah J. Selmer, Johnna J. Bolyard and James A. Rye

An analysis of food choices becomes a rich data-driven lesson set in a real-world context.

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Patricia S. Moyer and Johnna J. Bolyard

Article describes a game of classifying objects according to their attributes using a three-set Venn diagram, then analyzing the classification of the objects to determine their accuracy. Students attempt to capture opponents' game pieces (tangrams) by making mathematical arguments that identify misplaced pieces.

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Informing Practice: I-THINK I Can Problem Solve

research matters for teachers

Sararose D. Lynch, Jeremy M. Lynch and Johnna Bolyard

Students access the THINK framework that involves prompts exploring talk, how, identify, notice, and keep.

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Patricia S. Moyer, Johnna J. Bolyard and Mark A. Spikell

As a result of innovations in technology, the prevalence of the Internet, and the increasing availability of computers in classrooms and homes, an enhanced approach for teaching and learning mathematics using manipulatives and computers is emerging. This new approach essentially creates a new class of manipulatives, called virtual manipulatives, as well as new capabilities, or toolkits, for computer programs that use visual representations. These new virtual manipulatives have all the useful properties of existing computer manipulatives while overcoming many of their disadvantages, yet very little is known or written about them. The purpose of this article is to establish a working definition of virtual manipulatives, highlight examples of virtual manipulatives on the Internet, and discuss their current and potential classroom use.