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Theresa J. Grant and Mariana Levin

One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.

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Nesrin Cengiz and Theresa J. Grant

“How many teeth have you lost?” Imagine second graders collecting data from their peers about how many teeth each child is missing and then creating their own data representations that mean something to them. Instead of showing her students how to create a bar graph of the data, this teacher asks them to display the information in some way that helps them make sense of their data. Students work in small groups, discuss their ideas with peers, and create their own data representations. Then they share their data with the entire class, discussing differences in their representations and interpretations.

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Theresa J. Grant, Jane-Jane Lo and Judith Flowers

This article discusses the challenges and opportunities that arose in attempting to support prospective elementary teachers in developing mathematical justifications in the context of wholenumber computation. Justification for whole-number computation is important for three reasons. First, this is the introductory topic in the first of three mathematics courses for prospective elementary teachers. Second, the number and operations strand is a major focus in elementary school. Third, in our experience as teacher educators, prospective elementary teachers have a difficult time considering how and why to teach whole-number computation in a conceptual manner. If prospective teachers' reasoning and justifications can be shaped in this area of mathematics, sense making and mathematical justification in other areas of mathematics can be shaped as well (Simon and Blume 1996).