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• Author or Editor: Judith Flowers
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## Multiplication Fact Fluency Using Doubles

A sequence of mental math problems using reasoning can boost students' understanding and confidence in performing multiplication.

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## Developing Teachers' Computational Fluency: Examples in Subtraction

In the past, much of the discussion about elementary school mathematics revolved around arithmetic and children's facility with standard algorithms. Current recommendations, however, suggest that encouraging children to invent computational procedures that make sense to them and to analyze how those procedures work may be more beneficial (Campbell et al. 1998; Kamii 1998; Russell 1999; Schifter 1999). This expansion in the array of possible procedures children may use and the thinking they may do in analyzing them means that simply considering children's accuracy with computation is no longer reasonable. Instead, to clarify our changing expectations of elementary students'work in computation, mathematics educators now talk about computational fluency (NCTM 2000; Russell 2000).

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## Problems to Deepen Teachers' Mathematical Understanding: Examples in Multiplication

Details problems and instructional approaches intended to promote preservice teachers' understanding of the reasoning underlying whole number multiplication.

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## Supporting Teacher Learning: Shaping Prospective Teachers' Justifications for Computation: Challenges and Opportunities

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).