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Zvia Markovits, Rina Hershkowitz and Maxim Bruckheimer

Edited by Judith Sowder and Larry Sowder

Common sense has many aspects and is developed by a variety of experiences in and out of school. Number sense is one aspect of common sense that we rightly expect schooling to improve. But does it? Given a problem, do students pay any attention to the meaning of the numbers in the data or in the solution they obtain? In a study devoted to estimation and reasonableness of results, we found that sixth- and seventh-grade students either do not have a reasonably developed number sense or, if they have it, do not apply it to simple tasks in a mathematical context.

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Douglas A. Grouws and Thomas L. Good

Edited by Judith Sowder and Larry Sowder

Research on problem solving can assist teachers by raising issues to consider as instructional decisions are made. Research that focuses on the study of current classroom practice is one good way of identifying such is sues. This article first characterizes some results from our recent research on classroom teaching of problem solving and then summarizes the related issues that teacher should conider as they plan and teach problem-solving lessons.

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Larry Sowder, Paul Cobb, Erna Yackel, Terry Wood, Grayson Wheatley and Graceann Merkel

Edited by Judith Sowder

Our ongoing project involves twenty-three second-gradc teachers who are teaching all their mathematics, including computation, through mallgroup problem solving and wholeclas discusion. Typically the children first work on problem-centered mathematical activities in pair or occasionally in group of three. During this phase of the lesson, the teacher moves from group to group, observing and interacting with the children while they do mathematics. After fifteen or twenty minutes, the teacher asks the children to stop working and begins a whole-class di scussion of their solution to the problems.

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Megan M. Loef, Deborah A. Carey, Thomas P. Carpenter and Elizabeth Fennema

Edited by Judith Sowder and Larry Sowder

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Randolph A. Philipp, Rebecca Ambrose, Lisa L.C. Lamb, Judith T. Sowder, Bonnie P. Schappelle, Larry Sowder, Eva Thanheiser and Jennifer Chauvot

In this experimental study, prospective elementary school teachers enrolled in a mathematics course were randomly assigned to (a) concurrently learn about children's mathematical thinking by watching children on video or working directly with chil-dren, (b) concurrently visit elementary school classrooms of conveniently located or specially selected teachers, or (c) a control group. Those who studied children's mathematical thinking while learning mathematics developed more sophisticated beliefs about mathematics, teaching, and learning and improved their mathematical content knowledge more than those who did not. Furthermore, beliefs of those who observed in conveniently located classrooms underwent less change than the beliefs of those in the other groups, including those in the control group. Implications for assessing teachers' beliefs and for providing appropriate experiences for prospective teachers are discussed.