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Bilge Yurekli, Mary Kay Stein, Richard Correnti and Zahid Kisa

teachersbeliefs with the practices they are expected to enact. Despite considerable research on the role of teachersbeliefs in teaching mathematics since the early reform initiatives in the 1990s ( Skott, 2015 ), the research base lacks a measure

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Lawrence M. Clark, Jill Neumayer DePiper, Toya Jones Frank, Masako Nishio, Patricia F. Campbell, Toni M. Smith, Matthew J. Griffin, Amber H. Rust, Darcy L. Conant and Youyoung Choi

This study investigates relationships between teacher characteristics and teachers' beliefs about mathematics teaching and learning and the extent to which teachers claim awareness of their students' mathematical dispositions. A professional background survey, a beliefs and awareness survey, and a teacher mathematical knowledge assessment were administered to 259 novice upper-elementary and 184 novice middle-grades teachers. Regression analyses revealed statistically significant relationships between teachers' beliefs and awareness and teachers' mathematical knowledge, special education certification, race, gender, and the percentage of their students with free and reduced meal status. This report offers interpretations of findings and implications for mathematics teacher education.

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Wendy S. Bray

This collective case study examines the influence of 4 third-grade teachers' beliefs and knowledge on their error-handling practices during class discussion of mathematics. Across cases, 3 dimensions of teachers' error-handling practices are identified and discussed in relation to teacher beliefs and knowledge: (a) intentional focus on flawed solutions in class discussion, (b) promotion of conceptual understanding through discussion of errors, and (c) mobilization of a community of learners to address errors. Study findings suggest that, although teachers' ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher knowledge, some aspects of teacher response are more strongly linked to knowledge and others are influenced more by beliefs.

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Thomas L. Good, Douglas A. Grouws and DeWayne A. Mason

This study examines teachers' beliefs about, and practices in, small-group teaching of mathematics. A sample of 1509 teachers from 126 elementary schools in 10 districts in three states completed the survey. Roughly 80% of the teachers reported using the whole-class format as the basic organization for mathematics lessons. About 13% of the teachers reported using two or more groups and that while they worked with one group, students assigned to other groups worked alone. Only 5% of the teachers reported using two or more groups in which students were encouraged to work cooperatively. The paper discusses the various beliefs teachers report in deciding whether or not to group for instruction and describes how teachers use group instruction in mathematics classes. Grade-level differences are also explored.

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John K. Lannin and Kathryn B. Chval

Use these specific strategies to confront assumptions about teaching and learning mathematics.

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Carlos Nicolas Gomez and AnnaMarie Conner

students, prospective teachers, and practicing teachers ( Middleton et al., 2017 ; Philipp, 2007 ; Richardson, 1996 ; Thompson, 1992 ). Pajares (1992) argued that understanding teachersbeliefs about content areas, such as mathematics and science, is

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James A. Middleton

In this study I examine the structures of 2 teachers' beliefs about what makes mathematics intrinsically motivating and provide instances of the representations of their beliefs at 2 times: before the introduction of middle school mathematics curricula organized around the tenets of Realistic Mathematics Education and after 1 year of implementing a pilot program. Personalconstructs analyses are paired with observations of teachers' classrooms and their beliefs and perceptions as reported in semistructured interviews. Results indicate that the teachers became more attuned to the conceptual complexity and challenge of mathematics activities and placed less emphasis on task ease over their year of involvement in the pilot program. Results are discussed in relation to “job-embedded learning,” a form of staff development that fosters teachers' development of meaning with regard to reforms, and how such learning enables shifts in teacher beliefs and practice.

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Cheryl Ann Lubinski and Nancy Nesbitt Vacc

Seth was sitting in his second-grade classroom on the third day of school. He'd just finished writing on his paper after his teacher, Ms. Kates, had given the class a problem to solve.

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Nancy Nesbitt Vacc and George W. Bright

In this research, we examined changes in preservice elementary school teachers' beliefs about teaching and learning mathematics and their abilities to provide mathematics instruction that was based on children's thinking. The 34 participants in this study were introduced to Cognitively Guided Instruction (CGI) as part of a mathematics methods course. Belief-scale scores indicated that significant changes in their beliefs and perceptions about mathematics instruction occurred across the 2-year sequence of professional course work and student teaching during their undergraduate program but that their use of knowledge of children's mathematical thinking during instructional planning and teaching was limited. Preservice teachers may acknowledge the tenets of CGI and yet be unable to use them in their teaching. The results raise several questions about factors that may influence success in planning instruction on the basis of children's thinking.

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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.