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Have you ever noticed a gap between research and practice? How can research effect change in the classroom? The Connecting Research to Teaching department of Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to their practice. MT also invites education researchers to demonstrate how results from their studies shape classroom practice. Findings from collaborative action research projects are also encouraged. Evidence of connections from research to practice commonly includes student work and brief transcripts from interviews or classroom videos.

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The Editorial Panel of Mathematics Teaching in the Middle School is seeking submissions for a department titled Informing Practice. The articles written for this section should entice and invite classroom teachers to learn about aspects of research that are closely related to their classroom practice.

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Peter Kloosterman and Tracey L. J. Warren

Computer Aided Assessment of Mathematics focuses on assessment in college mathematics courses with a special focus on computer-based assessment as a means of providing partial credit and immediate feedback on student work. Written by Chris Sangwin, a senior lecturer in mathematics at the University of Birmingham in the United Kingdom, the book is an important resource for mathematicians or software developers interested in understanding the promise and the pitfalls of using computers to assess student work in college courses. Each chapter of the book addresses a different issue so readers have the option of reading most of them out of order or selecting the chapters that are most valuable to them. Thus, in addition to describing Sangwin's perspectives on teaching and assessing mathematics, this review is designed to help readers decide which chapters in the book will be useful to them.

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

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for teacher preparation and professional development programs.

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Katherine E. Lewis

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.

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Anita A. Wager

This article describes how teachers in a professional development course responded to what they noticed about children's participation in elementary mathematics classrooms and how what they noticed was connected to the teachers' positionality toward equitable mathematics pedagogy. Findings suggest that a lens of participation supported teachers as they considered how to provide more equitable mathematics instruction. Further, the depth to which teachers noticed children's participation was connected to their positionality as equitable mathematics educators.

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Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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Gayle Millsaps

Preservice elementary school teachers (PSTs) often have difficulty understanding hierarchical (i.e., class inclusion) relationships between geometric shapes. In particular, PSTs' predisposition to place squares and rectangles in separate categories can be attributed to their concept images. Although the larger mathematics community prefers the hierarchical definitions of special quadrilaterals, the concept images of special quadrilaterals such as squares and rectangles that PSTs develop in their early experiences contribute to a preference for partitional definitions. This study examines the benefits and limitations of using the Shape Makers curriculum unit to modify preservice teachers' concept images and their definitions of special quadrilaterals.

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Heidi L. Fleharty and Carolyn Pope-Edwards

Sixty-three teachers in a K–3 mathematics specialist certificate program conducted family projects in order to improve their skills in partnering with families around mathematics. Past studies have indicated that family involvement in children's education has many positive influences on academic achievement; however, parents' discomfort with math, and teachers' discomfort with working with parents, may be obstacles. The purpose of the present study was to examine 2 years of teachers' mathematical family projects and describe the types of projects chosen, the risks and benefits of these projects, and the quality of the parent–child interaction. It was found that the teachers implemented a variety of projects that promoted parent participation in mathematics. Teachers were also able to utilize a cycle of inquiry to examine the progress of their project. The results showed that teachers were able to create a strong connection between the math classroom and the home environment of the child, as shown, for example, by findings related to the themes of home–school connections and mathematics curriculum of the home.

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Margaret S. Smith

Building a trustworthy knowledge base for mathematics teacher education–the mission of Mathematics Teacher Educator–requires that manuscripts convey more than stories of practice, however compelling. Manuscripts must include evidence of the effectiveness of the intervention being described beyond anecdotal claims or personal intuitions. As the Editorial Panel articulated in the call for manuscripts, “the nature of evidence in a practitioner journal is different from that in a research journal, but evidence is still critically important to ensuring the scholarly nature of the journal. Thus, authors must go beyond simply describing innovations to providing evidence of their effectiveness. Note that effectiveness implies that something is better and not just different as a result of the innovation.” Hence, claims must be supported by evidence. In this editorial, I discuss the nature of evidence appropriate for articles in Mathematics Teacher Educator