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Jen Munson

Understanding mathematics teacher noticing has been the focus of a growing body of research, in which student work and classroom videos are often used as artifacts for surfacing teachers’ cognitive processes. However, what teachers notice through reflecting on artifacts of teaching may not be parallel to what they notice in the complex and demanding environment of the classroom. This article used a new technique, side-by-side coaching, to uncover teacher noticing in the moment of instruction. There were 21 instances of noticing aloud during side by side coaching which were analyzed and classified, yielding 6 types of teacher noticing aloud, including instances in which teachers expressed confidence, struggle, and wonder. Implications for coaching and future research on teacher noticing are discussed.

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C. Alan Riedesel and Marilyn N. Suydam

There is agreement between mathematicians and educators that future and inservice teachers need a good background in mathematics subject matter. Toward this end many colleges, universities, and school systems have developed content courses for elementary teachers that are very similar to the recommendations of the Committee on Undergraduate Program in Mathematics of the Mathematical Association of America.

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Michele B. Carney, Jonathan L. Brendefur, Gwyneth R. Hughes and Keith Thiede

As mathematics teacher educators, it is imperative that we have high-quality tools that conceptualize and operationalize mathematics instruction for large-scale examination. We first describe existing instructional practice survey scales, including their conceptualization of practice and related validity evidence. We then present the framework and initial validity evidence for our mathematics instructional practice survey. Survey participants were inservice teachers in a statewide mandated mathematics professional development course. Statistical analyses indicate the items measure two constructs: social-constructivist and transmission-based instructional practice. Of particular interest is the result that these two constructs were negligibly correlated. This is in contrast to the generally accepted notion that social-constructivist and transmission-based instructional practices are the two polar ends of a single construct for describing instructional practice.

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Eric Milou and Jay Schiffman

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed in this article was conducted with a group of preservice and inservice teachers, and the objectives included examining patterns, making conjectures, and using data analysis to construct scatter plots and tables, all in the spirit of discovering mathematics. This activity is based on a concept called the multiplicative digital root of an integer (Sloane 1973). Here we take the term integers, unless otherwise qualified, to mean positive integers.

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Welcome to another year of “Technology Tips.” I, Suzanne Harper, will be the primary editor for the 2005–2006 column issues, and it is my pleasure to introduce this year's new co-editor, Shannon Driskell. Shannon teaches undergraduate and graduate mathematics content courses at the University of Dayton in Ohio. Her main interests include the appropriate use of technology in K–12 mathematics, preservice and inservice teachers' pedagogical content knowledge, and the teaching and learning of geometry. We are always looking for new and interesting ways for teachers and students to use technology effectively. If you have a tip that can help other teachers learn how to use a technology application in the classroom, please send ideas to my contact address. I also would like to take the time to thank Hollylynne Stohl Lee for her amazing dedication and guidance as editor of the column last year.

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The TEACHERS' CENTER in San Diego offers a unique approach to inservice teacher education. Housed in two classrooms of an elementary school and combining the features of a library, a lounge, and a workshop, the Center is a place where teachers, in a comfortable setting and uninterrupted by bells, can exchange ideas, share materials, and examine the newest instructlonal aids. Consultant services are available, and a rich collection of resources and an exhibit of manipulative materials are featured. A series of eight Saturday sessions is offered and teachers can receive one unit of credit for every two Saturday sessions attended. Various other noncredit workshops, discussion groups, and special programs are presented; all an outgrowth of problems and needs defined by teachers. The Teachers' Center is supported jointly by the Center for the Improvement of Mathematics Education, the San Diego Unified School District, the Greater San Diego Mathematics Council, and the National Science Foundation. For further information contact Leonard M. Warren, Project Director, The Teachers' Center, Jackson Elementary School, 4365 54th Street, San Deigo, CA 92115

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Edward T. Ordman

A few years ago I showed a class of prospective elementary teachers a theorem that I had always assumed to be part of the folklore of topology. Apparently, however, it is little used today, either by teachers or by mathematical researchers. It was so well received by the class of prospective teachers that I then showed it to inservice teachers, and finally I visited a few elementary classes to try it on the pupils firsthand. It was regularly a success—in one instance pupils were so excited they showed it to fri ends during lunch and disrupted school for much of the afternoon. Even at the third-grade level, some pupils were able to follow the reasoning well enough to convince another classroom teacher (who had not seen the material in advance) of the truth o f the theorem. At higher grade levels, the theorem continues to be appropria te for any pupils who have not yet had exposure to the “theorem-proof” arguments of the sort common in Euclidean geometry.

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

. , & Bonner , S. M. ( 2016 ). Preservice and inservice teachers’ knowledge, beliefs, and instructional planning in primary school mathematics. Teaching and Teacher Education , 56 , 1 – 13 . doi: 10.1016/j.tate.2016.01.015 18

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Carlos Nicolas Gomez and AnnaMarie Conner

preservice and inservice teachers (e.g., Cooney, Shealy, & Arvold, 1998 …)” (p. 140). In these citations, CSA’s work was often cited as one of several studies that investigated something about beliefs, referring to their general topic rather than to one