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Erik D. Jacobson

This study (n = 1,044) used data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between field experience focus (instruction- or exploration-focused), duration, and timing (early or not) and prospective elementary teachers' intertwined knowledge and beliefs about mathematics and mathematics learning. Early instruction-focused field experience (i.e., leading directly to classroom instruction) was positively related to the study outcomes in programs with such field experience of median or shorter duration. Moreover, the duration of instruction-focused field experience was positively related to study outcomes in programs without early instruction-focused field experience. By contrast, the duration of exploration-focused field experience (e.g., observation) was not related to the study outcomes. These findings suggest that field experience has important but largely overlooked relationships with prospective teachers' mathematical knowledge and beliefs. Implications for future research are discussed.

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Kristen N. Bieda, Jillian Cavanna, and Xueying Ji

Field experience can be a rich site for intern teachers to develop the knowledge and skills they need for effective teaching. Lesson study has been shown to be a powerful form of professional development that enhances practicing teachers' mathematical knowledge for teaching through collaborative inquiry with their peers. In this article, we discuss the use of mentor-guided lesson study to support mentor and intern collaboration in the field and share what we have learned about its potential to support interns' attention to student thinking. We will also share insights from the field for those interested in implementing this activity in teacher preparation coursework.

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Corey Webel and Sheunghyun Yeo

Educators ( AMTE, 2017 ) has advocated for stronger connections between methods courses and field placements to support PSTs in navigating this tension, and some research has explored new models, such as using mediated field experiences ( Zeichner, 2010

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Crystal Kalinec-Craig, Emily P. Bonner, and Traci Kelley

al., 2012 ), SEE Math serves as a purposeful field experience and case study for TCs as they learn how to design, test, and revise equity-oriented practices that leverage what children already know about mathematics. SEE Math pairs a TC who is in

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Malcolm D. Swan and Orville E. Jones

Among the educational objectives for teaching social science and mathematics is that of developing the pupil's ability to understand the world in which he lives. Included in this ability is the development of percepts—commonly referred to as mental images—relating to distance, weight, height, volume, temperature, etc. If this objective is to be achieved, the teacher should provide pupils with experiences that will help them develop such understandings. Some teachers believe it almost impossible to do so without direct experience, while other teachers assume that pupils develop sufficiently adequate images through solving mathematical problems found in textbooks and other written source materials.

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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.

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Sarah A. Roller

Teachers and mathematics teacher education scholars have identified field experiences and quality mentoring as influential components of math teacher preparation and development. Yet, quality mentoring is a complex and demanding practice. Providing educative feedback to novices, particularly that which encourages reflection versus evaluation, can be challenging work for mentors. To study the potential of an intervention for providing professional development for mentors, I worked with pairs of mentors and prospective teachers (PSTs) offering Smith's (2009) noticing and wondering language as a way of structuring mentoring conversations that maintain both descriptive and interpretive analytic stances. Analysis of before and after conversations provided evidence of how mentor-PST pairs adopted noticing and wondering language, and in particular illuminated the ways in which the language structure might support interpretive mentoring conversations for studying teaching. The results suggest that mathematics teacher educators may want to consider what makes wondering challenging work and how to best support wondering in educative mentoring conversations.

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Linda L. Cooper and Martin C. Roberge

Let's go wading! Students connect fundamental mathematics concepts in this real-world, problem-solving field experience.

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Denise A. Spangler and Allyson Hallman-Thrasher

We describe an activity designed to help preservice elementary school teachers develop mathematical knowledge for teaching in the domain of facilitating mathematical discussions. The activity involved preservice teachers writing task dialogues, imaginary conversations between a child and teacher about a problem-solving task, in which they practice responding to correct, partially correct, and incorrect student responses. Preservice teachers then implemented these same tasks with children in a field experience setting. We describe 2 different iterations of the activity and field experience in detail as well as the insights into preservice teacher knowledge each iteration afforded us.

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Lewis H. Walker and Lynn S. Waldron

Typical of many teacher preparation programs, the preservice teachers at Lander University in Greenwood, South Carolina, engage in a number of field experiences prior to their extended student teaching. During the field experience that immediately precedes student teaching, each preservice teacher spends fifty hours working with students in a single classroom. In preparation for this experience, the preservice teachers develop and design ten-day units centering on social studies that integrate mathematics, language arts, natural science, health, and the creative and kinesthetic arts. One requirement of designing the unit is to include at least two integrated lessons involving mathematics in which the classroom students operate outside the school classroom.