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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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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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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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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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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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Denise S. Mewborn

Four preservice elementary teachers were studied during a field-based mathematics methods course. The purpose of the study was to investigate the elements of mathematics teaching and learning the preservice teachers found problematic and how they resolved those problems. Data were collected in the form of individual interviews, group discussions, and individual journals. The preservice teachers exhibited concerns about the classroom context, pedagogy of mathematics, children's mathematical thinking, and, to a lesser extent, the mathematics content. The data indicate a relationship between the preservice teachers' locus of authority and the reflective quality of their thinking.

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Gwendolyn Lloyd

This article describes one student teacher's interactions with mathematics curriculum materials during her internship in a kindergarten classroom. Anne used curriculum materials from two distinct programs and taught lessons multiple times to different groups of children. Although she used each curriculum in distinct ways, her curriculum use was adaptive in both cases. Anne's specific ways of reading, evaluating, and adapting the curriculum materials contrast with previous results about beginning teachers' curriculum use. Several key factors appeared to contribute to Anne's particular ways of using the curriculum materials: features of her student-teaching placement, her personal resources and background, and characteristics of the materials. Directions for future research about student teachers' and other teachers' curriculum use are suggested in accord with these factors.

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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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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.

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Lauren M. Siegel, Gail Dickinson, Eric J. Hooper and Mark Daniels

Preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high school students construct a working Dobsonian telescope. Eleven investigations with questions and answers are included.