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In this article the development of two teachers as they make the transition from pre-service teachers to experienced teachers is examined. While these teachers participated in the same mathematics methods course and similar collaborative environments in their practicum experiences, their mathematics classroom instructional practices revealed stark differences by the time they were experienced teachers. In an effort to investigate these differences, the teachers' beliefs were explored in relation to those promoted in their pre-service course and in relation to their implementation of current mathematics education reform practices. Interview Protocols are appended. (Contains 1 table and 2 figures.)

The increased popularity of lesson study in the United States--an approach to professional development initiated in Japan more than a century ago--is due in large part to findings from the 1995 Trends in International Mathematics and Science Study (TIMSS) video study and the subsequent book, "The Teaching Gap" (Stigler and Hiebert 1999). "Lesson study" refers to a classroom-based form of professional development consisting of a four-step cycle. Applying the lesson study model to professional development can impact classroom teachers and teacher educators who design professional development experiences for other teachers. Lesson study is not just about improving a single lesson, it's about building pathways for ongoing improvement of instruction. The authors engaged in a lesson study when designing a professional development workshop for classes with both in-service and preservice teachers. The goal was for teachers to reflect on how their own lessons develop students' understanding of mathematics. Specifically, the authors wanted teachers to think about the tasks and discourse promoted by various textbooks. Using the lesson study cycle, the authors looked at research, which they used to guide the design of a lesson. Then they implemented the lesson study in three settings: (1) a professional development meeting for in-service teachers; (2) a graduate-level mathematics education course; and (3) a preservice elementary mathematics education course. Each author led at least one session and observed the other two. After each professional development experience, they met to discuss what they perceived to be the strengths and weaknesses of the session. These debriefing meetings focused on what the participants had said and done during the workshop. After each debriefing, the authors revised the lesson before teaching it in subsequent settings. In this article, they describe their experience. (Contains 2 figures.)

Three widely used sixth-grade textbooks were studied to see how fraction concepts were represented. The textbooks selected were "Connected Mathematics," "Middle Grades MathThematics," and Glencoe's "Mathematics: Applications and Concepts Course 1." Three specific areas were examined: representation mode, model, and problem context. Results of the findings as well as classroom implications are explored. (Contains 6 tables.)

This article describes the author's struggles, journey, and resolve to reform her teaching practice to align with her beliefs about teaching and learning mathematics. (Contains 6 figures.)

This longitudinal study documents the development of mathematics teachers as they make the transition from preservice to experienced teachers. Collaborative learning environments were created for these teachers in their field-based classrooms during their last year in the teacher-education program. The authors anticipated that these learning environments would prepare more effective novice teachers. A comparison of baseline data with end-of-project data indicated that the participants' beliefs about the teaching and learning of mathematics, as well as their epistemological views, had changed; however, many participants did not base their instructional decisions on a careful analysis of their students' thinking processes. A follow-up study revealed a more accurate picture of the change in participants' beliefs and practices, as some of them, now experienced teachers, exceeded project expectations and had become effective teachers. Factors that either hindered or contributed to the development of teachers' practice are also identified. (Contains 2 tables and 2 figures.)