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This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices--in particular, their eliciting and interpreting of students' mathematical thinking--in the context of an elementary mathematics methods assignment, and the ways in which the scaffolds provided shaped their practice. We found that the scaffolds differentially supported their practice and suggest strategic improvement of the focus and organization of different types of scaffolds. Findings from the study contribute to the conceptualization and design of scaffolds for practice-based learning opportunities in teacher education. (Contains 3 figures and 3 tables.)

Despite its centrality in teaching, what it takes to identify the goals of instruction and use those goals to manage the work has yet to be articulated in ways that it can be adequately studied or taught. Using data from preservice teachers' mathematics lessons, this study identifies and illustrates seven central tasks of "steering instruction toward the mathematical point": attending to and managing multiple purposes, spending instructional time on mathematical work, spending instructional time on the intended mathematics, making sure students are doing the mathematical work, developing and maintaining a mathematical storyline, opening up and emphasizing key mathematical ideas, and keeping a focus on meaning. Findings can inform teacher education, research on teaching, and the design of curriculum materials. (Contains 4 notes, 1 figure and 8 tables.)

This paper investigates the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the mathematical quality of instruction by comparing the enactment of a fractions problem taught by two teachers with differing MKT. It was found that MKT seem to support teachers' precise use of mathematical language and to prevent errors; the curriculum materials provided a rich representational context for mathematical work. However, teachers' orientations toward mathematics and mathematics teaching and their goals for student learning also seemed to contribute to their use of curriculum materials to engage students with rich mathematics and to support students' participation in the development of the mathematics. Although orientations and goals made it more likely for a teacher to use multiple representations and elicit multiple solution methods, MKT was needed to productively use these elements in instruction. Based on this analysis, it is argued that there are aspects of developing orientations and goals that are related to MKT. (Contains 5 notes and 2 figures.)

Background/Context: Discussion is central to mathematics teaching and learning, as well as to mathematics as an academic discipline. Studies have shown that facilitating discussions is complex work that is not easily done or learned. To make such complex aspects of the work of teaching learnable by beginners, recent research has focused on approaches to teacher education that decompose practice into smaller tasks or routines that can be articulated, unpacked, studied, and rehearsed. Purpose/Objective/Research Question/Focus of Study: Drawing on the elements of Grossman et al.'s (2009) framework for pedagogies of practice in professional education, this article describes an approach to analyzing teaching practice that supports the design of teacher education in which novices to learn how to engage in high-leverage teaching practices and simultaneously develop a sense of why the work is done. Setting: The context for the study is a mathematics methods course for prospective elementary teachers. Research Design: The study involved qualitative analysis of both the design of the course and its implementation. Conclusions/Recommendations: Results from this study suggest that: (1) Decomposing teaching into nested practices of varying grain sizes that maintain the connection between techniques and domains can support beginning teachers in attending simultaneously to the how and the why of practice, as well as provide a map of teaching that teacher educators can use to support the learning of teaching. (2) Nesting early approximations of practice inside subsequent ones is a way to support beginning teachers in building toward recomposed teaching practice. As practices are nested, teacher educators can increase the complexity of the approximations by adjusting the content and authenticity of the context of practice as well as by decreasing the amount scaffolding provided. (3) Assessment is vital to pedagogies of practice. Decompositions, approximations, and representations of practice need to be developed in ways that support assessment for the array of teacher education purposes. (4) Because subject matter is at the heart of teaching, it is crucial to attend to the ways in which the content interacts with pedagogies of practice.

This article describes and analyzes a program of work in elementary mathematics teacher education at the University of Michigan that has, for a decade, been a site for the development of approaches to preparing beginning K-8 mathematics teachers that are both aimed at practice and centered in content. Among the products of this work are video records, instructional tasks, and assessments, as well as structures for collective work on our courses. These materials and ways of working comprise a collection of resources for both the systematic improvement of the knowledge base for teacher education and the professional development of teacher educators. This practice-based approach to the development of both our courses and their instructors has enabled us to improve professional instruction and to build knowledge that is useful beyond a particular course or the individuals who work in it. We begin by discussing 2 central problems of teacher education that our group has tried to address and then describe the types of materials and ways of working that we have developed. We analyze the features of the professional curriculum produced from this work, relate them to the problems, and consider issues about transferability to contexts beyond our own. (Contains 2 figures and 4 notes.)