No one would argue with the claim that teaching mathematics requires mathematics knowledge. However, a clear description of such knowledge needed for teaching has been surprisingly elusive. To differentiate teachers' levels of mathematical knowledge, numerous studies have examined whether a teacher has a certification in math or a degree as well…

Widespread agreement exists that U.S. teachers need improved mathematics knowledge for teaching. Over the past decade, policymakers have funded a range of professional development efforts designed to address this need. However, there has been little success in determining whether and when teachers develop mathematical knowledge from professional…

In this article we discuss efforts to design and empirically test measures of teachers' content knowledge for teaching elementary mathematics. We begin by reviewing the literature on teacher knowledge, noting how scholars have organized such knowledge. Next we describe survey items we wrote to represent knowledge for teaching mathematics and…

This article is the first in a series that connects the National Council of Teachers of Mathematics "Curriculum and Evaluation Standards" with the new document, "Professional Standards for Teaching Mathematics." The four focal components of the "Professional Teaching Standards" are given, followed by a deeper…

This study explored whether and how teachers' mathematical knowledge for teaching contributes to gains in students' mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders' mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found…

This paper illustrates an approach to analyzing the content and contexts of inservice teacher education programs. Two inservice programs in mathematics for elementary teachers are compared. One program is part of a large urban school district's initiative to revise its mathematics curriculum. The other program is conducted by a local college;…

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…

This paper offers a framework for examining the role of subject matter knowledge in the teaching of mathematics. Starting with a brief review of the history of efforts to investigate the role of subject matter knowledge, the paper continues with an in-depth look at what "subject matter knowledge of mathematics" might mean. An approach to…

Learning to teach mathematics for understanding is not easy. First, practice itself is complex. Second, many teachers' traditional experiences with and orientations to mathematics and its pedagogy are additional hindrances. This paper examines teaching practices and reviews some of what is known about prospective and experienced elementary…

Utilizing three exemplary problem-solving tasks within an arithmetic framework, this article discusses the four focal components deemed necessary for the improvement of mathematics teaching, namely task appropriateness, avenues of classroom discourse, the intellectual climate within the classroom, and proper and effective methods of analysis. (JJK)

This paper considers the role that teacher educators accord to subject matter knowledge in helping teachers to change their practice. Two inservice programs that aim to effect radical change in teachers' practices are examined, one focusing on the teaching of mathematics and the other on the teaching of writing. Drawing on data from interviews and…

This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of pedagogical content knowledge caught on, it was in need of theoretical development, analytic clarification, and empirical testing. The purpose of the…

Mathematics discussions are important for helping students to develop conceptual understanding and to learn disciplinary norms and practices. In recent years, there has been increased attention to teaching prospective teachers to lead discussions with students. This paper examines the possibilities of designing a formative assessment that gathers…

The Teacher Education and Learning to Teach Study of the National Center for Research on Teacher Education combines case studies of teacher education programs with longitudinal studies of teacher learning. In this paper, the development of the theoretical framework on which instrumentation for the longitudinal study is based is discussed.…

Based on a teacher's experience of teaching third-grade mathematics, this article reviews some of the problems faced in representing mathematical concepts to children, respecting children as mathematical thinkers, and creating a sense of community in the classroom. (MDM)