In the buzzing activity of the mathematics classroom, teaching in a way that effectively responds to and furthers students' thinking can be quite challenging. Given that teachers' instructional decisions will directly influence students' learning, it is extremely important to develop the sorts of practices that lead to productive in-the-moment…

With international exams (PISA and TIMSS) producing results every three or four years, there is near continual talk of East Asian dominance in mathematics education. Beyond the reporting of scores, some studies have compared mathematics teaching in these countries with U.S. instruction. However, researchers are not (usually) grade school math…

Division of fractions is often considered the most mechanical and least understood topic in elementary school. Enacting fraction division tasks in meaningful ways requires that teachers know not only "how" fraction division works but also "why" it works. The authors have created materials to help preservice teachers develop that knowledge. To…

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

Every day students from across the United States enter their math classrooms, take their seats, sit passively as their teachers teach the content, and then go home only marginally prepared to solve the problems their teachers assigned. Although the challenges of teaching are universal and as old as Methuselah, the advantage today is that educators…

In this article we examine the activities of 2 public lessons prepared and conducted by a group of elementary school teachers in China. We employ the conceptual lens of deliberate practice to understand how the public lesson activities possibly contributed to improvement of the teachers' knowledge and instructional performance. We found that…

Researchers (Ball, 2003; Ma, 1999; Schulman, 1986) have long investigated how a teacher's subject matter and pedagogical content knowledge impact on students' learning of mathematics. In an attempt to account for the relationship between teacher knowledge and student learning, this study examined four Romanian first grade teachers' knowledge about…

In this paper we explore the growth of understanding of a group of preservice teachers, and their instructor, as they work collectively together on what we describe as a "mathematics for teaching" task. Through drawing on elements of improvisational theory, in particular the notion of the "better idea," we analyse how the preservice teachers'…

The authors describe ways in which a history of mathematics course can help prospective teachers of mathematics develop knowledge they will need for teaching. The types of knowledge include content knowledge of mathematics, knowledge of mathematics for teaching, and pedagogical knowledge.

This article examines Finnish cooperating physics teachers' conceptions of teacher knowledge in physics. Six experienced teachers were interviewed. The data was analyzed to form categories concerning the basis of teacher knowledge, and the tradition of German Didaktik and Shulman's theory of teacher knowledge were used in order to understand the…

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

This paper analyses how the mathematical knowledge needed by a teacher has been described by several mathematics educators, all based on Shulman's notions of Subject Matter Knowledge and Pedagogical Content Knowledge. In particular, it looks at the notion of Mathematics Knowledge for Teaching, as elaborated by Ball and her research group. It then…

Teaching mathematics to elementary children requires highly developed content knowledge, and questions of how teachers acquire this knowledge are of significant concern to teacher preparation programs. Even with research to the contrary, some policy makers in the USA propose additional advanced mathematics courses. One voice that is missing when…

Principals are very aware that there is a great deal of competition in attracting qualified teachers of mathematics to their school, since there are just not enough qualified mathematics teachers out there. Recent studies of the qualifications of teachers in Australian schools have confirmed that there is a crisis in the supply of qualified…

This study is an evaluation on whether middle-level mathematics teachers' participation in a week-long in-service course on middle-level mathematics concepts increases their understanding of this content. A secondary purpose of this study is an exploration of teacher perceptions before and after the institute via self-report surveys. Participants…