A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of…

This article reports on the first 4 years of an effort to develop comprehensive and sustainable mathematics education reforms in high poverty middle schools. In four related analyses, we examine the levels of implementation achieved and impact of the reforms on various measures of achievement in the first 3 schools to implement the Talent…

This article discusses the challenge of improving the interrelationships between research and practice in mathematics education, and it outlines actions being taking to respond to that challenge. The need for improvement is bidirectional. The practice of classroom mathematics teaching needs to be better informed by an understanding of the…

Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we provide evidence that…

The No Child Left Behind Act of 2001 (NCLB, 2002) elevates the importance of educational research and thereby provides opportunities for mathematics education researchers in its support for and funding of rigorous research studies and its requirement of effective, research-based practices. At the same time, by demanding more of overburdened…

Monitoring educational changes over many years is problematic when there are differences in curricula, the nature of the variables being measured, and the selection of participants. Rasch measurement techniques provide a procedure that enables each of these issues to be examined. Using archived and specially collected data, tests of numeracy…

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of…

The relationship between normative patterns of social interaction and children's mathematical thinking was investigated in 5 classes (4 reform and 1 conventional) of 7- to 8-year-olds. In earlier studies, lessons from these classes had been analyzed for the nature of interaction broadly defined; the results indicated the existence of 4 types of…

Institutions of higher education are having a difficult time filling positions requiring a doctorate in mathematics education. This study reports that about one half of the 83 national searches by institutions for mathematics educators for the 2005-06 academic year were unsuccessful. Salaries for assistant professors were slightly higher in…

This article describes an investigation into mathematics for teaching in current teacher education practice in South Africa. The study focuses on formal evaluative events across mathematics teacher education courses in a range of institutions. Its theoretical orientation is informed by Bernstein's educational code theory and the analytic frame…

Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…

Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is…

The article discusses the ways that less successful mathematics students used graphing software with capabilities similar to a basic graphing calculator to solve algebra problems in context. The study is based on interviewing students who learned algebra for 3 years in an environment where software tools were always present. We found differences…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…