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Drawing on several decades of research findings, the National Council of Teachers of Mathematics (NCTM) produced, between 1989 and 1995, three volumes of Standards in which members of the mathematics education community formulated new visions of mathematics learning, teaching, and assessment. These new visions comprise an ambitious agenda for the mathematics classroom—one that includes, but surpasses, mastery of facts and procedures, the mainstay of extant practice—designed to engage students in the exploration of mathematical ideas and their interrelationships. Students would now be invited to articulate their ideas, and teachers to identify and mobilize those elements in children's thinking upon which stronger conceptions can be built. Paralleling this ambitious departure in teaching practice, new means of assessment were proposed to capture progress toward these far-reaching goals.

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Karen C. Fuson

Research on multidigit addition and subtraction is now sufficient to question some present textbook practices and suggest alternatives. These practices revolve around the organization and placement of topics within the curriculum and around teaching/learning methods. These questions are being raised because the evidence indicates that U.S. children do not learn place-value concepts or multidigit addition and subtraction adequately and even many children who calculate correctly show little understanding of the procedures they are using (e.g., Cauley, 1988; Karnii & Joseph, 1988; Kouba et al., 1988; Labinowicz, 1985; Lindquist, 1989; Resnick, 1983; Resnick & Omanson, 1987; Ross, 1989; Stigler, Lee, & Stevenson, in press; Tougher. 1981).

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Frank K. Lester Jr. and Dylan Wiliam

During the past few years, diverse individuals and groups have begun to promote a variety of old and new instructional approaches, programs, and policies for mathematics education (Dixon, Carnine, Lee, Wallin, & Chard, 1998; Jacob, 1997; Kilpatrick, 1997; Wu, 1997). Researchers are being exhorted to gather and analyze data for evaluating the efficacy of various instructional approaches and curricula. Moreover, individuals both within and outside of the mathematics education research community have offered “evidence” to support specific agendas. In view of this turbulent state of affairs, it seems especially timely for researchers and those interested in research to engage in discussions of the notions that are at the heart of all educational research activity. This essay addresses one of these fundamental notions—evidence.

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A central part of the charge to the Research Advisory Committee (RAC) from the Board of Directors of the National Council of Teachers of Mathematics (NCTM) is to “act as a catalyst within the mathematics education research community to support and to focus attention on important or under-discussed issues.” In this report we respond to this charge by raising issues related to the role and potential effect of research in a school culture that has become so complex that systematic study of problems seems almost impossible. Before launching into this discussion, we provide an update on research activities of special significance.

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Jill Adler and Zain Davis

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 builds on Ball and Bass' notion of “unpacking” in the mathematical work of teaching. The analysis of formal evaluative events reveals that across the range of courses, and particularly mathematics courses designed specifically for teachers, compression or abbreviation (in contrast to unpacking) of mathematical ideas is dominant. The article offers theoretical and practical explanations for why this might be so, as well as avenues for further research.

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Martin A. Simon

Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think about, and work with, the multiple theories available. I present alternatives to views of the competition or supersession of theories and indicate the kinds of discussions that will support effective theory use in mathematics education research. I describe the potential for mathematics education researchers to make informed, justified choices of a theory or theories to address particular research agendas.

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Paola Sztajn

This Research Commentary addresses the need for standards for describing mathematics professional development in mathematics education research reports. Considering that mathematics professional development is an emerging research field, it is timely to set expectations for what constitutes high-quality reporting in this field. Through an examination of the research reports on the topic published in the Journal for Research in Mathematics Education during the past decade, I offer a framework and a set of features to be used in initiating discussions about pros and cons of having reporting standards. I contend that when researchers have standards for describing the mathematics professional development they are studying, better quality will be attained in the new research field.

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Eva Thanheiser, Amy Ellis and Beth Herbel-Eisenmann

In this Research Commentary, 3 JRME authors describe the process of publishing their research in JRME. All 3 authors published parts of their dissertation in JRME and are sharing their stories to help (new) researchers in mathematics education better understand the process and to offer (experienced) researchers in mathematics education a tool that can be used to mentor their less experienced colleagues and students. The authors address preparing, conceptualizing, and writing a manuscript as well as responding to reviewers.

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Addressing Racism

JRME Equity Special Issue Editorial Panel

Beatriz D'Ambrosio, Marilyn Frankenstein, Rochelle Gutiérrez, Signe Kastberg, Danny Bernard Martin, Judit Moschkovich, Edd Taylor and David Barnes

This is a dialogue extracted from a conversation among some members of the Equity Special Issue Editorial Panel (Beatriz D'Ambrosio; Marilyn Frankenstein; Rochelle Gutiérrez, Special Issue editor; Signe Kastberg; Danny Martin; Judit Moschkovich; Edd Taylor; and David Barnes) about racism in mathematics education. It raises issues about the use of terms such as race and racism; understanding fields of research outside of mathematics education; the kinds of racialization processes that occur for students, teachers, and researchers; the social context of students; the achievement gap; and the role of mathematics education in the production of race.

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Introduction to the JRME Equity Special Issue

JRME Equity Special Issue Editorial Panel

Beatriz D'Ambrosio, Marilyn Frankenstein, Rochelle Gutiérrez, Signe Kastberg, Danny Bernard Martin, Judit Moschkovich, Edd Taylor and David Barnes

This article provides an introduction to the JRME Equity Special Issue. It includes a rationale for the special issue, the process for selecting articles, and a description of the kinds of articles that will appear in the special issue. It concludes with a set of questions that teachers and researchers can and should ponder as they read the articles in the special issue.