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May 2003, Volume 34, Issue 3

FEATURES

Border Crossing: Relating Research and Practice in Mathematics Education
Edward A. Silver
The Journal for Research in Mathematics Education (JRME) is rare among major educational research journals. It is one of very few published by an organization whose membership consists primarily of teachers at the precollege level. JRME is also rare in the portfolio of publications produced by the National Council of Teachers of Mathematics (NCTM). The intended target audience for NCTM's other journals and most of its books is teachers and those who work to prepare and support teachers in their work. In contrast, although JRME also contains research reports that could be of interest to practitioners, especially in the face of recent calls for research-based evidence, the journal's primary target audience is researchers. This unique situation offers many opportunities, yet it also poses some challenges. Over the years, the journal has depended on the effective management of these opportunities and challenges not only by its editors but also by staff at NCTM's Headquarters.

We Want a Statement That Is Always True: Criteria for Good Algebraic Representations and the Development of Modeling Knowledge
Andrew Izsak
This article presents a case study in which two eighth-grade students developed knowledge for modeling a physical device called a winch. In particular, the students learned (a) to distinguish equations that are true for any value of the independent variable from  equations that constrain the independent variable to a unique value and (b) to solve the latter type of equation to determine when specific physical events occur. The analysis of how these understandings emerged led to two results. First, the analysis  demonstrated that students have and can use criteria for evaluating algebraic representations.  Second, the analysis led to a theoretical frame that explains how students can develop modeling knowledge by coordinating such criteria with knowledge for  generating and using algebraic representations. The frame extends research on students’ algebraic modeling, cognitive processes and structures for using mathematical representations, and the development of mathematical knowledge.

Teacher Variables That Relate to Student Achievement When Using a Standards-Based Curriculum
Harold L. Shoen, Kristen J. Cebulla, Kelly F. Finn, Cos Fi
We report results from a study of instructional practices that relate to student achievement  in high school classrooms in which a standards-based curriculum (Core-Plus) was used. We used regression techniques to identify teachers' background characteristics, behaviors, and concerns that are associated with growth in student achievement  and further described these associations via graphical representations and logical analysis. The sample consisted of 40 teachers and their 1,466 students in 26  schools. Findings support the importance of professional development specifically aimed at preparing to teach the curriculum. Generally, teaching behaviors that are consistent with the standards' recommendations and that reflect high mathematical  expectations were positively related to growth in student achievement.

Setting the Record Straight or Setting Up a Research Agenda?—A Review of Standards-Based School Mathematics Curricula
Jinfa Cal
In the late 1980s and early 1990s, the National Council of Teachers of Mathematics (NCTM) published its Standards documents, which provided recommendations for reforming and improving K–12 school mathematics. With extensive support from the National Science Foundation, a number of Standards-based school mathematics curricula were developed and implemented to align with the recommendations in the Standards. The implementation of Standards-based instructional materials requires change not only in how mathematics is viewed but also in how mathematics is taught and learned. Thus, teachers and school districts face challenges when trying to implement Standards-based curricula. Moreover, because the Standards-based curricula claim to have different learning goals and they also look very different from traditional mathematical curricula, some parents, professionals, and school communities challenge both the new goals and the efficacy of these new curricula.