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Jennifer Ruef

article shares a study of a drawing task administered at the beginning and end of a master’s level teacher education program ( Appendix A ). PSTs were tasked with drawing an optimized vision of teaching and writing a brief description of their depiction

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Dawn M. Woods and Anne Garrison Wilhelm

variation is likely what teachers are aiming for instructionally. Relevant Literature Instructional Vision Teachers’ instructional visions are the discourses that they employ to describe ideal classroom practice, both with respect to the structures

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Charles Munter

This article introduces an interview-based instrument that was created for the purposes of characterizing the visions of high-quality mathematics instruction of teachers, principals, mathematics coaches, and district leaders and tracking changes in those visions over time. The instrument models trajectories of perceptions of high-quality instruction along what have been identified in the literature as critical dimensions of mathematics classroom practice. Included are a description of the methods by which an analysis of interview data was integrated with previous findings from the research literature in order to develop leveled rubrics for assessing visions of high-quality mathematics instruction, a report of the results of using the instrument to code more than 900 interviews, and a discussion of the possible applications and benefits of such a methodological approach.

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Frank K. Lester JR and Diana Lambdin Kroll

Edited by Frances R. Curcio and Alice F. Artzt

Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.

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Ralph W. Cain and Patricia A. Kenney

The NCTM's Curriculum and Evaluation Standards for School Mathematics proposes a vision for assessment in the mathematics classroom that would “help teachers better understand what students know and make meaningful instructional decisions” (NCTM 1989, 189). For assessment to be truly aligned with the mathematics curriculum, teachers would give more emphasis to taking a holistic view of mathematics—using multiple assessment methods, including written, oral, and performance formats, and incorporating calculators, computers, and manipulatives as part of assessment. Thus, mathematics teachers would be empowered to trust their own abilities and judgments in the area of mathematics assessment (Clarke, Clarke, and Lovitt 1990; Cooney and Badger 1990; Schoen 1989; Webb and Briars 1990).

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Sharyn L. Stein

The boxed paragraph's objective can also be considered one of the fundamental concepts found in NCTM's Curriculum and Evaluation Standards for School Mathematics, published in 1989. Making the underlying assumption that a metamorphosis was drastically needed in our nation's mathematics curriculum, the standards document thoroughly examined and analyzed all aspects of the current methods by which mathematics is presented at all grade levels (K–12), as well as what is considered to be essential material that must be presented to students. (For an overview of the Curriculum and Evaluation Standards, see Thompson and Rathmell [1988].) However, the succinct statement below is not the product of the NCTM's standards; rather it is the wisdom of Jacob William Albe1t Young (1865–1948), a tum-of-thecentury pioneer in the field of educational pedagogy. (J. W. A. Young is not to be confused with John Wesley Young, 1879–1932, a professor of mathematics at Dartmouth College during the same era.)

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Ray Robicheaux

What does it mean to “know” mathematics? This philosophical question was initially debated before the framing of the Currculum and Evaluation Standards for School Mathematics (NCTM 1989). For several years, “knowing” mathematics has meant knowing a set body of rules and procedures; more specifically, “knowing” mathematics has meant “knowing how” to perform an algorithm. Students in the United States fared poorly on problem solving and reasoning questions as measured by the National Assessment of Educational Progress (Carpenter 1988); their status has been even worse in international comparisons in this area (Steen 1987). These combined findings have caused people in business and indusby, the mathematics and science community, and the educational community to call for reform of mathematics education. The question has become one of either “fixing” what we have or forging an entirely new approach that focuses on mathematics as a complex, holistic thought process featuring heuristics and analyses. The latter interpretation of “knowing” mathematics has prevailed, bolstered by a broad-based, grass roots following. to become the vision of the Standards.

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Richard Kalman

It is 21 February 2004. Mathematics teacher Mark Downe enters his high school classroom and checks its layout. The fifteen computers set against the walls and the two round tables in the center create an open, spacious look. His twenty-eight tenth graders follow him in, heading for the computers m pairs. Downe quickly settles them down to work. As usual, Patrick and Patricia need special urging.

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Peter M. Eley, Kelly J. Charles and Latonya L. Leeks

Classroom observation presents evidence that using meaningful data and exciting presentations can help strengthen student interest in STEM fields.

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Jeremy A. Kahan and Harold L. Shoen

Problems and problem solving have a long history in mathematics education (Dewey, 1910; National Council of Teachers of Mathematics [NCTM], 1980; Pólya, 1945; Schoenfeld, 1992; Stanic & Kilpatrick, 1988). The Curriculum and Evaluation Standards for School Mathematics asserted, “Problem solving should be the central focus of the mathematics curriculum” and placed it as Standard 1 (NCTM, 1989, p. 23). The 1990s saw the development of school mathematics curricula based on various interpretations of these Standards. In most of these curricula, the mathematics emerges from the solution of problems, and there is a growing body of research evidence supporting the effectiveness of these curricula (Senk & Thompson, 2003). Teaching mathematics through problem solving also continues to be a focus of mathematics educators independent of the curriculum that is used (Schoen & Charles, in press).