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James T. Fey

One of the most beautiful, yet puzzling, features of mathematics is the occurrence, in apparently unrelated situations, of important numerical constants and patterns.

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James T. Fey

When I was a high school student 50 years ago, the mathematical tool kits of teachers and students included only chalkboards, paper and pencils, compasses, rulers, protractors, tables of trig and logarithm function values, and handmade models of geometric figures. Fortunately, the situation is now very different. Anyone who works at mathematics teaching and learning has access to powerful computational tools for statistical data analysis, graphical displays and drawing experiments, numerical approximations and spreadsheet analyses, modeling and simulation, and the symbolic manipulations that are central to algebra and calculus.

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James T. Fey

One of the most urgent practical problems facing mathematics education today is the challenge to define minimum levels of competence in mathematics and to devise teaching strategies that ensure student achievement of that competence. The phrase “minimum competence” has many meanings. For parents and employers of school graduates, dismayed by an apparent recent decline in student mathematical achievement, “minimum competence” often implies the arithmetic skills essential for survival in daily life and occupation in business or skilled trades. Teachers, confused by urgings of curriculum innovators and the criticism of skeptics. seek the secu rity of widely accepted standards for mathematical performance at various levels of schooling. College and university mathematics faculty also hope to improve the performance of entering students by specifying minimum levels of secondary school preparation.

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James T. Fey

When educators are asked to identify the crucial problems in school mathematics today, they frequently point an accusing finger at the teachers and cu rricula in elementary and middle school grades.

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Robin Marcus, Tim Fukawa-Connelly, Michael Conklin and James T. Fey

NCTM's Standards and Navigations series, NSF-funded curricula, presentations at professional conferences and workshops, and countless articles in this journal offer many attractive ideas for introducing new mathematics, applications, and instructional approaches. After encountering such ideas, we invariably return to our mathematics classrooms with some great new lessons or enhancements to try. But unless the topics that pique our interest are on the high-stakes tests that our students face, we are inevitably stymied by the sense that we do not have time to cover essential concepts and skills and take even a couple of days off for mathematical explorations that are intriguing to students and teachers but are often considered not good use of classroom time by those responsible for political decisions. We have been puzzling over this frustrating situation—trying to reconcile the persuasive recommendations for change in the content and teaching of high school mathematics with the constraints of increasingly influential testing programs and prescriptive district curricula.

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Jane Lincoln Miller and James T. Fey

Developing facility with proportional reasoning should be “one of the hallmarks of the middle grades mathematics program” (NCTM 1998, 213). Such reasoning has long been a problem for students, however, because of the complexity of thinking that it requires. Several standards-based curriculumreform projects have explored new approaches to developing students' proportional reasoning concepts and skills. Instead of offering direct instruction on standard algorithms for checking equivalence of ratios or solving proportion equations, these new approaches encourage students to build understanding and strategies for proportional reasoning through guided collaborative work on authentic problems.

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Christian R. Hirsch, Arthur F. Coxford, James T. Fey and Harold L. Schoen

Current policy reports addressing mathematics education in American schools, such as Everybody Counts (NRC 1989), Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), Professional Standards for Teaching Mathematics (NCTM 1991), and Assessment Standards for School Mathematics (NCTM 1995), call for sweeping reform in curricular, instructional, and assessment practices. Implementing the proposed reforms poses new opportunities and challenges for school districts, mathematics departments, and classroom teachers.

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Mary Ann Huntley, Chris L. Rasmussen, Roberto S. Villarubi, Jaruwan Sangtong and James T. Fey

To test the vision of Standards–based mathematics education, we conducted a comparative study of the effects of the Core-Plus Mathematics Project (CPMP) curriculum and more conventional curricula on growth of student understanding, skill, and problem-solving ability in algebra. Results indicate that the CPMP curriculum is more effective than conventional curricula in developing student ability to solve algebraic problems when those problems are presented in realistic contexts and when students are allowed to use graphing calculators. Conventional curricula are more effective than the CPMP curriculum in developing student skills in manipulation of symbolic expressions in algebra when those expressions are presented free of application context and when students are not allowed to use graphing calculators.

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Eric Gutstein, James T. Fey, M. Kathleen Heid, Iris DeLoach-Johnson, James A. Middleton, Matthew Larson, Barbara Dougherty and Harry Tunis

The NCTM's Research Committee has prepared this article as a means to raise the awareness about equity and issues surrounding equity from a research perspective as well as to support the NCTM's commitment to the Equity Principle. The committee discusses the concept of equity from three perspectives: as a subject of research, as a “critical lens” with which to examine research, and as a cross-disciplinary theme. Equity issues offer a unique opportunity to unite research and practice within mathematics education and across other disciplines.