One of the most beautiful, yet puzzling, features of mathematics is the occurrence, in apparently unrelated situations, of important numerical constants and patterns.
James T. Fey
Among the objectives of school mathematics instruction, one of the most important is to develop understanding of the structure, properties, and evolution of the number systems. The student who knows the need for, and the technique of, each extension from the natural numbers through the complex numbers has a valuable insight into mathematics. Of the steps in the development, that from the rational numbers to the real numbers is the trickiest.
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.
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.
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.
For mathematics educators of a certain age or those with particular expertise in the history of mathematics education, the appearance of a book that purports to describe, analyze, and explain the “new math” movement of the 1950s and 1960s quite reasonably prompts the question: What else could possibly be said about that iconic era? Others with less experience in or historical knowledge of the field might pass on the book because they are only vaguely aware of the new math as a longago and thoroughly discredited effort to reform school mathematics curricula and teaching. However, I think mathematics educators in both groups–knowledgeable veterans and newcomers to the field–will find Christopher J. Phillips's retelling of the new math story a fascinating read that is filled with timeless insights into the academic and political dynamics of school mathematics and, more broadly, American education.
Richard Hollenbeck and James Fey
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.
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.