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Articles > A Response to the Critics
A Response to the Critics
The case for reform in mathematics instruction
By James Fey, Professor
Departments of Curriculum & Instruction and Mathematics, University of Maryland
American School Board Journal, April 2000
In the relentless debate about current proposals to revitalize mathematics curricula and teaching in American schools, news articles, op-ed essays, letters, and paid advertisements in local and national media are filled with confident assertions about presumed weaknesses of the new mathematics programs. It is clear that some basic principles of these new approaches to school mathematics challenge some people's strongly held beliefs about learning, teaching, and mathematics. But before the persistent criticism stalls much-needed change in K-14 mathematics, the objections should be weighed against a strong case for reform that has been made by leading professional organizations in mathematics and education.
Calls for change in school and collegiate mathematics are in response to consistent evidence that traditional American approaches to mathematics education do not yield satisfactory student learning. Reports from international studies of mathematics achievement have suggested various ways that our textbooks and teaching could be improved with insight from practices in countries that are more effective in mathematics education. To replace a curriculum often described as 'a mile wide and an inch deep,' most of the new school mathematics programs focus attention on a core agenda of important and broadly useful mathematics. To replace instruction that asks students to watch passively while a teacher demonstrates computational techniques, the new programs encourage classroom activity that engages students in solving challenging mathematical problems.
As one of the contributing authors in two of the new programs rated "exemplary" in a recent Department of Education review, I find it hard to recognize either the intentions or accomplishments of our work in the angry rhetoric that has dominated recent media reports and opinions. Critics of intended reforms scan student text and teacher materials in search of items which, when taken out of context, make the new programs appear to be fatally flawed. They describe the content of new programs as 'remedial' and 'dumbed-down' mathematics, but that complaint has rarely been voiced by mathematicians who have advised the authors on design of the material or by experienced teachers whose advice has helped shape the content and organization of the new curricula. Critics often describe the instructional strategies of the new programs as a rigid ideology of discovery learning that is too inefficient to take all students through the mathematics that they need to master. In practice, teachers use engaging problems, games, and hands-on activities of the new programs in a variety of ways-from small-group cooperative learning to teacher-directed full-class discussions-and students respond with enthusiasm to their new roles and responsibilities in the mathematics classroom.
Professional reviews of several new programs have praised their content and presentation of mathematics, and thousands of teachers across the country have been stimulated by considering new ways to teach mathematics. But the most important recommendation for use of the new curricula and teaching methods is the simple fact that they produce improved student mathematics achievement. Programs judged exemplary in the recent Department of Education review provided evidence from extensive and careful evaluations of their use–evidence that students acquire essential basic skills in arithmetic, algebra, and geometry as well as conceptual understanding and problem-solving ability.
When critics try to glibly and sarcastically dismiss recent innovations as ill-conceived forays into "fuzzy math," their complaints should be weighed against the carefully considered judgment of outstanding mathematics teachers and the extensive evidence showing that traditional practices have consistently proven ineffective while many recent innovations have shown great promise. The broad implementation of innovative curricula is being watched closely, as it should be, but there is certainly plenty of evidence justifying exploration of new approaches to school mathematics.
© 2000 American School Board Journal
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