Through extensive education programs and institutional reform, we must help teachers become comfortable with the new view of mathematics, Mr. Battista says -- because, once they fully understand and believe in the reform movement, teachers will lead the way in implementing it.
TEACHERS are key to the success of the current reform movement in U.S. mathematics education. However, many teachers have beliefs about mathematics that are incompatible with those underlying the reform effort. Because these beliefs play a critical role not only in what teachers teach but in how they teach it, this incompatibility blocks reform and prolongs the use of a mathematics curriculum that is seriously damaging the mathematical health of our children.
THE REFORM MOVEMENT
With its release of Curriculum and Evaluation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics (NCTM) spawned a major reform movement in school mathematics. The movement calls for abandoning curricula that promote thinking about
mathematics as a rigid system of externally
dictated rules governed by standards
of accuracy, speed, and memory....
A mathematics curriculum that
emphasizes computation and rules is
like a writing curriculum that emphasizes
grammar and spelling; both put
the cart before the horse. There is no
place in a proper curriculum for mindless
mimicry mathematics. Instead, proponents of reform envision classrooms in which students
have numerous and various interrelated
experiences which allow them to solve
complex problems; to read, write, and
discuss mathematics; to conjecture,
test, and build arguments about a conjecture's
validity; to value the mathematical
enterprise, the mathematical
habits of mind, and the role of mathematics
in human affairs; and to be encouraged
to explore, guess, and even
make errors so that they gain confidence
in their own actions.
To appreciate the magnitude of such reform, it is important to recognize that fundamental change is being called for in two areas. The first is the content of school mathematics. Historically, computational skill has been considered the most important part of mathematics for the masses. To be sure, mathematics educators of the past lamented the fact that students often did not understand concepts or why certain procedures worked. But there seemed to be universal agreement that computation was important. Computational topics drove the mathematics curriculum, especially in the elementary years.
However, the situation has changed dramatically over the last decade. Technological advances have all but eliminated the need for paper-and-pencil computational skill. As a result, a major thrust of the reform movement has been the effort to replace the current obsolete, mathematics-as-computation curriculum with a mathematics curriculum that genuinely embraces conceptual understanding, reasoning, and problem solving as the fundamental goals of instruction.
The second area in which fundamental change is being sought is in the way we view teaching and learning. When computation dominated the mathematics curriculum, the prevailing psychological view of mathematics learning was behaviorism, and attention was focused on observable behaviors, not on mathematical thinking. Education (generating understanding) and training (producing specific performance) were confused. Views of school mathematics and school learning were thus mutually reinforcing: school mathematics was seen as a set of computational skills; mathematics learning was seen as progressing through carefully scripted schedules of skill acquisition.
But current research in learning has uncovered deficiencies in instructional approaches based on behaviorism. …