Background

"State of the art" is a goal that every school mathematics program in the United States would say it strives for. It is a goal owed our children and it is attainable. State of the art depends upon curriculum reform. In the current national curriculum reform movement, initiated by the National Council of Teachers of Mathematics and supported at all levels by those involved with mathematics education, it is particularly exciting to be engaged in transforming mathematics teaching and learning to reach the state of the art.

Major curriculum reform is not new in the field of school mathematics. The last such reform was the "new math" of the late 1950s and 1960s which emphasized the unifying mathematical concepts of logic and set theory. For a variety of reasons the new math did not receive widespread acceptance. Specifically, it did not pay close attention to how students learn and what they are capable of learning at different ages. It also did not address what teachers know about mathematics and pedagogy or how they can best enhance their own knowledge.

The new math was followed by the "back to basics" movement which emphasized rote memorization of arithmetic facts and the learning of paper-and-pencil algorithms. The current reform movement grew out of the inability of the back to basics movement to address key issues, including

Neglect of higher order thinking and problem-solving skills;
Disquieting findings about American students in recent international studies on mathematics achievement, despite the return to basics;
Changing mathematical skills needed in the work force;
New research findings on teaching and learning mathematics; and
The mushrooming of inexpensive calculators and computers.

In an effort to systematically address these issues the National Council of Teachers of Mathematics (NCTM) established in 1986 the Commission on Standards for School Mathematics. This commission comprised a cross section of mathematics educators, including classroom teachers, supervisors, educational researchers, teacher educators, university mathematicians, and PTA representatives. Over the next three years, the commission developed a document, Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), which incorporates the suggestions of the mathematics community and is now accepted as the world class standards for mathematics. By a similar process, NCTM also developed the Professional Standards for Teaching Mathematics (NCTM, 1991). Both sets of standards have been endorsed by groups representing the mathematics community from kindergarten through graduate school, as well as by many other groups with a stake in mathematics education.

The new standards imply fundamental shifts in the teaching and learning of mathematics toward a classroom environment that promotes the development of every student's capability. To create such an environment, the NCTM recommends five major shifts:

toward classrooms as mathematical communities--away from classrooms as simply a collection of individuals;
toward logic and mathematical evidence as verification--away from the teacher as the sole authority for right answers;
toward mathematical reasoning--away from merely memorizing procedures;
toward conjecturing, inventing, and problem solving--away from an emphasis on mechanistic answer-finding; and
toward connecting mathematics, its ideas, and its applications--away from treating mathematics as a body of isolated concepts and procedures.

                 (National Council of Teachers of Mathematics 1991, p. 3.)

In addition, NCTM recommends a shift in the early years away from emphasis on the formal, abstract representation of concepts toward their introduction via manipulatives, experiments, and computer simulation.

These shifts make it essential for teachers to acquire new mathematical and pedagogical knowledge. But at a more fundamental level they require changes in many teachers' and parents' beliefs about the nature of mathematics and how it can best be taught and learned. The U.S. Department of Education has identified 10 ideas for transforming mathematics teaching and learning that are backed up by research or by promising practical experience. These ideas are intended to be useful to teachers--the key agents in the transformation process--for making the fundamental changes needed to help every student realize his or her mathematical potential.

This document is also addressed to parents and school administrators who share with teachers the common goal of educating children for excellence. Toward this end they can and must support teachers in their endeavors to transform the teaching and learning of mathematics to state of the art.
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[All students can and must learn mathematics, which should serve as a "pump," not a "filter."]

This page was last updated January 4, 2002 (jca)