Balancing Perspectives on Mathematics Instruction

Focus on Exceptional Children, May 2003 by Jones, Eric D, Southern, W Thomas

Following the publication of new standards for the reform of mathematics education (National Council of Teachers of Mathematics, 1989, 2000), published articles have been decrying the status of mathematics achievement in the United States, arguing for constructivist or behavioral models for instruction, and occasionally denouncing proponents of one model or the other. At the same time, relatively little effort has been given to documenting the effectiveness of instructional practices, whatever their roots. Thus, the ideological arguments seem to have generated far more heat than light.

The debates survive, without seeming to have had much influence on instructional practice, curriculum development, or teacher training. The current mathematics achievement crisis is at least as acute as it ever has been and may be even more desperate. The shortage of mathematics teachers across the nation continues and is projected to become more acute. In the next decade a large proportion of today's teachers, especially those in special education, math, and science, will be eligible for retirement (Ingersoll, 2001). Urban districts are finding it particularly difficult to hire mathematics teachers, and those they do hire generally do not stay long (Ingersoll, 2001 ; Merrow, 1999; National Education Association, 2002). Arguably, the standards for mathematics education reform proposed by the National Council of Teachers of Mathematics (1989, 2000) have not had documented effects on mathematics instruction, particularly in urban and rural communities, where the shortage of math teachers has been an increasingly acute, with a growing number of teachers teaching out of their licensure areas.

BALANCED INSTRUCTION: AN IMPLIED COMPARISON

A discussion of balanced instruction involves comparing the different models or approaches to instruction. In the case of mathematics, this is generally assumed to involve a comparison of behavioral and constructivist approaches. Proponents of both behavioral and constructivist approaches have made frequent and strong criticisms of traditional approaches to mathematics education. Proponents of each of these perspectives have been strong critics of the other as well. In their criticisms of each other's approaches, advocates of behavioral and constructivist approaches frequently have equated the opposing perspective to "traditional" approaches to mathematics instruction.

Before we compare the characteristics and the value of balancing behavioral and constructivist approaches, we will consider the nature of "traditional" approaches to mathematics instruction. Then we will discuss the relative merits of the different approaches to instruction and consider the value of balancing their use in practice. First, though, we will define these approaches.

Traditional or Current Approaches

Defining the features of so-called traditional or current approaches to mathematics instruction is an illusive task. Although we possibly can describe, through interviews and observational study, the precise nature of instruction in any given classroom, it would be difficult to discuss in detail the characteristics of mathematics instruction as it is delivered across a wide range of classrooms. Consequently, it is difficult to describe "typical" mathematics instruction precisely. The term typical practices must encompass the wide variations in organization, content, and delivery of instruction among teachers. The tradition of mathematics instruction in the United States provides for a great deal of autonomy and discretion by teachers. Despite the difficulties in defining what amounts to typical approaches to instruction, we can piece together some of the more general characteristics of mathematics instruction as it is practiced in the United States.