Balancing Perspectives on Mathematics Instruction

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

Controversies in educational literature are often formed in the tones of a debate. Debate, however, has the effect of emphasizing contrasts in two bodies of literature and deemphasizing similarities, overlap, and the potential complementary use of different approaches. Pressley and his colleagues (Pressley, Roehrig, Bogner, Raphael, & Dolezal, 2002) published an article in this journal (volume 34, issue 5, January 2002), describing the balance that effective teachers provide between skills instruction and holistic opportunities for developing literacy. The thesis of their article is that productive efforts to develop literacy in children will require that teachers balance the efforts and the opportunities they provide for skills instruction (e.g, phonics, comprehension strategies), as well as opportunities to participate in authentic literary experiences (e.g., reading real literature, writing reports). In that article, effective teachers are reported as using a range of instructional procedures to promote the development of literacy.

Pressley et al. (2002) discuss the importance of teachers' making rational and balanced choices in selecting instructional procedures and experiences rather than merely responding to ideologies that supposedly are grounded in theoretical models for instruction. Pressley et al.'s discussion of teachers' practices echoes the suggestions by Dixon and Carnine (1994) that educators should focus their attention on the effectiveness and the efficiency of instructional practices rather than worrying a great deal about the apparent congruence of instructional procedures with specific ideologies.

The ideological debate in literacy education centers on the relative merit of so-called traditional skills instruction versus constructivist approaches to literacy development. A similar debate is being waged in mathematics education. Generally, the argument of constructivists has been that traditional teacher-led instruction does not lead to proficiency in mathematical reasoning and problem solving. They argue for more opportunities for students to engage in authentic problem-solving activities. Students are presumed to find mathematical experiences more meaningful and, thus, more motivating if they are able to construct their own knowledge than if they are fed knowledge, directed through mathematical procedures, and led to the teacher's understandings.

In more extreme instances, the arguments for constructivism have veered off to discussions of personal freedom, social politics, and morality (cf. Brantlinger, 1977; Dixon & Carnine, 1992; Heshusius, 1991; Kauffman, 2002) In a less polemic vein, Mercer, Jordan, and Miller (1996) described the breadth of the constructivist conceptualizations of instruction and their compatibility with more behaviorally grounded theories of instruction.

We agree that becoming ensnared in ideological discussions about the merits of constructivism or its alternatives is generally unproductive. Those discussions tend to pit otherwise rational individuals against each other, and they are variously labeled with unflattering terms such as silly, flaky, and barbaric. Although one can sometimes achieve or maintain certain social and political cachets by labeling, the name-calling is unnecessary and unkind, and it also obfuscates the important issue of how pupils should be taught mathematical skills and strategies.

The arguments themselves have become important, we be lieve, because they have been going on for a long time and have not contributed constructively to practice in math education. The ideological arguments themselves are insufficient, sometimes misleading, and distracting. Generally, they have come to have limited value in providing direction to the reform of mathematics education.

In this article we discuss the debate over approaches to mathematics instruction. In other forums the debate has been generalized to mathematics education. Here we will also address issues that are more specific to teaching mathematics to students with special needs. We will begin with a brief discussion of the development and hardening of ideologies within the mathematics reform. After explaining the ideological controversies, we will discuss principles of learning and instruction that have been empirically validated and should be noncontroversial in their application to mathematics instruction, particularly in their application to the instruction of students with special education needs. Finally, we will consider the implications that developing (or failing to develop) more balanced conceptualizations of instruction can have on teacher education and practice.

This article will not provide a comprehensive analysis of the philosophical underpinnings of the debate. Our intent is to provide a discussion that will look at the history of the controversies, describe both approaches, and finally discuss the strengths of constructivism and of direct instruction, drawing conclusions as to how the two approaches might complement each other for the instruction of students with special education needs.