Balancing Perspectives on Mathematics Instruction

Controversies in educational literature are frequently formed in the tones of a debate. Debate, however, has the result of emphasizing contrasts in sum of two units 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 unfold literacy in children will require that teachers balance the efforts and the opportunities they provide for skills instruction (eg phonics, comprehension strategies), as well as opportunities to participate in authentic literary experiences (eg reading real literature, writing reports). In that article, effective teachers are reported as using a range of instructional processs to promote the development of literacy.

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

The ideological debate in literacy education center upon the relative merit of so-called traditional skills instruction versus constructivist approaches to literacy disentanglement 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 question at issue solving. They argue for more opportunities for pupils to engage in authentic problem-solving activities. scholars are presumed to find mathematical experiences more meaningful and, thus, more motivating if they are able to set up their own knowledge than if they are f knowledge, directed [i]or[/i] part of to the other mathematical procedures, and led to the teacher's understandings.

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

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

The arguments themselves have become important, we be lieve, because they have been going upon 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 approach to have limited value in providing direction to the reform of mathematics education.

In this article we discuss the debate above 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 pupils with special needs. We will begin with a brief discussion of the exhibition 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 learners with special education needs. Finally, we will consider the implications that developing (or failing to develop) more balanced conceptualizations of instruction can have upon 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 gaze at the history of the controversies, describe the couple approaches, and finally discuss the forces of constructivism and of direct instruction, drawing conclusions as to in what way the two approaches might full number each other for the instruction of scholars with special education needs.