Balancing Perspectives on Mathematics Instruction

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

Second, it must be determined that general instructional practices are characterized by the specific elements. Third, critics must provide clear evidence that those elements account for the shortcomings of the general curriculum. These second and third conditions are unlikely to be met because there have not been, and probably will never be, any studies that adequately characterize the diverse and sometimes idiosyncratic instructional behaviors that take place in mathematics instruction.

Fourth, comparisons between direct instruction and constructivism must be focused rather than relying on the current method of criticism-by-proxy. This condition can be addressed, but it requires that both direct instruction and constructivism be adequately characterized to" avoid irresponsible constructions of straw-man arguments. It is difficult to arrive at definitions of constructivism and direct instruction that completely capture their essence. Although direct instruction and constructivism have some pronounced conceptual differences, other distinctions between the two are more apparent than real.

Direct Instruction

For more than 20 years direct instruction has been favored in special education. Support for direct instruction, however, has been more apparent within research and teacher-education programs than it has been in either general education or special education classrooms. Direct instruction also has been variously defined (Gersten, 1985). The term direct instruction has been used broadly to refer to behaviorally based instructional activities that are directly related to increasing achievement in basic academic skills. Accordingly, instructional procedures are considered to be "direct" if the explicit purpose of instructional activities is to increase academic achievement and if instruction emphasizes teacher behaviors and variables related to classroom structure, such as small-group instruction, teacher direction of learning, academic focus, high rates of accurate responding, controlled practice, use of higher cognitive-level questions, group responding, independent practice, and feedback to student responses (Rosenshine, 1978, 1979; Stevens & Rosenshine, 1981).

The earliest iteration of the model was evaluated and found to be the leading model of instruction in the national Follow Through Study (Stebbins, St. Pierre, Proper, Anderson, & Cerva, 1977). Unlike the more generic approaches to direct instruction (e.g., Good, Grouws, & Ebemeier, 1979; Rosenshine 1978, 1979; Stevens & Rosenshine, 1981), the University of Oregon Model of Direct Instruction places considerable emphasis on task demands and their presentation in the instructional sequence. Instructional sequences are based on the careful selection and sequencing of instructional examples.

Watkins and Slocum (2004) describe the University of Oregon Model and identify three characteristics that define and provide for its success: content analysis, curriculum design, and clear communication between the teacher and the student. Direct instruction involves extensive preparation before teacher/student interactions take place. It begins with analyses of the potential content of mathematics curricula to: (a) determine the scope and sequence of knowledge and skills that will be learned within and among the domains of mathematics, (b) identify the critical concepts and skills, and (c) identify important relationships between math concepts and skills. The curriculum then is designed based on the content analysis. Curriculum design has five elements: