Direct Instruction Mathematics Programs: An Overview and Research Summary.

This paper provides an overview and research summary of Direct Instruction (DI) mathematics programs, specifically DISTAR Arithmetic I and II (Engelmann & Carnine, 1975, 1976), Corrective Mathematics (Engelmann & Carnine, 1982), and Connecting Math Concepts (CMC; Engelmann, Carnine, Kelly, & Engelmann, 1996a). A comparison of the constructivist approach to the direct or explicit approach to math instruction was conducted. Overviews and ways in which DI math programs meet the 6 principles for improving math instruction as provided by the National Council of Teachers of Mathematics (NCTM; 2000b) are noted. Finally, a research review and analysis of DI math programs published since 1990 (yielding 12 studies) was completed. Seven of the 12 studies compared DI math programs to other math programs. Four studies investigated the efficacy of DI math programs without comparison to other math programs. A meta-analysis conducted by Adams and Engelmann (1996) was also described. Study characteristics (i.e., reference, program or program comparison, participants, research design, dependent variable(s)/measures, and results) were examined for each of the 12 studies. Eleven of the 12 studies showed positive results for DI math programs. Eight areas for future research are included. This paper provides a review of DI mathematics programs including DISTAR Arithmetic I and II, Corrective Mathematics, and CMC. In addition, the constructivist approach and the direct or explicit approach to math instruction are compared. Primary emphasis was placed on the direct approach and how DI math programs meet NCTM’s six principles for improving math instruction. A research review of studies published after 1990 using these programs was also conducted. Finally, areas for future research on DI math programs are provided. Overview of Math Statistics In our rapidly changing and technologically dependent society, we are faced with the need for a solid understanding of mathematical skills and concepts. This need is no longer limited to scientific and technical fields. Virtually every type of employment requires a more sophisticated understanding of mathematics. For example, in a 1989 report by the National Research Council, over 75% of all jobs required proficiency in simple algebra and geometry, either as a prerequisite to a training program or as part of a licensure examination. Further, in a more recent report by the Bureau of Labor Statistics (2002), estimates indicate that four of the top five employment growth fields will require a bachelor’s degree in technical studies such as mathematics or computer science. Given the emphasis of mathematical skills in our society, it seems critical that our students should demonstrate basic mathematiJournal of Direct Instruction 53 Direct Instruction Mathematics Programs: An Overview and Research Summary Journal of Direct Instruction, Vol. 4, No. 1, pp. 53–84. Address correspondence to Angela Przychodzin at aprzychodzin@mail.ewu.edu ANGELA M. PRZYCHODZIN, NANCY E. MARCHAND-MARTELLA, RONALD C. MARTELLA, and DIANE AZIM, Eastern Washington University cal and higher order thinking skills to be successful in present and future environments. In 1995, the largest international study (Third International Mathematics and Science Study [TIMMS]) of academic achievement was conducted by the International Study Center (ISC) at Boston College. This study included over half a million students from 41 countries. According to the ISC’s report (2001), when compared to other countries, math scores in the United States were ranked in the bottom half of the participating countries. American 4th graders ranked 12th out of 26, 8th graders ranked 28th out of 41, and 12th graders ranked 19th out of 21 countries who participated in the assessment. The National Center for Education Statistics (2001) published its most recent results of the 2000 National Assessment of Educational Progress. In this report, known as The Nation’s Report Card, the mathematics achievement levels of 4th-, 8th-, and 12th-grade students were assessed. The following three levels of performance were identified: 1. basic: this level denotes partial mastery of prerequisite knowledge and skills that are fundamental for proficient work at each grade. 2. proficient: the proficient level represents solid mathematical performance for each grade assessed. Students reaching this level have demonstrated competency over challenging subject matter, including mathematical knowledge, application of such knowledge to real-world situations, and analytical skills. 3. advanced: the advanced level signifies superior performance. (p. 9) The proficient level is the overall performance goal for all students. Results indicated that only 26% of 4th-grade students, 27% of 8th-grade students, and 17% of 12th-grade students performed at the proficient level in math. NCTM Principles Given the mathematical performance of our students on various assessments and comparisons conducted within and beyond the U.S., it seems imperative to examine how best to teach math in our public schools. The NCTM is the world’s largest mathematics education organization, founded in 1920. The mission of the NCTM (2000a) is “to provide the vision and leadership necessary to ensure a mathematics education of the highest quality for all students” (p. 1). In order to accomplish this mission, the NCTM (2000b) developed five overall curricular goals for student success in mathematics: (a) learning to value mathematics, (b) becoming confident in one’s own mathematical ability, (c) becoming a mathematical problem solver, (d) learning to communicate mathematically, and (e) learning to reason mathematically. The NCTM (2000b) developed Principles and Standards for School Mathematics as a framework for guiding educational professionals in meeting these five goals. While the standards describe the mathematical content and processes that students should learn, the principles describe features of high quality mathematics education (2000b). In an earlier paper, Kelly (1994) provided examples from various levels of CMC to illustrate how these standards can be met through CMC. This paper focuses on how the principles (vs. standards) were met by CMC, DISTAR I and II, and Corrective Mathematics. According to the NCTM (2000b), the six principles should be used to influence the development and selection of curricula, instructional planning, assessment design, and establishment of professional development programs for educators (see Table 1). It is through these six principles that educators can begin to address the composite themes of high quality mathematics education. Primary Approaches to Math Instruction There are two primary approaches to mathematics instruction. These include the constructivist approach and the direct or explicit