Shrinking achievement differences with anchored math problems: challenges and possibilities.(Enhanced Anchored Instruction )

Multiple measures administered in repeated waves within a nonequivalent dependent variables quasi-experimental design were used to test the effects of a reform-oriented instructional method called Enhanced Anchored Instruction (EAI) on the math achievement of 128 middle school students, including students with learning disabilities (LD). EAI problems are presented in multimedia and hands-on formats, a potential benefit for students with low skills in both reading and math. Overall, students of all ability levels benefited from EAI with effect sizes ([[eta].sup.2]) ranging from .53 to .59. Results revealed that although students with LD scored lower on pretests, their learning trajectories matched those of students without LD. A maintenance test administered several weeks after instruction showed that students with LD retained what they had learned. Implications for instruction and suggestions for future research are provided.

**********

Government and professional groups have urged educators to help all students acquire mathematical preparedness for post-secondary education and employment (e.g., Standards for Technological Literacy: Content for the Study of Technology, International Technology Education Association, 2000; Goals 2000: Educate America Act, U.S. Department of Education, 1994; What Work Requires of Schools: A SCANS Report for America 2000, U.S. Department of Labor, 1991). The most recent of these initiatives, the No Child Left Behind Act of 2001 (NCLB), outlines a national initiative for improving elementary and secondary education tied to high-stakes assessments. In response to these pressures, the National Council of Teachers of Mathematics (NCTM, 2000) has called for curricular reform that emphasizes more problem-based learning. According to the NCTM, these problems should develop the skills and concepts of middle school students in (a) working flexibly with whole numbers, fractions, and decimals; (b) constructing and interpreting scale drawings; (c) converting units of measure; and (d) interpreting tables and graphs.

Recent test scores show that these reforms may be paying off. Results from the National Assessment of Educational Progress (Perie, Grigg, & Dion, 2005) indicated that eighth graders scored higher in 2005 than in any previous year since the test was administered. However, this good news was accompanied by less positive findings showing more than one quarter of students without disabilities (28%) and more than two thirds of students with disabilities (69%) still scoring below Basic performance levels. Basic means students "should complete problems correctly with the help of structural prompts such as diagrams, charts, and graphs" and include "the appropriate use of strategies and technological tools to understand fundamental algebraic and informal geometric concepts in problem solving" (p. 20). Thus, the new standards call for a range of skills beyond procedural competency.

Higher expectations coupled with the sluggish math performance of students with disabilities have led some special educators (e.g., Jones, Wilson, & Bhojwani, 1997; Woodward, 2004; Woodward & Baxter, 1997; Woodward & Montague, 2002) to question whether traditional instructional methods for students with learning disabilities (LD) are appropriate and adequate. Central to this issue is how and to what extent the teaching practices used in special education--which have leaned toward behaviorist principles---can and should be modified to align with current reform-oriented practices in general education promoting more constructivist methods.

Shifting to a more constructivist approach will not be easy for several reasons. First, special educators (e.g., Vaughn, Klingner, & Hughes, 2000) have cautioned against embracing the reform-oriented methods for less capable students without an adequate research foundation because (a) students who have low math skills may not be able to solve more difficult types of math problems advocated by NCTM and (b) having such students spend time on problems they are not able to solve may limit the time available for basic skills. Various meta-analyses of special education research have shown the benefits of drill and repetition for many students with LD (Swanson, 2001; Swanson & Hoskyn, 1998). These methods carefully sequence content so task difficulty does not overload students' working memory (e.g., Carnine, 1998; Swanson & Deshler, 2003). Abandoning proven approaches at this time may be unwise, especially when general education is reevaluating their instruction of procedural skills (Star, 2005).

A second important question concerns how to individualize instruction for students with LD who are certain to face more complex content in general education math classrooms. In the past, most students with LD received their math instruction in small-group settings where teachers tailored specialized instruction to each student's learning needs. As more students with LD are included in general education classrooms, the question of whether and how they will get the support in regular education classes is still largely unanswered (Baker & Zigmond, 1990). Research suggests that pullout settings do not produce satisfactory results in school achievement over the long term (Fuchs & Fuchs, 1995; Rea, McLaughlin, Walther-Thomas, 2002), but few studies have identified practices that promote effective math instruction for students with LD in inclusive, reform-oriented settings.