Meeting the curricular needs of academically low-achieving students in middle grade mathematics.

An important component of the National Council of Teachers of Mathematics Standards is the equity principle: All students should have access to a coherent, challenging mathematics curriculum. Many in the mathematics reform community have maintained that this principle can be achieved through one well-designed curriculum. However, the extant research on equity--which focuses on either ethnic diversity or academic achievement--suggests that this principle is illusive. The current study compares the effectiveness of two curricula in teaching a range of math concepts to 53 (28 male; 25 female) middle school students at risk for special education services in math. The yearlong, quasi-experimental study involved achievement and attitudinal measures. Results indicated that students in the intervention group who used materials designed according to instructional principles described in the special education literature achieved higher academic outcomes (p

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A central tenet of the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000) has been that all students can succeed in complex mathematics. This tenet is commonly referred to as the equity principle, and while it is acknowledged that students do not need to be treated in the same way, the NCTM Standards and other influential policy documents (e.g., Measuring What Counts, National Academy of Sciences, 1993) nonetheless advocate that all children should have access to a coherent, challenging mathematics curriculum. Since the early 1990s, some critics have been understandably skeptical of this principle, particularly given the NCTM Standards' considerable emphasis on conceptual understanding, problem solving, and constructivist pedagogy (Harris & Graham, 1996; Woodward & Montague, 2002).

Some of the more widely cited studies of equity in the mathematics literature have focused on low-income, ethnically diverse students. Results from the Algebra Project (Moses, 2001), QUASAR (Quantitative Understanding Amplifying Student Achievement and Reasoning; NCTM, 1999; Silver, Smith, & Nelson, 1995), and Cognitively Guided Instruction (Fennema, Franke, Carpenter, & Carey, 1993) indicate that challenging mathematics programs--which emphasize conceptual understanding, problem solving, and communication--have promise for minority students. These findings are important because there is a historical tendency to place far too many poor students from ethnically diverse backgrounds in low-track, skills-based classrooms (Schoenfeld, 2002; Secada, Fennema, & Adajain, 1995).

However, efforts to craft one rigorous curriculum for all students has proven more difficult than many in the mathematics reform community had anticipated (Carey et al., 1995). Research in the late 1990s indicates that naturalistic efforts to raise the achievement of low-ability, low-income secondary students produces mixed results. Gamoran and his colleagues (Gamoran, Porter, Smithson, & White, 1997; Gamoran & Weinstein, 1998) reported that efforts to eliminate general track math classes and to replace them with transition courses (i.e., courses that allow students to keep up with students who enroll in college prep classes) have been only partially successful. Achievement levels tend to be somewhere between students in low-track, skills-based classrooms and students in college prep courses. Increasing the rigor of the class alone is insufficient, and tenets such as the equity principle often underestimate the technical complexities of teaching a mixed ability group of students, particularly at the secondary level. Nonetheless, the findings generally reinforce the view that low-track students should not be placed in "dead end" general-track math classes with little access to challenging content.

One of the most difficult arenas for the equity principle involves students at risk for special education or students with learning disabilities. The beneficial effects of challenging mathematics on these students are often anecdotal (e.g., Silver et al., 1995; Fennema, Franke, Carpenter, & Carey, 1993). In-depth examinations of this population indicate that without substantive modifications, these students do not exhibit high levels of success on either academic measures or everyday activities (e.g., small group work and whole class discussions; Baxter, Woodward, & Olson, 2001; Baxter, Woodward, Wong, & Voorhies, 2002; Woodward & Baxter, 1997).

Special education intervention research in mathematics has articulated instructional principles potentially beneficial to this population of students. Research supports the use of visual models or manipulatives (Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Cass, Cates, & Smith, 2003; Jitendra, Hoff, & Beck, 1999; van Garderen & Montague, 2003; Witzel, Mercer, & Miller, 2003; Woodward, Baxter, & Robinson, 1999), carefully distributing practice on key concepts and skills (Kameenui, Carnine, Dixon, Simmons, & Coyne, 2002), as well as controlled pacing and high expectations (Fuchs & Fuchs, 2001).