Accessing the General Education Math Curriculum for Secondary Students With High-Incidence Disabilities

Use of numbers, variables, and symbols associated with mathematics. FIGURE 11 The concrete-semi-concrete-abstract instructional sequence and more exclusionary settings, including JC schools (Cass, Cates, Smith, & Jackson, 2003; Maccini et al., 2006; Maccini & Hughes, 2000; Maccini & Ruhl, 2000). Within the empirical studies, students reached criterion performance, maintained the skills over time, and generalized to more difficult problem types. For example, researchers (Maccini & Hughes, 2000; Maccini & Ruhl, 2000) found that the CSA sequence helped students to represent and solve word problems involving integer numbers and problem solving. The students used algebra tiles at the concrete level to build conceptual knowledge and a mnemonic strategy (STAR) to assist them with the procedural knowledge. Figure 9 provides an overview of the way in which the CSA strategy was implemented within the STAR strategy. In a study that varied the CSA progression, Cass and colleagues (2003) noted that geoboards helped secondary students with LD establish a conceptual understanding of perimeter and area that could transfer to real-world problem solving. Students received instruction using only the concrete (geoboard) and the abstract components of the CSA strategy and demonstrated generalization of these skills by measuring the room and window sizes of a dollhouse and then converting these measurements from scaled size to actual size to determine the needed amount of flooring and window treatments. Although studies show some support for limiting the progression to the concrete and abstract stages, more support exists for using the entire CSA sequence. Use of the CSA sequence on a daily or weekly basis helps students across settings understand math concepts via a multisensorial approach prior to advancing to more abstract tasks (Cass et al., 2003; Hudson & Miller, 2006; Maccini & Hughes, 2000; Maccini & Ruhl, 2000). However, as Figure 12 shows, over half of the teachers in JC schools reported using this strategy only monthly, if at all. The infrequent use of the entire CSA sequence in JC schools is consistent with other studies of teachers in public schools (Gagnon & Maccini, 2007). Teachers in JC schools primarily noted that they needed more training and additional materials and resources to effectively and frequently use the CSA sequence. Like certain teachers in more inclusionary schools, some teachers in juvenile corrections noted that their views of teaching do not match the CSA approach. This disconnection between teachers' views of instruction and CSA may span a variety of classroom settings and could be related to teachers' views that a conceptual, rulebased approach is more appropriate for secondary students. One additional complication inherent in JC school settings is that security concerns may limit a teacher's approach to mathematics instruction. Manipulatives can be a serious security issue. However, specific adaptations to the use of manipulatives can and should be made (Maccini et al., 2006). The implications for practice noted next consider the