This study determined the effects of the Explicit Inquiry Routine (EIR), a teaching routine, on the math performance of 14 middle-school students with math learning disabilities. The routine integrates validated mathematical teaching practices from general education (inquiry, dialogue) and special education (intensive, explicit instruction) to engage students in an interactive inquiry process across multiple modes (concrete, representation, and abstract) of illustration and manipulation to develop an understanding of the one-variable equation. A multiple-baseline-across-students design was employed. Both statistical analysis and visual inspection indicated that students' scores increased and were maintained for up to 11 weeks after instruction was terminated. In addition, students transferred their skills to textbook word problems and standardized math achievement measures.

Strategic competence is one of the many critical components necessary for students to be successful in mathematics. Broadly, strategic competence is the ability to "formulate mathematical problems, represent them, and solve them" (National Research Council, 2001, p. 124). This involves both the knowledge of strategies including representations that may be used to solve a problem and the ability to effectively and efficiently use strategies while flexibly switching between strategies in response to the demands of a problem situation (National Research Council, 2001). Central to strategic competence are representations. While there are various definitions of a representation (e.g., Goldin, 2003; Kaput, 1987; Pimm, 1995), for this study, a representation is considered to be "a combination of something written on paper, something existing in the form of physical objects and a carefully constructed arrangement of idea in one's mind" (Davis, Young, & McLaughlin, 1982, as cited in Smith, 2003, p. 266). Clearly, many different representational forms (e.g., mental image, written language, oral language, action movements, symbols, manipulatives) exist (Zawojewski & Lesh, 2003). A critical idea about representations, however, is that they are not static end products but rather tools for cognitive activity (Pape & Tchoshanov, 2001). As the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 2000) noted, a representation refers "both to process and to product. .. to the act of capturing a mathematical concept or relationship in some form and to the form itself" (p. 67). Therefore, when viewed as a tool of cognitive activity for solving mathematical problems, representations can be used for analyzing problems and planning solutions, justifying and explaining actions, predicting consequences, monitoring and evaluating progress, and integrating and communicating results in forms that are useful to others (Pape & Tchoshanov, 2001). Diagrams and Mathematical Word Problem Solving Although all representational systems are important for developing mathematical understanding (Owens & Clements, 1998; Pape & Tchoshanov, 2001; Presmeg, 1986) and various representational systems can be used to solve word problems, the focus of this study is specifically on self-generated diagrams. According to Diezmann and English (2001), a 438558L DQ36310.

The use of visual representations (VRs) in mathematics is a strongly recommended practice in special education. Although recommended, little is known about special educators’ knowledge of and instructional emphasis about VRs. Therefore, in this study, the authors examined special educators’ own knowledge of and their instructional emphasis with VRs in mathematics for students with disabilities (SWDs) in Grades K-12. A total of 146 teachers (pre- and in-service) responded to an online survey. A mixed methods triangulation research design was utilized. Findings include the following: (a) teachers hold conceptions about VRs and the roles they serve in problem solving; their ideas, however, lack depth and are narrow in perspective; (b) what teachers emphasize about VRs to SWDs tends to match their own conceptions, but the explanations they provide for SWDs need expanding and refinement; and (c) given their narrow conceptions, VRs may be limited to a peripheral role in special educators’ instruction.

Special education and mathematics teachers are under pressure to respond to the needs of an increasingly diverse range of students in mathematics. One way for them to meet the instructional needs of struggling learners is through collaboration where, ideally, the knowledge one teacher brings can address the gaps of the other. However, the differing perspectives and approaches they bring to the collaborative effort may also impede it. The purpose of this article is to describe a sampling of the recent research within both the mathematics and special education fields. This is done to enable collaborating teachers to create an effective learning environment for students who struggle in mathematics. Fifty recent studies focused on struggling learners in mathematics, were identified, and then analyzed to highlight the similarities and differences between the educational fields. C 2008 Wiley Periodicals, Inc.

No abstract

This study was an examination of the extent to which sixth-and seventh-grade mathematics textbooks incorporated recommended instructional practices for students with learning disabilities to help develop representational ability. Results indicated that the textbooks (a) provided very little explicit instructional information about representations (e.g., how to generate); (b) expected that students use representations to complete math tasks, however, the levels of involvement were varied with a greater number of completed representations being provided rather than student generated representations for solving problems; and (c) provided very little instructional information and support to develop representational ability for teachers of students with disabilities. This was evident in student and teacher materials as well as corresponding supplemental resources designed specifically for students with disabilities.Keywords instructional materials, mathematics, middle school van Garderen et al.

No abstract

While often recommended as a strategy to use in order to solve word problems, drawing a diagram is a complex process that requires a good depth of understanding. Many middle school students with learning disabilities (LD) often struggle to use diagrams in an effective and efficient manner. This article presents information for teaching middle school students with LD about diagrams and how to use them to solve word problems.