Amy Scheuermann

Examining How Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems.

This study examined students’ understanding of diagrams and their use of diagrams as tools to solve mathematical word problems. Students with learning disabilities (LD), typically achieving students, and gifted students in Grades 4 through 7 (N = 95) participated. Students were presented with novel mathematical word problem-solving tasks and interviewed for their understanding of diagrams for solving problems. Scoring rubrics were designed to assess for levels of problem-solving performance, evidence of diagram use, type of diagram generated, how the diagram was used to solve problems, their definition of a diagram, and their reason for why a diagram can be used to solve problems. Results indicated that students with LD typically generated diagrams of a poorer nature and used them in a less strategic manner than their peers. Concerns regarding the impact of content knowledge on the quality of diagram generation as well as implications regarding instruction to use diagrams to understand and solve problems are discussed.

Developing Representational Ability in Mathematics for Students with Learning Disabilities: A Content Analysis of Grades 6 and 7 Textbooks.

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.

Applying a Universal Design for Learning Framework to Mediate the Language Demands of Mathematics.

This article provides information about the relationship between mathematics, language, and literacy and describes the difficulties faced by students with disabilities with math content based on the language demands of mathematics. We conceptualize mathematics language as a mode of discourse for math learning that can be thought of as receptive (reading and listening) and expressive (speaking and writing). We present the principles of universal design as a means of creating curriculum that is more flexible and accessible for all learners. Thus, universal design for learning serves as a framework for examining the goals, methods, materials, and assessment of instruction to help educators identify potential barriers to learning and develop solutions to mitigate the language demands of mathematics for the wide range of diverse learners in todays classrooms.

Diagramming Word Problems A Strategic Approach for Instruction

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.

Students’ Understanding of Diagrams for Solving Word Problems: A Framework for Assessing Diagram Proficiency

A visual representation, such as a diagram, can be a powerful strategy for solving mathematical word problems. However, using a representation to solve mathematical word problems is not as simple as it seems! Many students with learning disabilities struggle to use a diagram effectively and efficiently. This article provides a framework for supporting special educators’ use of diagnostic assessment as a means of understanding and identifying areas of need for students with learning disabilities in order to promote diagram proficiency for solving mathematical word problems.

Visual Representation in Mathematics: Special Education Teachers’ Knowledge and Emphasis for Instruction:

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 Teachers’ Perceptions of Students’ With Disabilities Ability, Instructional Needs, and Difficulties Using Visual Representations to Solve Mathematics Problems

In this article, we present findings that examined special education teachers’ perception of students’ with disabilities ability, instructional needs, and difficulties for using visual representations (VRs) as a strategy to solve mathematics problems. In addition, whether these perceptions differed by instructional grade or setting currently teaching was examined. Survey data from 97 in-service teachers revealed, regardless of instructional setting or grade level taught, that they believe students with disabilities have the ability to learn about and use VRs and need to be taught to use VRs. Furthermore, the special education teachers perceived students with disabilities to have difficulty with all aspects related to using VRs in mathematical problem-solving. Implications for teacher training and development are provided.