Date of Graduation
College of Education and Human Services
Barbara L. Ludlow
Cathy Gaylon Keramidas
Richard T. Walls
Students with learning disabilities or learning difficulties in mathematics often have difficulties solving word problems with fractions. These difficulties limit students' abilities to solve everyday math problems and develop the skills necessary for higher level mathematics. Prior research on problem solving indicates that direct instruction on problem schemas can improve problem solving performance. Previous research also suggests that instruction using the concrete-representational-abstract (CRA) sequence and instruction with virtual manipulatives can enhance understanding of mathematical concepts. However, a CRA sequence that incorporates virtual manipulatives has not been combined with schema-based instruction to help students solve word problems with fractions. The purpose of this study was to examine the effects of using an intervention that combined the CRA sequence with virtual manipulatives and schema-based instruction to improve the problem solving performance of students with learning disabilities or learning problems in mathematics on word problems with fractions. This sequence of instruction was combined with a mnemonic strategy called the LISTS strategy to help students remember the steps in the problem solving sequence. Using a single-case multiple baseline across participants design, the researcher provided an intervention to five students in the fifth grade that included instruction in three problem schemas for addition and subtraction (change, compare, and group). Results indicated that all students made some gains in performance on problems similar to those presented during the intervention, but the three students who were able to make connections between problem schemas and equations demonstrated significant gains in performance. The concrete models and virtual models used in the CRA sequence enhanced understanding of fraction word problems for some, but not all, students. Additionally, analysis of student performance on pre- and post-tests of problems with novel features indicated that students made only small gains in performance on fraction word problems that included difficult vocabulary, irrelevant information, or information that required different conceptualizations than those presented during the intervention.
Reneau, Julie L., "Using the Concrete-Representational-Abstract Sequence to Connect Manipulatives, Problem Solving Schemas, and Equations in Word Problems with Fractions" (2012). Graduate Theses, Dissertations, and Problem Reports. 210.