Purpose: Students with disabilities tend to lag behind their peers in mathematics achievement. On the 2007 National Assessment of Educational Progress, 19 percent of students with disabilities in Grade 4, and 8 percent of students with disabilities in Grade 8 were at or above the proficient level in mathematics for their grade. A number of interventions have been developed to address the mathematics needs of students with disabilities, but relatively little high quality research has been conducted to test the efficacy of such interventions. This project will test the efficacy of Solve It!, an intervention designed to teach students with learning disabilities how to understand, analyze, solve, and evaluate mathematical problems by developing the processes and strategies that effective problem solvers use. The participants in the study will be middle school teachers and students in the Miami-Dade County Public Schools. A cluster randomized design will be employed, and outcomes will include tests of mathematics achievement, problem solving, and self-efficacy for learning.

Project Activities: During year 1, the project will conduct a pilot study to refine instruments and procedures. During year 2, the project will conduct an initial study involving 40 schools and 40 7th grade teachers. During year 3, the project will conduct a replication and extension study involving 40 schools and 40 8th grade teachers.

Products: Anticipated dissemination activities include ongoing articles in scholarly and practitioner journals, presentations at state and national meetings, and regular reports via the University of Miami's School of Education website.

Structured Abstract

Purpose: Students with disabilities tend to lag behind their peers in mathematics achievement. On the 2007 National Assessment of Educational Progress, 19 percent of students with disabilities in Grade 4, and 8 percent of students with disabilities in Grade 8 were at or above the proficient level in mathematics for their grade. A number of interventions have been developed to address the mathematics needs of students with disabilities, but relatively little high quality research has been conducted to test the efficacy of such interventions. This project will test the efficacy of Solve It!, an intervention designed to teach students with learning disabilities how to understand, analyze, solve, and evaluate mathematical problems by developing the processes and strategies that effective problem solvers use. The participants in the study will be middle school teachers and students in the Miami-Dade County Public Schools. A cluster randomized design will be employed, and outcomes will include tests of mathematics achievement, problem solving, and self-efficacy for learning.

Setting: The study will involve middle school teachers and students in Florida.

Population: The ethnic distribution of Miami-Dade is 10 % white, 29 % African-American, 59 % Hispanic, and 2 % other. About 60% of the students qualify for the free/reduced lunch program. Many Miami-Dade students are at risk for poor academic outcomes and school dropout due to a variety of factors, including low SES. During the first year, the study will involve eight math teachers and their students. During the second and third years, the study will involve 40 teachers and their students each year.

Intervention: Solve It! is based on "explicit instruction" characterized by structured lessons, appropriate cues and prompts, guided and distributed practice, immediate feedback, positive reinforcement, overlearning, and mastery. Solve It! embeds other research-based instructional strategies such as active student participation, verbal rehearsal, and cognitive modeling. Cognitive processes include reading the problem, paraphrasing, visualizing (forming internal representations), hypothesizing about solutions, estimating the outcome or answer, computing the outcome or answer, and checking. Metacognitive strategies include self-instruction, self-questioning, and self-monitoring. The duration of the Solve It! intervention, including pretests and progress checks, is about 15 days, which is consistent with the intent of the program to supplement the standard curriculum.

Program materials include a detailed instructional guide, informal assessments, curriculum-based measures, scripted lessons, instructional materials, and procedures for helping students apply, maintain, and generalize skills and strategies. The mathematical problems include typical textbook problems, problems similar to those found on the Florida Comprehensive Assessment Test, and authentic, real-life problems.

Research Design and Methods: This study will utilize a cluster randomized design with schools as the unit of assignment. Matched pairs of schools will be formed. The Year 1 pilot study will involve two matched pairs of schools. During Year 2, 20 matched pairs of schools will be involved, and one grade 7 math teacher from each school will be invited to participate in the study. For Year 3, one grade 8 teacher from each school will be invited to participate. Some of the students will participate for one year (i.e., grade 7 students who did not return for grade 8 and some grade 8 students who were not in the grade 7 cohort), while a subset of students will participate for both years (i.e. students in both grade 7 and grade 8 cohorts). During Years 2 and 3, experimental and comparison teachers (40 in each year) will have approximately five math classes in which an estimated 125 students are enrolled for a total estimated enrollment of 5,000 students for grade 7 in Year 2 and 5,000 for grade 8 in Year 3.

Control Condition: The control group will receive standard instruction based on the district curriculum.

Key Measures: Student measures will include the Test of Mathematical Abilities-2, the Florida Comprehensive Assessment Test, curriculum-based measures developed for Solve It!, the Math Problem Solving Assessment-Short Form, the Self-Efficacy for Learning Scale, and mathematics academic and conduct report card grades.

Teacher measures will include the Solve It! Fidelity of Treatment Observation System, and teacher logs, interviews, and focus groups.

Data Analytic Strategy: The analyses for this study will include growth curve modeling as well as more traditional univariate and multivariate procedures and qualitative analyses. The study will examine student- and school-level predictors of achievement using a hierarchical linear modeling analysis, which will incorporate student-, teacher-, and school-level covariates to explore possible interactions and assess, for example, whether Solve-It! is differentially effective across school performance levels. Subsets of students with learning disabilities and at risk students will be identified for comparative analysis.

Products and Publications

Book

Montague, M. (2013). Solve It! Teaching Mathematical Problem Solving in Inclusive Classrooms – Grades 7–12. Reston, VA: Exceptional Innovations.

Book chapter

Montague, M. (2011). Effective Instruction in Mathematics for Students With Learning Difficulties. Multiple Perspectives on Difficulties in Learning Literacy and Numeracy (pp. 295–314). London: Springer Publishing.

Montague, M., and Castellani, J. (2011). Instructional Technology and Math Problem Solving. In J. Castellani, and B. Heiman (Eds.), Instructional Technology: Helping Students Access Curriculum Content (pp. 23–30). Reston, VA: Technology and Media Division, Council for Exceptional Children.

Montague, M., and Jitendra, A. (2012). Research-Based Mathematics Instruction for Students With Learning Disabilities. In F.D. Rivera, and H. Forgasz (Eds.), Equity and Diversity in Mathematics Education (pp. 481–502). London: Springer. doi:10.1007/978–3–642–27702–3_44

Journal article, monograph, or newsletter

Kingsdorf, S., and Krawec, J. (2014). Error Analysis of Mathematical Word Problem Solving Across Students With and Without Learning Disabilities. Learning Disabilities Research and Practice, 29(2): 66–74. doi:10.1111/ldrp.12029

Krawec, J., and Montague, M. (2014). The Role of Teacher Training in Cognitive Strategy Instruction to Improve Math Problem Solving. Learning Disabilities Research and Practice, 29(3): 126–134. doi:10.1111/ldrp.12034

Krawec, J., Huang, J., Montague, M., Kressler, K., Sarduy, L., and Melia de Alba, A. (2013). The Effects of Cognitive Strategy Instruction on Knowledge of Math Problem-Solving Processes of Middle School Students With Learning Disabilities. Learning Disability Quarterly, 36(2): 80–92. doi:10.1177/0731948712463368

Montague, M., and Krawec, J. (in press). Solve It!: A Cognitive Strategy to Improve Middle School Students' Math Problem Solving. Teacher Education and Special Education.

Montague, M., Krawec, J., Enders, C., and Dietz, S. (2014). The Effects of Cognitive Strategy Instruction on Math Problem Solving of Middle-School Students of Varying Ability. Journal of Educational Psychology, 106(2): 469–481. doi:10.1037/a0035176

Montague, M., Penfield, R.D., Enders, C., and Huang, J. (2010). Curriculum-Based Measurement of Math Problem Solving: A Methodology and Rationale for Establishing Equivalence of Scores. Journal of School Psychology, 48(1): 39–52. doi:10.1016/j.jsp.2009.08.002

Sweeney, C., Krawec, J., and Montague, M. (2011). Metacognitive Strategy Use of Eighth-Grade Students With and Without Learning Disabilities During Mathematical Problem Solving: A Think-Aloud Analysis. Journal of Learning Disabilities, 44(6): 508–520. doi:10.1177/0022219410378445

Nongovernment report, issue brief, or practice guide

Krawec, J., and Montague, M. (2012). Current Practice Alerts: Cognitive Strategy Instruction, Issue 19. Charlottesville, VA: Council for Exceptional Children. Full text