Purpose: The purpose of this project was to develop materials for teaching mathematical problem solving to students with moderate and severe intellectual disabilities. The goal was to combine methods used to teach problem solving to students with high-incidence disabilities and evidence-based practices for teaching mathematics to students with moderate/severe intellectual disabilities. Students with significant cognitive impairments often have difficulty participating in key aspects of the mathematics learning process. Many of these students have not had access to the general education curriculum. The major mathematics textbooks on educating students with severe disabilities included minimal information on teaching mathematics, aside from money and measurement. However, research has indicated that students with moderate and severe intellectual disabilities are capable of problem solving in mathematics. The intervention was planned to include scripted teacher read alouds and a standard problem format to improve accessibility for nonreaders; adapting schema-based instruction, including use of a graphic organizer; teaching students to generalize the problem solving across problems, real life activities, and education settings; and a peer-tutoring component to be implemented in general education math classrooms.

Project Activities: The research team planned to develop 150 word problems and a teaching script, followed by generalization strategies and a word problem assessment. For the pilot study, a multiple probe single-case design was planned across dyads, and replicated across classrooms, to evaluate the potential impact of the intervention on word problem solving as well as generalization to real-world activities and a general education context. The team planned to develop a manual with the instructional package and supporting materials upon completion of the pilot study.

Structured Abstract

THE FOLLOWING CONTENT DESCRIBES THE PROJECT AT THE TIME OF FUNDING

Setting: The research takes place in elementary and middle schools in North Carolina.

Sample: This project will involve eight students with moderate/severe intellectual disabilities in grades 4–8 during the first 2 years and an additional eight students during the third year. Four special educators will be selected to implement the intervention across the 3-year time span, and four general education teachers will be selected to include the participants within their general education math classrooms to work with peer tutors during Years 2 and 3.

Intervention: The fully developed word problem-solving intervention will include four main components: interactive read aloud, mapping of the problem with objects and manipulatives, calculation of solution via task analysis, and generalizing the problem solving to other contexts. The intervention will incorporate instructional strategies shown to be effective for students with moderate and severe intellectual disabilities in mathematics. These include creating access to the text, promoting comprehension of the problem, teaching calculation skills, teaching the use of symbols, and promoting generalization. The intervention also includes a peer tutoring component to promote the use of the intervention in general education mathematics classrooms.

Research Design and Methods: The project involves an iterative development process for development and revision of the math problems, problem mapping, calculation, and generalization components of the intervention. The design for the pilot study involves a multiple probe, across-dyads, single-case design study. This design will be replicated across four classrooms and adhere to the criteria for single-case design developed by the What Works Clearinghouse (WWC). Each student will be the unit of analysis.

Control Condition: During the single-case design pilot study, individual students will serve as their own controls.

Key Measures: During the project, the team will develop a criterion word problem-solving test for mathematics understanding and inter-observer agreement procedures to promote reliability in the administration of this test. The team will also develop fidelity measures to assess teacher implementation of the scripted mathematics materials. As a more distal measure of math performance, the KeyMath3 Diagnostic Assessment will be used.

Data Analytic Strategy: Single-case data will be analyzed using visual analysis of the data pattern for each student on word problem-solving performance following WWC recommendations. These recommended steps include the prediction of the baseline data, identification of the within-phase pattern for the intervention phase, comparison of intervention phase to the baseline phase, and determination of at least three demonstrations of effects. In reviewing the within- and between-phase data patterns, the six variables to be considered are level, trend, variability, overlap, immediacy of effects, and consistency of data patterns across similar phases. Descriptive analyses of mean, range, and overall slope will also be provided for comparison between phases.

Related IES Projects: Math and Science Teaching that Promotes Clear Expectations and Real Learning across Years for Students with Significant Cognitive Disabilities (R324A080014)

Products and Publications

ERIC Citations:  Find available citations in ERIC for this award here.

Select Publications:

Browder, D. M., Saunders, A., and Root, J. (2016). Technology-Assisted Learning for Students With Moderate and Severe Developmental Disabilities. In S. Ferrara, Y. Rosen, and M. Tager (Eds.), Handbook of Research on Technology Tools for Real-World Skill Development, Volume 2. Hershey, PA: IGI Global.

Saunders, A. F., Browder, D. M., & Root, J. R. (2017). Teaching mathematics and science to students with intellectual disability. In M. Wehmeyer & K. A. Shogren (Eds.), Research-based practices for educating students with intellectual disability (pp. 343–364). New York, NY: Routledge.

Browder, D. M., Spooner, F., Lo, Y.-y., Saunders, A. F., Root, J. R., Ley Davis, L., & Brosh, C. (2017). Teaching students with moderate intellectual disability to solve word problems. The Journal of Special Education. doi: 10.1177/0022466917721236

Root, J. R., & Browder, D. M. (2017). Algebraic problem solving for middle school students with autism and intellectual disability. Exceptionality, 27(2), 118–132. doi://10.1080/09362835.2017.1394304

Root, J. R., & Saunders, A. F. (2015). Explicit instruction to teach early numeracy skills. DADD Express, 26(4).

Root, J. R., Browder, D. M., Saunders, A. F., & Lo, Y. (2017). Schema-based instruction with concrete and virtual manipulatives to teach problem solving to students with autism. Remedial and Special Education, 38, 42–52. doi: 10.1177/0741932516643592

Root, J., Saunders, A., Spooner, F., & Brosh, C. (2017). Teaching personal finance mathematical problem solving to individuals with moderate intellectual disability. Career Development and Transition for Exceptional Individuals, 40(1), 5–14.

Saunders, A. F., Spooner, F., & Ley Davis, L. (2017). Using video prompting to teach mathematical problem solving of real-world video simulation problems. Remedial and Special Education, 39(1), 53–64. doi:10.1177/0741932517717042

Spooner, F., & Browder, D. M. (2015). Raising the bar: Significant advances and future needs for promoting learning for students with severe disabilities. Remedial and Special Education, 36(1), 28–32.

Spooner, F., Saunders, A., Root, J., & Brosh, C. (2017). Promoting access to common core mathematics for students with severe disabilities through mathematical problem solving. Research and Practice for Persons with Severe Disabilities, 42(3), 171–186. doi: 10.1177/1540796917697119