A Meta-Analysis on Teaching Mathematics to Students With Significant Cognitive Disabilities

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NICHCY’s Structured Abstract 79 describes the following:

Title | A Meta-Analysis on Teaching Mathematics to Students With Significant Cognitive Disabilities

Authors | Browder, D. M., Spooner, F., Ahlgrim-Delzell, L., Harris, A., & Wakeman, S. Y.

SourceExceptional Children, 74(4), 407-432.

Year Published | 2008

Abstract
This article reports on a comprehensive literature review and meta-analysis of 68 experiments on teaching mathematics to individuals with significant cognitive disabilities. Most of the studies in the review addressed numbers and computation or measurement. Within the computation studies identified, most focused on counting, calculation, or number matching. For the measurement studies, nearly all focused on money skills. Of the 54 single subject design studies, 19 were classified as having all quality indicators for research design (13 representing the National Council of Teachers of Mathematics Measurement standard and 6 representing the Numbers and Operations standard). These studies offer strong evidence for using systematic instruction to teach mathematics skills and for using in vivo settings. [Abstract from Author.]

Background
Mathematics instruction for students with significant cognitive disabilities has historically focused on the functional uses of mathematics during daily living activities, such as paying for public transportation or buying food.   Federal education laws such as the No Child Left Behind Act of 2001 require that the assessment of mathematical achievement, even for students with significant cognitive disabilities who are assessed with alternate assessments, be based on state academic content standards.  Thus educators of students with significant cognitive disabilities are faced with the challenge of creating lessons which both teach functional math skills and address academic content standards.

In 2000, the National Council of Teachers of Mathematics (NCTM) provided a comprehensive set of mathematics standards. The NCTM listed five key areas of mathematics instruction:

  1. Number and Operations: the ability to understand and represent numbers, relationships among numbers, and number systems (e.g., the number 36 is 3 tens and 6 ones);
  2. Measurement: the ability to understand measurable quantities (e.g., time and money);
  3. Data Analysis and Probability: the ability to collect, organize, and display relevant data to answer questions with appropriate statistical methods (e.g., calculating percentages, plotting data);
  4. Geometry: the ability to analyze characteristics and properties of two- and three-dimensional shapes, apply transformation and use symmetry to analyze mathematical situations (e.g., length, width, area, and volume);
  5. Algebra: the ability to understand patterns, relations, and functions of numbers, and use mathematical models to represent and understand quantitative relationships (e.g., x + 2 = 7, solve for x).

This study examined mathematics instruction for students with significant cognitive disabilities to see if skills representing the NCTM components were included in their instruction and how successful various instructional practices had been with this population of students.

Research Questions

1. Which of the NCTM components of mathematics were represented in the research on mathematics instruction for students with significant cognitive disabilities?

2. What types of skills are represented within the NCTM components taught to individuals with significant cognitive disabilities?

3. What evidence exists about the ability of individuals with significant cognitive disabilities to learn mathematics?

4. What evidence-based instructional practices have been successfully employed to help individuals with significant cognitive disabilities acquire skills in mathematics?

Research Design
Single Subject Design Meta-analysis (i.e., Percentage of Non-Overlapping Data analyses)*

  • Number of Studies Included | 68 studies, 54 of which were single-subject design studies and 14 of which used group designs
  • Number of Subjects | 493
  • Years Spanned | 1975-2004

Research Subjects
Students with significant cognitive disabilities participating in mathematics instruction.

Age/Grade of Subjects
Students ranged in age from preschool to adult.

Specified Disability
Significant cognitive disabilities, including moderate to severe intellectual disabilities, autism, and developmental delays.

Intervention
Mathematics instruction

Duration of Intervention
Not reported

Findings

  1. Of the five components of mathematics instruction examined, only two were commonly emphasized in the studies examined: measurement skills (e.g., counting money) and computation.
  2. Students with significant cognitive disabilities are able to learn both specific target skills (e.g., matching shapes, counting money, graphing, and computation) and functional life skills involving mathematics.
  3. Systematic instruction curricula were found to have moderate to strong effects for teaching students with significant cognitive disabilities mathematics.  However, since these curricula came in packages using various forms of instruction, prompting, and feedback, it was impossible to determine which components of each treatment package accounted for the greatest amount of the treatment’s effectiveness.

Combined Effects Size
The median Percentage of Non-Overlapping Data (PND)* value for the studies in which systematic instruction including all components of mathematics instruction laid out by the NCTM was 92.15%.  The instructional practice with the highest median PND was in vivo training (100%).  Other practices with median PNDs over 97% were stimulus prompting, physical guidance, and reinforcing correct responses.

Conclusion/Recommendations
Students with significant cognitive disabilities benefit from systematic mathematics instruction that includes procedures such as prompting, prompt fading, and feedback.  Opportunities to learn skills “in vivo” (i.e., in the actual type of situation where they will be used) are also recommended, such as counting money to buy something at the grocery store.  The majority of research studies in this analysis focused on number operations and measurement concepts.  Research is needed to explore mathematics instruction for students with significant cognitive disabilities in the three remaining areas identified by the NCTM: geometry, algebra, and data analysis.

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*Terms Defined

Meta-Analysis | A widely-used research method in which (1) a systematic and reproducible search strategy is used to find as many studies as possible that address a given topic; (2) clear criterion are presented for inclusion/exclusion of individual studies into a larger analysis; and (3) results of included studies are statistically combined to determine an overall effect (effect size) of one variable on another.

Percentage of Non-Overlapping Data (PND) | A measure of effectiveness. A PND between 50% and 70% is considered to show that a treatment’s effectiveness is questionable. A PND of 70% is considered the lower limit for a reliable treatment.

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