# Mathematical Problem-Solving Profiles of Students with Mathematics Disabilities With and Without Comorbid Reading Disabilities

By: Lynn S. Fuchs and Douglas Fuchs

## Purpose of the research

The purpose of the study was to describe the mathematical problem-solving profiles of students with math disabilities with and without comorbid, or co existing, reading disabilities.

## Background information

- 6-7% of school-aged children have math disabilities.
- Research tends to look more at arithmetic skill deficits and basic one-step problem solving. These problems involve basic skills such as addition and subtraction.
- Research looking at more complex mathematical problem solving skills is limited.
- Research has not looked carefully at the impact of reading ability on mathematical abilities.

## Who participated?

Subjects in this experiment were 4th graders. From the overall class of 4th graders a smaller group was selected. This group of children were students with identified special education needs. They also had math goals stipulated in their IEP's.

62 students met this criteria. These students then took a math test to measure their basic math competency. This test, the Test of Computational Fluency, has norms. Thus the test scores achieved by each of the 62 students could be compared to national math abilities. Those students who achieved scores significantly below the national mean for this test were identified as having a math disability.

Specifically students with a standard deviation of more that 1.5 were included in the math disability group. Here is what this means. Mean, or average IQ and achievement test scores are often set at 100 using a statistical procedure. Standard deviations on achievement tests are frequently 15 points. Thus a student with a standard deviation of 1.5 would have a score of 77.5. (100-15-7.5=77.5.)

Scores in the current research were reported as raw scores, or the number of problems solved correctly on a test in which students were given 3 minutes to write the answers to 25 second-grade addition and math problems. The researchers could then compute the average and standard deviation scores for all students on the test. FRom this they were able to tell which students in the group had a significant reading or math learning problem.

40 students had math test scores that were 1.5 standard deviations below the scores expected from an average fourth grader in math.

The researchers also needed a comparison group, a group of students with math disabilities who also had reading disabilities. In order to obtain the comparison group, the researchers gave the 40 students with the math disability a comprehensive reading assessment. Those with reading scores more that 1.5 standard deviation below the average scores to be expected of fourth grade readers were now classified as having both a math and reading disability.

Thus the researchers had a group of subjects who had significant math disabilities without apparent reading problems and a group of students with math disabilities and reading disabilities. When this is the case it is possible to compare performance on tests to see if there is a significant difference in how math problems are solved. Does one group do much better than the other?

## How did they do the experiment?

Students in the two groups were then given math problems of different levels of complexity. There were one-step problems that required only skills arithmetic such as skills of adding and subtracting. At then next level were more complex story problems and at the highest level were real world problems that reflected multi-leveled math thinking that a person might use each day. Once these problems were completed the scores were calculated and compared.

## Results

As expected all students had more difficulty as the type of problem presented became more complex.

Students with comorbid reading disorders did worse. They had more problems with the basic skills as well as the more complex math problems.

These results speak to the semantic, or word abilities, of children with reading disabilities. Difficulty with reading seems to impact other types of academic achievement as well.

From this type of study the researchers hope to find out more about the specific factors involved in math problem solving.

A brief summary of the study and journal article by Lynn S Fuchs and Douglas Fuchs

Journal of Learning Disabilities Volume 35, 6, November/December 2002.

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