Tougaloo College Institute for Mathematics (TCIM)
Empirical Research Article
Math Disabilities, Responsiveness to Instruction
Fuchs, L.S., Fuchs, D., & Prentice, K. (2005). Responsiveness to mathematical problem-solving instruction: Comparing
students at risk of mathematics disability with and without risk of reading disability. Journal of Learning Disabilities,
Introductory/Purpose/Objective/Research Question/Focus of Study
The study asked the question: Does third grade students’ responsiveness to generally effective classroom instruction
on math problem solving vary as a function of disability risk status and performance dimension?
The setting of this study was six schools in a southeastern urban district. There were sixteen third grade teachers who
participated. The teachers were randomly assigned to two conditions (eight transfer plus self-regulation and 8 control). There
were 301 students present for pre and post-testing and there were four groups of students (n=201).
These students were identified by using the following criteria: not at risk of reading or mathematics difficulties (no
disability risk NDR), at risk of co morbid mathematics and reading disabilities (MDR/RDR), and at risk of reading disabilities
only (RDR only).
The control group included the following: 20 MDR/RDR students, 5 MDR only students, 12 RDR only students, and 60 NDR students.
The experimental condition included the following: 12 MDR/RDR students, 8 MDR only students, 15 RDR only students, and
69 NDR students.
The intervention was a 16 week long process that examined the disability risk status on understanding, computation, and
labeling scores for two problem-solving measures. This treatment combined explicit instruction to transfer and self-regulated
All teachers followed the district’s curriculum. They followed the Math Advantage math program.
Basic math problem solving included six lessons and was delivered across three weeks. The format was explicit instruction,
worked examples, dyadic classroom, and homework practice.
The transfer lessons included three components: teachers explicitly taught the concept of transfer, familiar problems
were formatted to look novel, dyadic classroom, individual classroom, and homework practice occurred.
Six major activities were included in self-regulation: students scored the independent class problem, students charted
daily scores, students inspected the charts and set goals to beat the highest scores, students scored their homework, teachers
provided students with an opportunity to report examples of how they transferred the problem to another part of the school
day, and teachers recorded the number of students who had completed, scored, and submitted homework and the number of pairs
that reported a transfer event.
There were six lessons in each of the five units plus two cumulative review sessions after winter break. The lessons lasted
25 to 40 minutes. The research assistants taught the first problem solution lesson and transfer lesson while the teachers
taught the remaining sessions.
Fidelity of Treatment
Research assistants make a checklist of the important information before the delivery of each lesson and every session
was audio taped.
Regression-discontinuity was the research design.
Data Collection and Analysis
The scores from the TerraNova state test identified the risk of disability. The TerraNova Computation subtest was used
to measure responsiveness to treatment for mathematics. The Reading Comprehension subtest was also used to index responsiveness.
Training research assistants collected data in a whole-class arrangement. Three weeks before the treatment, pre-testing occurred.
Three weeks after treatment post-testing occurred.
MDR/RDR students improved the least on conceptual underpinnings. MDR/RDR, MDR only, and RDR only students improved less
than NDR students on computation.
MDR/RDR students improved less than NDR students on conceptual underpinnings. MDR/RDR, MDR only, and RDR only students
improved less than NDR students on computation. MDR/RDR, MDR only, and RDR only students improved less than NDR students on
labeling as well.
Conclusions and Recommendations
There were different levels of responsiveness of students’ risk status with MDR and RDR students demonstrating
less improvement. Children who enter problem solving instruction with MDR or RDR will need explicit assistance in computation
Students with MDR or RDR may be pre selected and randomly assigned to treatment in future studies. This may improve the
current study’s design. To incorporate larger numbers of students, future research must be designed.
Students with MDR only or RDR only obtained comparable benefits as their NDR peers. The students with MDR/RDR responded
The study’s intervention seemed to be effective and beneficial when used in a whole-class format. Instruction
should focus on computation and labeling for MDR only, RDR only, and MDR/RDR students.
My Reaction to the Study
My hypothesis was correct in stating that MDR/RDR, MDR only, and RDR only students would improved less than NDR students
on computation and labeling. The intervention was a 16 week long process that examined the disability risk status on understanding,
computation, and labeling. I would like to know the effects of the intervention if it lasted longer, perhaps 32 weeks. Also,
the lessons lasted 25 to 40 minutes. My hypothesis is that the results would have been better for MDR/RDR, MDR only, and RDR
only students if the lessons lasted longer. In addition, the research assistants taught the first problem solution lesson
and transfer lesson while the teachers taught the remaining sessions. I believe that the results could have varied depending
on the competence of the research assistants and the teachers. I think the same individual should have taught the entire sessions
for better results. Furthermore, there were familiar problems that were formatted to look novel. I would want to know how
the results would differ had the problems been foreign to the students.