Tougaloo College Institute for Mathematics (TCIM)
Empirical Research Article
Math Learning Disability, Responsiveness to Intervention
Fuchs, L.S., Compton, D.L., Fuchs, D., Paulsen, K., Bryant, J.D., & Hamlett, C.L. (2005)
The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97(3),
Introductory/Purpose/Objective/Research Question/Focus of Study
The purposes of the study were to observe the effects of preventive tutoring (with classroom instruction), estimate the
prevalence and severity of math disabilities (MD) at the end of the first grade (with or without tutoring), and investigate
cognitive abilities associated with the development of mathematics competence in first grade.
The setting for this study was a southeastern metropolitan school district. First grade teachers in six Title I and four
non-Title I schools participated in this study. Not at risk (NAR) and at risk (AR) students were identified in September and
a whole-class format was used. The students in the study were tested using several different testing measures which were used
to identify the lowest scoring students. These students, along with 11 other students, were considered as potentially AR.
The staff administered an individual battery test to the 319 students.
The Curriculum-Based Measurement (CBM) indicated 139 of the lowest performing students were AR. They were randomly assigned
to control or tutoring conditions. There were four different categories that were formed. The first included 69 AR control
students. The second included 70 AR tutored students. The third included 180 students who were tested individually and designated
as NAR. The fourth included 348 NAR students who were only group tested. Groups three and four were combined. The NAR students
performed higher than the AR students on the intelligence measures. The control and tutored groups performed comparably.
The small-group tutoring portion of the intervention was based on the concrete-representational-abstract model. This model
relies on concrete objects to promote learning. Twelve tutors worked in groups of two or three students. The lessons followed
a sequence of 17 scripted topics, which each including a worksheet and manipulative. Each group completed 48 sessions and
mastery of the topic was assessed each day. This included testing for identifying and writing numbers, identifying more, less,
and equal objects, and identifying operations. The tutors followed scripts to ensure consistency. During the last ten minutes
of each intervention session, the students used Math Flash. Math Flash provided students with repeated opportunities to hold
associations between problem stems and their answers in working memory. This allowed facts to be committed to long-term memory.
The research design for this study was experimental with a treatment group and control group.
There were whole-class and individual sessions. The individual sessions took place in the school library, an empty classroom,
or hallway. Seven math measures were administered. They measured computation, concepts and applications, and story problems.
Reading measures were also administered. The battery of cognitive assessments was administered only at pretest. It measured
intelligence, language, nonverbal problem solving, phonological processing, processing speed, and working memory.
There were four identification method categories that were used to determine the percentage of students identified as
MD. They were IQ-achievement discrepancy, low achievement, average IQ, and final low achievement RTI.
Efficacy of First-Grade Preventive Tutoring
The NAR students’ performance exceeded that of both of the AR groups.
Prevalence and Severity of MD
Tutoring reduced MD prevalence. The prevalence was lowered by 35.64%.
Cognitive Variables Associated with Early Mathematics Development
The variables that accounted for the most of the variance in the regression analyses were phonological processing, pretreatment
nonverbal problem solving, and pretreatment working memory. The strongest predictor of outcome was attention.
Conclusions and Recommendations
In this study, the authors noted two limitations: the AR students were low normal, which was contradictory to local normative
information and the tutoring was added to regular class math instruction, which was necessary to generalize findings to a
response-to-intervention model. The authors also noted that future work might broaden the search for cognitive determinants
and other variables, such as classroom features, and instructional quality, that may enhance the prediction of students’
first grade mathematical development.
My Reaction to the Study/Implications to Education
My hypothesis was correct in that the not at risk (NAR) students would perform better than the at risk (AR) students.
I was also correct in assuming that tutoring would reduce mathematics disabilities (MD) prevalence. Because no one test should
be a determining factor, it was important that this study involved a variety of assessments. This variety ensured the validity
of the results. In the future, more experiments should be conducted that are similar to this one in order to identify the
cognitive abilities relating to the development of mathematics competence.