The Effects of Modeling and Direct Instruction on Learning Disabled Children's Atypical Numerical Cognition

Despite the widespread nature of mathematical learning disabilities, research within this area has been minimal. This study investigated the basis of atypical numerical concept development. Seriation, one of the most important components of concrete logical reasoning, was studied to determine the existence of a developmental delay or horizontal decalage in the Piagetian stage transition from preoperational to concrete operational thought. The influence of modeling and modeling plus direct instruction on the induction of seriation behavior was examined, using 60 learning disabled children and 40 remedial math students in a 4 x 2 analysis of covariance. Students were selected on the basis of parental permission and failure to successfully complete a seriation assessment instrument. Data from the randomized control design indicated that while all experimental groups significantly exceeded the control groups at posttest, a significant advantage was displayed by subjects who received the additional component of direct instruction. The two control conditions (one receiving a like amount of time for interaction and the other receiving only a pretest and posttest) did not differ from each other. Furthermore, in all comparisons for specific effects, the learning disabled groups did not differ from the remedial math groups. Theoretical and instructional implications were identified and discussed. Suggestions for future research were presented.