Examination of Cognitive Processes in Effective Algebra Problem-Solving Interventions for Secondary Students with Learning Disabilities

Algebra problem solving is one of the most difficult areas in the mathematics curriculum for secondary students with learning disabilities (LD) due to the higher-order reasoning demands and strategic thinking required. The purpose of this review is to examine how effective algebra problem-solving interventions conceptualize the cognitive processes of problem solving, and to examine the types of instructional supports or strategies embedded in each problem-solving phase to facilitate cognitive processes. In 11 effective algebra interventions, we identified four conceptualizations of the cognitive processes involved in problem solving: (a) sequential concrete–semi-concrete–abstract, (b) sequential virtual-abstract, (c) integrated concrete–semi-concrete–abstract, and (d) abstract only. We also found that each intervention incorporated several instructional strategies (i.e., scaffolds) to support students through the cognitive process of problem solving. Educational implications, future directions, and limitations are discussed.