This project explored the Concrete to Representational to Abstract instruction (CRA instruction) as a strategy to teach abstract math concepts for secondary students with learning disabilities. Through the review of literature, multiple researchers suggested that students with learning disabilities need to be exposed to a variety of instructional strategies to develop problem solving skills in algebra concepts.

Specific to the recommendation of the National Council of Teachers of Mathematics (1980) to identify and analyze problem solving strategies and the settings in which the development of these strategies could be optimized, this study is a compilation of three case studies which describe what elementary school children say and do when solving verbal mathematics problems in small groups. Persuant to this goal, three four-member groups were selected and asked to reach a consensus within each group on the solution to a variety of routine and non-routine problems. In this relatively unstructured setting, transcriptions of verbal interactions, written records of all computations, and observer notes were compiled for each group. The resulting identification and description of the problem solving behaviors which occurred were analyzed in terms of two broad interactive functions by which children seek to understand verbal problems: the construction of mental representations or physical displays of the problems and the evaluations of these constructions. Representations, in this perspective, are constructed at two levels: a contextual level at which the problem situation is linguistically interpreted and a structural level at which a statement of a problem underlying mathematical structure is defined. Evaluations also occur which allow group members to monitor their understanding and direct the course of the problem solving effort. The findings indicate that intermediate aged children when solving problems in small groups display general patterns of behavior. These patterns of behavior include: the manner in which the groups approach and effectively isolate the contextual elements of a verbal problem, the propensity of groups to change the mode in which a problem is represented by utilizing manipulatives, diagrams, tables and other physical displays, and the manner in which groups monitor the course of problem solving and reach consensuses on solution proposals. Within this general pattern, however, specific subject and task variables characterize individual groups, affecting both the group interaction and the incidence of specific problem solving behaviors. These findings suggest practical classroom applications for group problem solving formats in the elementary school classroom. Additional research, however, must provide the link between group problem solving and individual performance.

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education