Effects of a Problem-Solving Strategy on the Introductory Algebra Performance of Secondary Students With Learning Disabilities

Abstract

We investigated the effects of an instructional strategy within a graduated teaching sequence (i.e., concrete, semiconcrete, abstract) on the representation and solution of problem-solving skills encompassing integer numbers for secondary students with learning disabilities. Students advanced through three levels of instruction: (a) concrete application (i.e., manipulating physical objects to represent mathematics problems), (b) semiconcrete application (i.e., drawing pictorial representations of the mathematics problems), and (c) abstract application (i.e., writing mathematical symbols to represent and solve problems). Students also learned a strategy designed to cue effective problem-solving procedures. A multiple-probe design across participants was used (Tawney & Gast, 1984). Results indicated problem-solving skills involving integer numbers dramatically improved following instruction at the concrete, semiconcrete, and abstract levels. Students' strategy-use also increased over these instructional levels. Furthermore, generalization of treatment effects was evident in a far-transfer generalization task and over time for multiplication and division of integers.