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As today's classrooms become more and more diverse, there is a growing need to explore the intersection between English Learners (ELs) and students with learning disabilities (LD) in the content-specific instruction of mathematics problem solving. The aim of this study was to determine which types of instructional scaffolds may be used by math teachers to effectively support ELs with LD learning multiplicative reasoning. To this end, we employed an exploratory case study based on a frequency count analysis of four scaffold types used by the students and the teacher in their sessions. The results showed that kinesthetic and linguistic scaffolds were the most beneficial for helping ELs with LD to cultivate mathematical thinking with both concrete and abstract units, while also helping to increase the sophistication of their mathematical content-language usage. In combination with small-group interactions, these scaffolds provide an effective instructional method for improving multiplicative reasoning among ELs with LD.

The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth graders with learning disabilities or problems (LP). An adapted multiple-probe-across-participants design was employed to examine the functional relationship between the intervention (the COMPS program) and students' performance on solving multiplication and division word problems and algebraic model expression. The results indicate that the computer-assisted COMPS program seemed to benefit students with LP; it enhanced their problem-solving skills and promoted "algebra-readiness". Discussion also includes ideas to enhance the COMPS program. (Contains 5 figures and 2 tables.)