The overall purpose of this project is to increase the understanding and decrease the prevalence of disability in mathematical problem solving (MPS; word problems requiring more than one step and/or presented realistically with relatively long narratives and/or irrelevant information). On the one hand, research on MPS has been confined largely to middle- and high-school students without significant difficulties. On the other hand, research on mathematics disability in younger children has focused primarily on arithmetic, with some attention to arithmetic word problems (linguistically simple one-step problems requiring adding/subtracting basic facts). Arithmetic word problems do not, however, represent the kinds of math problems incorporated in school curricula beyond the earliest grades or those required in life. So, the generalizability of findings to math disability as it occurs in and out of school is tenuous. This creates the need for the explicit study of MPS disability (MPSD) at 3rd grade, when students are first expected to solve multi-step problems with longer narratives and/or irrelevant information. Another reason to increase the breadth of math disability study is that, given the demands of MPS, the profiles associated with deficient arithmetic or arithmetic word problems may differ from those associated with deficient MPS. Consequently, a focus on MPS is required to understand and prevent math disability as it develops in schools and pertains to real-world competence. This project employs randomized controlled trials to test the efficacy of classroom-level and tutoring treatments designed to decrease the prevalence of MPSD, with the contribution of an innovative component tested annually for classroom-level and tutoring treatment. Within the context of those trials, the prevalence and diagnostic stability of MPSD is estimated as it occurs with or without reading disability (RD), with or without using an IQ-achievement discrepancy, and with or without prevention. The demographic, academic, attention, and cognitive profiles associated with the development of MPSD with or without RD and with or without IQ-achievement discrepancy are explored, and students are followed longitudinally to understand how classroom and tutoring prevention efforts at 3rd grade, when complex MPS develops, affect outcomes as curricular difficulty intensifies through the 5th grade.
Four specific aims are therefore proposed: (1) investigating the demographic, academic, attention, and cognitive profiles associated with the development of MPSD with or without RD and with or without IQ-achievement discrepancy; (2) estimating the prevalence and stability of MPSD with or without RD, with or without IQ discrepancy, and with or without prevention; (3) building effective classroom-level prevention for MPSD; and (4) identifying effective preventive tutoring for students at risk for poor MPSD outcomes with and without risk for RD.
