Facilitating Multiplicative Reasoning Among Third-Grade Students With or at Risk for Mathematics Difficulties: A Pilot Study.

This study investigated the efficacy of a Tier 2 multiplicative reasoning (MR) intervention designed to help third-grade students at risk for mathematics difficulties (MD) develop conceptual understanding of MR. The MR intervention included opportunities for students to engage in critical thinking as they generalized big ideas, participated in classroom discourse, and modeled multiplicative relationships with multiple representations. Sixteen elementary teachers from a southwestern U.S. school district were randomly assigned to a treatment or control (business-as-usual, BAU) condition. Participants included 86 third-grade students who demonstrated MD. Data analyzed after 6 weeks of instruction revealed statistically significant and nonnegligible differences between conditions on a researcher-developed MR assessment, with posttest differences favoring treatment classrooms. However, treatment was not a significant predictor of the Group Mathematics Assessment and Diagnostic Evaluation posttest scores. Results demonstrated that the MR intervention was on average more effective than the BAU approach in improving students' ability to reason with multiplicative concepts and procedures.