R & D: Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-Modeling Environmenty (NMRSD-CCME)

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Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-Modeling Environment (NMRSD-CCME) is a five-year research and development project that will augment teaching practice by providing the tools to analyze student conceptions and enact best-practice on an individual, student-needs basis. The purpose of this project is to: (a) create a research-based model of how students with learning disabilities (SLDs) develop multiplicative reasoning via reform-oriented pedagogy, (b) convert the model into a computer system that dynamically models every student's evolving conceptions and recommends tasks to promote her/his advancement to higher level, standard-based multiplicative structures and operations, and (c) study how this computerized teaching tool impacts student outcomes, including diminishing the gap between SLDs and their normal achieving peers (NAPs). The PIs draw upon universal design and three research-based frameworks: machine (or statistical) learning from computer sciences, generalization of word-problem underlying structures (story-grammar) from special education, and a constructivist view of learning from mathematics education. The latter consists of recognizing teaching can promote transformation of students' available mathematical conceptions into intended ones via tasks that orient student reflection on activity-effect relationship and content-specific constructs informed by established research. The development is done in three stages. The first is a teaching experiment to determine learning trajectories for multiplicative reasoning with SLDs. The second is the development of a computerized modeling system to support students' construction of multiplicative reasoning (includes alpha, beta and pilot testing). The final stage is the evaluation of the system by comparing the learning process and outcomes of 15 SLD students with 15 non-SLD to judge the effect of the system on closing the achievement gap. In addition, the effect of the system on SLDs' performance will be compared to the effect of traditional teacher-delivered instruction on SLD. The products include software that is flexible and adaptive to the learner and protocols for teachers. The project also tests the viability of dynamic recommendation algorithms, which is likely to be important in other domains beyond multiplicative reasoning and with other students who have difficulties learning mathematics concepts.