The main goal of this mathematics education research project is to determine through experimentation specific teaching strategies that can be used to support middle school students in drawing connections between mathematical representations (fractions and ratios). The potential instructional strategies were identified from the Third International Mathematics and Science Study (TIMSS) video analyses study as the ones that best distinguished high performing countries from low performing countries.
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My body of research explores the ways that children learn to reason inferentially and analogically. We use an integration of experimental, interactional, cross-cultural, and computational approaches to better understand children's development of reasoning skills in complex, naturally occurring contexts of STEM (Science, Technology, Engineering and Mathematics). My current projects include studies of interactional supports for students' comparative reasoning in mathematics - specifically with relation to ratio and proportions, learning from visual and spatial representations in middle school science and mathematics, investigations of the processing mechanisms underlying children's development of reasoning skills, comparative reasoning and problem solving in naturally occurring contexts, and the design of learning environments based upon these interactional and cognitive analyses.