CAREER: Learning to Make Mathematical Connections

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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 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. Prior studies were used to pilot the research approach and potential results. The problem, expected solution responses, and instructional sequences are drawn from a model of a Japanese lesson. This CAREER award will be operated through the University of California-Irvine by Assistant Professor Lindsey Richland. Six experiments will be conducted, each on one strategy and designed to help develop optimal instructional routines. The six conditions are: 1) making student responses or key ideas visible, 2) making compared student responses or key ideas visible simultaneously, 3) visually organizing the student responses or key ideas to highlight key connections, 4) using at least one well-known student response or key idea to compare with something new, 5) using gestures between connected student responses, and 6) using visual imagery. Fifth and sixth grade students from three classrooms will be randomly selected to participate in one of two conditions (high support and low support) for the six experiments. For each experiment, each condition will be studied with 30 students. Data for all six experiments will be collected from a total of 360 students. All students will be given the same word problem requiring proportional reasoning. Then students will be shown an instructional video of a teacher presenting a lesson related to the problem. Students will be given pre- and post-tests and a new problem to solve as measures of effects. An ANOVA (pretest/posttest) with conditions as a between-subjects variable (high support/low support) will be used in the analysis. Two additional case studies will investigate the training of two teachers to use the most effective of the strategies in the first six experiments. Videotapes of these two teachers using the optimal strategies in their classrooms will be analyzed using the same protocol used in TIMSS. A highly qualified advisory board will serve as the external evaluation. An education plan includes mentoring graduate students and undergraduate researchers; educating pre-service teachers; collaborating through in-service teacher professional development with teachers from regional schools; and disseminating results in academic venues.Positive results of this application of cognitive science to the teaching and learning of mathematics will inform the field of mathematics education on routine of practices that distinguish high performing countries in mathematics achievement. The work may be of greatest benefit to English language learners and other under-represented groups. If the instructional strategies are viable, then teachers will have specific ways they can reduce the cognitive load on students who may be processing two languages while trying to learn mathematics.