An Instructional Complexity Approach to the Science of Learning by Analogy

University Of Chicago, Chicago IL

Investigators

Abstract

Mathematics teaching that is flexible, transferrable, and connected across topics is crucial to high quality instruction. This exploratory project addresses this goal by a potentially transformational approach that leverages and extends science of learning research on analogy, a promising mode for supporting flexible and connected mathematical thinking. This study proposes an approach different from much of lab-based research designed to focus on isolating specific mechanisms of learning for study. Instead, the researchers will intentionally examine multiple learning processes combinatorially and as situated in classrooms. Many mechanisms of learning operate simultaneously in naturalistic classroom situations, and may either augment or undermine each other. Therefore, more theories that explain how students learn from the interaction of cognitive principles/processes is urgently needed. Research that is better aligned with learning in classroom settings will also make research findings more applicable for use, enabling teachers to more easily adopt research-based recommendations for classroom practice. The investigators will test this approach by leveraging a set of "translation ready" principles" for spatially supporting analogy during STEM learning. These are principles that produce high learning outcomes and for which there is classroom evidence for their usability and efficacy. As these principles are implemented in naturalistic classroom settings, this study takes seriously the diverse ways in which they may be realistically enacted (or not) in the classroom, in different combinations and sequences that may change the expected outcomes. The principles for supporting mathematics classroom analogy in this study were developed by the NSF supported Spatial Intelligence and Learning Center (SILC), and they include: simultaneous visual representations, spatial alignment, linking gesture, and sensitivity to children's cognitive resources. Study 1 is a new analysis of existing data to compare how teachers in the U.S. versus two higher achieving regions: Hong Kong and Japan, use and combine these principles when teaching 8th grade mathematics by analogy. Study 2 will be deep interviews with a set of expert teachers for dissemination of these principles and the results about their combinatorial frequencies. Teacher feedback on these alternatives will be elicited, as well as their input regarding best practices of analogy for their own students. Study 3 will experimentally compare three versions of a video-based lesson - one involving multiple support strategies as modal in the high achieving regions, one involving the modal U.S. combination of supports or violations, and one with the optimal combination predicted by SILC. WM and EF measures will also be administered to explore whether combined supports increase or reduce processing load. Together, these studies will provide rich data on the way spatial analogy principles are 1) typically combined in practice, and 2) optimally integrated to support students' learning in mathematics classrooms. This data will support the generation of theory that addresses how cognitive mechanisms interact to support students' mathematical thinking. Broader Impacts: The project has the potential for broad impact on mathematics teaching as well as on research in the science of learning. The project takes an innovative approach to shifting the focus of theory driven research to incorporate complexity without losing rigor, making learning theory better able to explain and inform teaching practice within the complexity of everyday classrooms. A broad dissemination plan for best practices of analogy instruction is in place.