Leveraging Pedagogical Comparisons in Mathematical Thinking and Learning

The primary goal of this project is to help students improve their relational reasoning, that is, a way of attending to and recognizing relations, including commonalities and differences, between mathematical objects and concepts. Relational reasoning has been shown to support learners in developing their problem-solving skills, skills that are helpful not only in mathematics, but also in subjects like science, engineering, and healthcare, where strong reasoning skills are important for learning and problem solving. The project studies aim to identify instructional supports that help students develop a “relational mindset” as well as to enhance their conceptual flexibility in problem solving. Drawing on cognitive science literature on relational reasoning, the project includes three experimental studies designed to test whether directing students' attention toward relations can foster a relational mindset and consequently enhance students' conceptual flexibility. The studies include a) explicitly directing students’ attention to mathematical relations through classroom discourse; b) implicitly priming relational attention through completing a relevant task; and c) engaging students in antithetical thinking during practice. Analyses will include both descriptive analyses and multiple regression analyses. Study results will provide insights into effective instructional approaches designed to foster students’ attention to and interaction with mathematical relations. This project is funded by the STEM Education Postdoctoral Research Fellowship (STEM Ed PRF) program that aims to enhance the research knowledge, skills, and practices of recent doctorates in STEM, STEM education, education, and related disciplines to advance their preparation to engage in fundamental and applied research that advances knowledge within the field. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.