Collaborative Research: Supporting Mathematical Instruction around Definitions through Values-Centered Collaboration

This project aims to serve the national interest by improving undergraduate mathematics instruction through a values-centered collaboration between mathematics education researchers and mathematics instructors. The project will focus on the norms and values associated with mathematical definitions. Definitions are fundamental across different undergraduate courses, yet there is growing evidence of differences in mathematicians' and students' understandings of their nature.

The project will use mathematics instructors' norms and values for definitions to guide discussions around instructional change. It will provide a practical model of how mathematics instructors and mathematics education researchers can leverage their respective strengths to develop new approaches to instruction.

The project has four main aims: (1) characterize instructors' norms and values around definitions and determine barriers and supports in communicating them to students; (2) characterize instructional moves that communicate specific norms and values; (3) examine the relationship between the norms and values communicated in instruction and what students take away from courses, including their views of mathematics; and (4) develop a toolkit to assist instructors in enacting practices that support their mathematical values. The project will pursue a novel approach to innovation by focusing on collaborations between mathematics education researchers and mathematicians, determining mathematics instructors' values and norms around definitions, and assisting instructors in instantiating those values and norms in their pedagogical practice in ways that are comfortable to them.

The project will draw on a range of qualitative methods, including focus groups, classroom observations, interviews, and surveys with instructors and students, combined with design research. Assessment will examine instructors' characterization of changes in their teaching practices and sense of community around discussing teaching, and students' descriptions of experiences with the new teaching practices.

Evaluation will be conducted by an advisory board and an external evaluator. Both will examine the research team's work and provide suggestions for improvement, while the external evaluator will, in addition, follow up with participants to better understand instructors' experiences in the focus groups and their intentions for sustaining change, as well as students' experiences with the new instruction.

Dissemination will focus on providing professional development that demonstrates the toolkit to mathematics instructors in a variety of practitioner settings, in addition to research presentations and journal publications.

The NSF IUSE: EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.

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.