Preparing Secondary Mathematics Teachers with Video Cases of Students' Functional Reasoning

This project seeks to address a critical area of mathematics, function, which is a unifying concept in K-12 mathematics that applies to the study of algebra, geometry, probability, and statistics, but persists as a challenge for students. To this end, this project will develop a series of video-based online learning modules for use in undergraduate mathematics courses so that prospective secondary mathematics teachers (PSMTs) are better equipped to recognize, analyze, and make connections between the patterns found in students' functional reasoning. Many students leave high school with serious limitations in their ability to reason with functions. At the same time, teacher education programs are faced with the challenge of preparing teachers to teach in ways that build upon the informal knowledge students bring to the classroom. Teachers who are adept at building upon students' ideas have a specialized knowledge of how mathematical ideas are related, how to represent ideas in meaningful ways, and common patterns in students' reasoning. This type of mathematical knowledge cannot be developed through field-based work alone.

The theoretical foundation for this project arises from (1) students' informal and formal reasoning related to key mathematical ideas, (2) students' thinking about functions, (3) the use of video to engage PSMTs in learning about student thinking, and (4) the design and use of video-based learning environments which feature online components. Using a design-based research methodology, the first two years of this project will focus on the development and beta-testing of four video modules in an undergraduate mathematics course designed for PSMTs. The final two years of the project will focus on the dissemination and implementation of these modules at partner UTeach institutions, as well as the study of data emanating from the implementation. Throughout the project, about 250 PSMTs and 20 university instructors will engage with the modules. The completed module series will provide teacher education programs a straightforward way to integrate mathematical content specific to teaching within their existing mathematics curriculum while simultaneously increasing well-designed hybrid learning opportunities at the undergraduate level. Through evaluation and research, the project will result in (1) an empirically-based model for PSMT learning about student thinking in the context of the module learning environments, and (2) theory and design principles for supporting PSMT learning with video cases of student thinking. Information about the project, its materials, and its outcomes will be shared with local and national educational audiences via research publications, conference presentations, and university instructor workshops. This project is supported under the NSF Improving Undergraduate STEM Education (IUSE) program and the Robert Noyce Teacher Scholarship program, with the goal of helping to improve secondary mathematics teacher preparation through implementation of online video modules that highlight carefully selected cases of student thinking. This project will enable teacher educators to better equip their undergraduate PSMTs in making functional reasoning accessible to a broad population of students, thereby potentially broadening student participation in STEM fields.