Collaborative Research on Learning and Tteaching at the Physics-Mathematics Interface

点击翻译按钮获取中文摘要

This award supports a project to investigate the development of undergraduate students' mathematical understanding in the context of learning physics, particularly while solving challenging upper-division physics problems. The project team will conduct an integrated program of research, curriculum development, and assessment of topics covering a typical sophomore- or junior-level course in mathematical methods. The broad goals are to conduct research on student resources, study the process of transfer from mathematics to physics and the coevolution of knowledge in the two disciplines, and develop a set of Math / Physics tasks suitable for instruction, research, and assessment materials that will integrate challenging math content with topics covered in upper-division physics core courses. This project has the potential to impact a gateway course to the upper division for physics majors. Curricular materials will be shared through electronic clearinghouses and via published research and it is anticipated that the project will inform instruction - both of math methods courses and subsequent physics courses in which the mathematics is used - nationally and internationally. The student population at California State University Fullerton includes many students from groups traditionally underrepresented in physics, so this project will provide access to research-based materials for these students and also ensure a diverse research population. This interdisciplinary project brings together physics education research (PER) and research in undergraduate math education (RUME). It blends efforts at identifying and addressing student conceptual difficulties in physics with efforts toward understanding knowledge transfer in mathematics. The work targets a key course for physics majors, the mathematical methods course that is offered in most departments at the sophomore- or junior-level. This course is typically intended to be a bridge between introductory physics and calculus courses and the more challenging mathematics and physics encountered by students in the core courses of electricity and magnetism, classical mechanics, and modern physics / quantum mechanics. The project will strengthen the research base in a portion of the curriculum that has, to this point, largely gone unexamined, and will touch upon, and build upon, work in several related areas, including PER in other upper-division courses as well as the extensive research base in undergraduate mathematics education. This proposed work will provide significant insights into transfer by probing the extent to which the nature of student understanding depends upon the disciplinary context. The research team has many years' experience in PER and RUME and have collaborated on successful research and curriculum development projects at the upper division in thermal physics and the physics-mathematics interface.