Mathematical Sciences (21) This project is creating learning materials and teaching strategies for mathematical analysis. Project outputs include: annotated sets of conceptual questions to generate student-student discussion; guided discovery tasks and scaffolded collaborative tasks to bridge connections among various concepts; historical vignettes to enhance understanding; and capstone connections tasks to focus on interconnections between mathematical analysis and other areas of mathematics. These materials with their accompanying annotations for instructors facilitate the use of research-based methods in the teaching of analysis. This, in turn, empowers students in gaining a deep understanding of real analysis and in using this understanding to continue further study, to communicate the ideas effectively, and use them in a meaningful way beyond the course.
The learning materials and teaching strategies being developed in the Empowering Student Learning in Mathematical Analysis project are innovative in their application to this advanced level of undergraduate mathematics. The guided-discovery exercises for in-class use is bringing active learning into a course that is often teacher-centered and taught in a passive format. The project addresses needs in a course that often serves as a filter to further study of mathematics at the graduate level and is a major stumbling block to perspective secondary mathematics teachers who must have a course in mathematical analysis to provide the rigor in understanding required to teach upper-level mathematics in the secondary schools.
