The Design of a Research Based Curriculum for Real Analysis

Arizona State University, Scottsdale AZ

Investigators

Abstract

Mathematical Sciences (21): This project is studying student learning patterns in undergraduate advanced analysis, a critical course for students who intend to do advanced work in mathematics. The ultimate goal of the project is to design a research based curriculum with learning materials for the undergraduate mathematics course in Real Analysis at Arizona State University (ASU), as well as for other institutions throughout the U.S. This project will positively affect STEM undergraduate programs by: 1. Creating learning materials and teaching strategies, including lesson modules and an instrument to gauge students' readiness, 2. Implementing educational innovations through a whole-class teaching experiment and task-based interviews with individual students, and 3. Conducting research to explore students' understanding, obstacles and their learning patterns; and effective teaching strategies to enhance learning. Intellectual Merit: There is little research about students' obstacles and their learning patterns in upper level abstract mathematics courses, such as advanced undergraduate analysis. While much research on the application of educational theories has been done and materials have been developed for K-12 and some lower division undergraduate mathematics, there is no evidence that this work applies to advanced abstract courses. This project is a step toward filling this gap in the research literature. Broader Impact: Analysis courses, such as the one being studied at Arizona State are also present at most 4-year colleges and universities in the U. S. and are often required for undergraduate degrees in mathematics and secondary mathematics education. The proposed project will help a significant pool of mathematics students and future high school teachers across the nation to have a successful transition to upper division mathematics courses. This project is also developing faculty expertise by illuminating challenges to and opportunities for adapting innovations in diverse educational settings.