This project deals with the fact that many college students fail in their goals to become scientists and many scientists and engineers are blocked from modern developments in their discipline by their inability to master advanced mathematical topics. Mathematics is the language of science, but students and their instructors often focus on the grammatical rules of the language and ignore the semantics - how mathematics can be used to make sensible meaning. Over the past 20 years, the PI and his colleagues have been studying student learning and the use of technology in physics education at the introductory level. This research has shown that an understanding of how students learn (or fail to learn) combined with appropriate technological tools can create learning environments that produce dramatic improvements both in student learning and in their attitude towards the subject. This project is applying the ideas developed in the PIs' earlier work in introductory physics to the more complex mathematical structures and tools of upper division science courses. The project combines research into student learning with modern pedagogy and computer technology to create a set of non-traditional lessons and activities. The project is developing both an improved understanding of the barriers to students' learning advanced mathematics for science as well as new tools to help them surmount those barriers. The readings, active-learning lessons, and non-traditional problems prepared for this project are being distributed openly via the web.
