Advances in technology and the calculus reform movement have resulted in several recent curricular reform efforts in differential equations. These reform efforts have decreased the traditional emphasis on analytic techniques for finding exact solutions to well-posed problems and increased the use of computing technology to incorporate qualitative and numerical methods for understanding the behavior of solutions to differential equations. Research on student learning of differential equations, however, has lagged behind these curricula efforts.
This project will enlarge our understanding of how emerging analyses of student thinking, technology, context problems, and symbol use can be profitably coordinated to promote student learning of advanced, undergraduate mathematics, using differential equations as a specific case. The proposed research project will illustrate how theory-driven work at the elementary and secondary level can inform, guide, and sustain the learning and teaching of university mathematics in technology-rich classrooms. Long-range research plans include analyses that focus on effective means by which university mathematics instructors proactively support students' mathematical development in technology-rich classrooms.
In broad terms, the research methodology employed in this project falls under the heading of "developmental research" and highlights the relationship between research and practice, centering on the learning-teaching process with particular attention to the mental activities of students. Three, semester-long classroom teaching experiments and individual student interviews will be conducted over a period of five years. Data sources will include videorecordings of all classroom sessions, videorecordings of student interviews, copies of student work, and records of project meetings. Data analysis will follow the constant comparative method adapted for longitudinal classroom videorecordings and multiple data sources.
