This paper reports on the main results of a study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Ma ...

This paper reports on the main results of a study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education- Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially serving as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level