3. Project Objectives

Our project is a large, complex endeavor that seeks to improve the way thousands of faculty teach and hundreds of thousands of students learn in quantitative courses across New York. The project objectives fall into three major themes.

These three themes are interconnected. For example, a planned new course on the mathematics of fairness will be designed to be taught with group learning activities and extensive writing assignments. The course would appeal to students who had previously associated mathematics solely with the physical sciences. Likewise, an effort to coordinate the use of differential equation models in physics, chemistry, engineering and mathematics courses might use new project-developed curricular materials showing how particular DEs arise in diverse settings. These materials would involve topics for group projects. Minority- and female-support workshops could use DE modeling projects to re-enforce quantitative reasoning skills across several disciplines.

The following three principles of instructional reform underlie all project activities.

• Develop connections in both instruction and curriculum between mathematics and mathematically based disciplines.
• Increase the use of technology in all courses.
• Continually assess and refine the project's activities, materials, and strategies.

Both the course in the mathematics of fairness and the planned DE materials are designed to highlight interdisciplinary connections. Both would use computer simulations and, because of their innovative and experimental nature, both would require continual assessment and refinement.

A premise underlying many of the project activities is that instruction today is too narrowly focused on the subject of an individual course or the point of view of a particular discipline. The scientific and business workplace today is characterized by multidisciplinary thinking that draws on the paradigms and problem-solving strategies of many different disciplines. Many business groups, such as the risk assessment divisions of major banks, value physicists, mathematicians and engineers for their common training in quantitative problem-solving. It is as if faculty in these different disciplines see themselves as specialists in Bach or Tchaikovsky or jazz, while the world wants broadly trained musicians. Faculty in quantitative disciplines must collaborate more fully to give students this broader, multidisciplinary point of view in their training. For example, quantitative finance today uses partial differential equations arising from physical science models of diffusion and methods of discrete optimization common in the decision sciences, as well as extensive data structures and statistical methods. Faculty today should work together to bring out the connections inherent in the common mathematical themes and the methods of reasoning and application that pervade quantitative disciplines.

An NSF-funded Mathematical Association of America case studies project (directed by Alan Tucker) of highly effective undergraduate mathematics programs is finding that faculty in such exemplary programs are doing everything very well� teaching effectively to a broad range of students, interacting with students outside of class, career advising, etc.� and that simultaneously they are critical of everything they do. Initially these programs had only a few activists but they succeeded in getting all of their colleagues engaged. These faculty are constantly experimenting with different approaches to teaching and student learning. While these faculty have quite diverse views and interests, they share ideas constantly. Although they are all working very hard in their instructional efforts, they are having a wonderful time. This project seeks to engender such a cooperative, supportive spirit among instructors in all quantitatively based disciplines.

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The Long Island Consortium is sponsored by the NSF Initiative: Mathematical Sciences and Their Application Throughout the Curriculum, DUE #9555142. The original NSF proposal can be accessed by clicking here.