The SCHOL ODE Project at the University of Maryland, College Park (UMCP)

• To enhance students' understanding of the fundamental concepts of mathematics presented in the traditional courses at the sophomore level and above;
• To provide students with a tool, in the form of a modern mathematical software system, for exploring, understanding, and using mathematics; and
• To improve students' abilities to communicate their understanding of mathematics to faculty, peers, and others.

Since 1992, SCHOL has been experimenting with several mathematical software systems in Math 246, the sophomore ordinary differential equations course at UMCP. These experiments have resulted in the writing of three texts, Differential Equations with Mathematica, Differential Equations with Maple, and Differential Equations with Matlab, all published by John Wiley & Sons, Inc. The first appeared in 1994, the second in 1995, and the third in 1998. The second edition of the Maple volume, updated for Maple, Version V4, appeared in 1997; the second edition of the Mathematica volume, updated for Mathematica, Version 3.0, appeared early in 1998; and the second edition of the Matlab volume, updated for Matlab 7, is under development. In the latter effort, Dr. Jonathan Rosenberg has joined the team of authors, and Drs. Coombes and Stuck have departed. These books are supplements to the text Elementary Differential Equations, by Boyce & DiPrima (the latest version of which is the eigth), also published by Wiley (although they are suitable for use with almost any sophomore level ODE texts). The SCHOL books have three components: computer platform instruction; non-traditional ordinary differential equations (ODE) supplements; and original computer problem sets. Each of these is unusual in its own way.

1. Computer Platforms and Mathematical Software Systems. In these chapters students are instructed in the rudiments of the mathematical software system (either Mathematica, Maple, or Matlab), and in the remarkable interfaces through which the students interact with the system (Notebooks in the case of Mathematica, Worksheets with Maple, and the Desktop or M-Books with Matlab). They are also trained to use all the special features of the software that have a direct bearing on the solution of differential equations. The chapters are written with explicit and simple instructions for the most common platforms: Windows or Linux (on PC's), Macs or the X Window System (on Unix machines).
2. ODE Supplements. In these chapters students are introduced to those aspects of differential equations that, while vitally important and most relevant to the needs of practising scientists and engineers, are usually omitted, or only treated briefly, in a traditional text: namely, numerical, geometric, and qualitative methods. The software systems render these topics, virtually untreatable in an old format, easily and stimulatingly accessible to undergraduate students.
3. Problem Sets. In these sets the student brings to bear newly acquired skills in the computer system to solve non-traditional problems in differential equations. The emphasis is on the symbolic, numeric, geometric, and qualitative aspects of the subject. The problems, each of which is a small project, are designed to force the student to engage in critical, analytic, and interpretive thinking beyond rote manipulation of algebra and calculus formulas.

Very little formal instruction on the platforms or software system is presented in class. Students learn about them from the SCHOL text, from on-line help, Graduate Assistant tutors (acting as first-aiders), each other, faculty assistance in office hours, or from the math software books written by the authors The Mathematica Primer and A Guide to Matlab.

The effects of the project, aside from achieving the goals indicated above, include: creating a mathematical computational culture among students (they use the tools they take away from this course in other courses, in lab reports, and later on in their jobs); fostering cooperative learning (students are encouraged to work in teams, and they quickly become acclimated to cooperative problem-solving in a team setting); enhanced visual and communication skills (the interfaces allow the student to integrate textual, symbolic, and graphical material in an informative and effective way). Most importantly, the intellectual level of the course has been raised---without a drop in student performance.

July, 2004