The SCHOL ODE Project at the University of Maryland, College Park
(UMCP)
SCHOL is an acronym for the developers (Drs. G. Stuck, K. Coombes,
B. Hunt, J. Osborn, and R. Lipsman) of a computer supplement for the
sophomore Ordinary Differential Equations course.
The goals of this project are:
- 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.
- 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).
- 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.
- 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.
Students do all their work in campus computer Labs. All
platforms are available, and students select those they feel most
comfortable with. Because of
the remarkable interfaces, faculty barely notice any difference in
the output generated by students working on different platforms.
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