Mathematics
Ohio State University'What does this have to do with a student learning calculus?'
Reproduced with permission from NeXT
Computer, Inc.
A Reference
Guide to NeXT in Higher Education, Fall 1992
ª
1992 NeXT Computer, Inc
That's the question three mathematics professors-William
Davis of Ohio State University and Horatio Porta and Jerry
Uhl of the University of Illinois-repeatedly found
themselves asking one another as they created
Calculus&Mathematica, an innovative
calculus-learning device.
"From the beginning," says Davis, "the project has been
primarily concerned with the teaching of calculus. All
content and design decisions were based on that one
fundamental question."
Originated by Porta and Uhl at the University of Illinois,
the Calculus&Mathematica project is supported
by the National Science Foundation at both the University
of Illinois and Ohio State University. Currently, calculus
instructors at more than 20 institutions use
Calculus&Mathematica. Half the schools use the
application on the NeXT platform-including Ohio State,
which has a 60 NeXTstation Mathematica lab.
"We chose NeXT computers for our lab for several reasons,"
explains Davis, "primarily the value-per-dollar of the
machine. All the features we needed for our lab situation
come with the NeXT. The critical
software-Mathematica-is bundled along with TEX and
NeXTmail. Networking that is built in and easy to use and
maintain is also essential for a learning lab. NeXT
includes the physical Ethernet connections as well as
NetInfo, NFSí,
and TCP/IP for file and traffic management. In addition, we
are quite pleased with NeXT's friendly user interface, easy
networking, true multitasking, and virtual memory."
Calculus&Mathematica is presented through 40
Mathematica Notebooks that students complete at a
rate of about one a week. Each Notebook is divided into
three sections-Basics, Tutorials and Give It a Try. Basics
and Tutorials provide completed exercises that illustrate
the principles students will learn about in Give It a Try.
According to Davis, the Give It a Try problems, which allow
students to discover and then apply the basic principles of
calculus, are the "centerpiece" of the course.
"Everything is there in Give It a Try," he says, "the
experiences introducing ideas and topics, the challenges to
intellect and patience, the excitement of beating the
course and solving a very difficult problem. There is no
more rote manipulation in this class. Problems are
open-ended. Students no longer simply memorize a formula
and then plug it in to solve a particular equation. They
play, conjecture, test, conjecture, play more, and almost
always come to the correct conclusion."
Davis teaches Calculus&Mathematica completely
as a lab course-there are no lectures although the
instructor typically devotes 10 minutes of class to
answering student questions. Students are then assigned
lessons and exercises and spend class time and one to two
hours after each class working on a Notebook. During the
class session, Davis walks from student to student
answering any individual questions they may have.
Adds Davis, "With NeXT, we're finally able to tell students
that all of their work will be preserved on our network.
Other platforms provide irritating features that make it
mandatory that students carry their own work with them on
floppy disks. Inevitably, the floppy disks fail, students
forget to save their work to their disks as they leave the
lab, they forget to bring their disks to class, and so
forth. With the NeXT, students receive their lessons from
the lab's server and turn in homework via NeXTmail. Now,
faculty can grade assignments while sitting at remote
machines with the lab's server mounted. That was not
possible in our previous labs."
For more information, please contact:
William J. Davis
Department of Mathematics
Ohio State University
231 W. 18th Ave.
Columbus, OH 43210
(614) 292-0635
davis@function.mps.ohio-state.edu