The introduction of technology into mathematics instruction at the
University of South Carolina has largely been a matter of
individual initiative, to some extent supported by the
department, and more enthusiastically supported by the higher
administration, but not systematically coordinated or assessed. This
has had both advantages and disadvantages: on the negative side,
progress has not been as fast as some of us would have liked, but on
the positive side we have not been locked into large commitments and
expensive failures.
Technology use in the department goes back at least ten years when a
special track of our linear algebra course (Math 526) was set up with
an additional laboratory credit hour for computer work. The additional
work is more or less loosely bound into the lecture portion of the
course, but is generally taught by a teaching assistant rather than
the professor. The language for most of this time has been Matlab,
which is introduced from scratch. Macintosh and workstation labs have
both been used. Enrollments in the past were as high as 60 students a
semester, but with a change in the Computer Science program we are now
seeing around 25 students a semester. Instructors of other applied
math courses (Math 524 -- Nonlinear optimization, Math 527 -- Numerical
analysis, Math 570 -- Discrete optimization) have periodically
required programming exercises or use of software
packages, but there is little institutional memory of what is done.
There are no scheduled laboratory hours or programming prerequisites
for these courses. However, enrollments in these courses are low,
perhaps 20 students total in a good semester, so massive commitment of
time and resources has not seemed warranted. Graduate applied math
courses have been handled in a similar way.
Thus to see a major impact of technology on instruction we had to
introduce it into the freshman and sophomore service courses. Several
other factors were also at work. Various faculty both in the
Mathematics Department and the other departments that it serves became
interested in curricular reform. Maple, once solely a research tool,
became much more user friendly and amenable to instructional use, and
could be purchased under a university wide site license. The NSF, the
Lilly Foundation, and a host of other funding agencies began to support
instructional innovation, and publications resulting from this support,
including new texts, began to appear.
Locally, under pressure from the engineering faculty we undertook to
reassess our calculus curriculum and mode of instruction. After
extensive consultation with faculty from other departments a number of
us launched a reform calculus course that runs alongside the
traditional one. Technology is indispensable in this course, but is
not the central focus; for this reason we were able to agree to
disagree on just what technology to use. In 1993--1994 we ran one
section that used the HP 48G graphics calculator, and one that used
Maple (in facilities provided by the College of Engineering: a PC lab
for use outside of class hours and PC projection capability in class).
Of the three sections (enrollment 60 apiece) that we have run each Fall
semester since 1994, one has used the HP and two have used Maple. An
NSF ILI grant, matched by money from the College of Science and
Mathematics, provided 30 workstations, of which 15 are in a lab and 15
are arranged around the periphery of the classroom used by the reform
calculus sections (and any other courses that might profitably make use
of the machines during class time). In the Spring semester enrollments
amount to the equivalent of two sections of 40 students each. A
projection device and portable Macintosh (later PC) also became
available for demonstration purposes, and a number of instructors began
making use of Maple in particular for calculus, differential equations,
and vector calculus. Another projection device, compatible with Mac,
PC, and workstation environments, has been purchased with funds from
the department, college, and university administration.
With the advent of the WWW, sharing of files such as Maple worksheets
has become commonplace, but in the early years of our experimentation
transmission of files between instructor and students, and between
platforms, was a source of irritation and problems. The creation of a
central and open departmental site was a major step that enabled less
committed faculty (and interested students) to sample what the
activists were doing, and for the activists themselves to avoid
continually reinventing the wheel. One of the major contributions to
this file bank is a Maple worksheet called day1.ms that has served as a
template for numerous other versions. Usable by an instructor, who may
not himself be experienced in Maple, it provides a gentle guided tour
for the novice student.
Also in cooperation with Engineering a parallel differential equations
course was established; thus far sections of the standard size of 30
have run in the Fall 1994 and Spring 1996 semesters. Maple plays a much
more central role in this course, which has a strong emphasis on
modeling, so it has been offered in dedicated computer (PC)
classrooms. In a similar vein, but for a very different audience, a
mathematical biology course was run in the Fall semester of 1995; it
attracted 10 students and will be offered again in the Spring of 1997.
Maple is available at a number of the open computer labs on campus, but
student use still tends to be restricted to class assignment. This
may change over time as students are introduced to it earlier in their
careers. Approximately 140 students have been exposed to Maple in their
Engineering 101 course in the last two years, and it will be
interesting to see if they begin to make independent use of the
software.
In this workshop you will have an opportunity to see how we use Maple
in the classroom. Our goal is to bring students to the point that they
can, if not generate their own Maple code, at least modify existing
worksheets to solve new problems. We begin, as students do, with
day1.ms. After that, you are invited to walk through our collection, to
get some idea of the variety of topics and approaches that are
possible. Some worksheets are essentially gee-whiz demonstrations, with
minimal student involvement (and for some topics this is perfectly
appropriate). Others are to be meticulously worked through, line by
line, with questions to be answered. Note that while Maple is our
language of choice, this is not at all essential. Certainly the more
elementary programs can be replicated on graphics calculators, and the
more advanced ones in other computer algebra systems. Maple itself
changes from release to release, and none of these worksheets is so
perfect that it never needs improvement. Please feel free to make use
of these worksheets yourselves and with your students--and if you have
suggestions for improvement or questions by all means contact us.
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