Web-Based Learning Materials: Design, Usage and Resources
Presented at the International Conference on the Teaching of Mathematics,
Samos, Greece, 1998.
Michael R. Colvin
Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407 U.S.A.
mcolvin@calpoly.edu
Lester N. Coyle
Department of Mathematical Sciences
Loyola College in Maryland
4501 N. Charles St.
Baltimore, MD 21210, U.S.A.
coyle@fischer.loyola.edu
Lawrence C. Moore
Department of Mathematics
Duke University
Box 90320
Durham, NC 27708-0320, U.S.A
lang@math.duke.edu
Donald Hartig
Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407 U.S.A.
dhartig@polylog1.cpunix.calpoly.edu
William J. Mueller
Department of Mathematics
University of Arizona
Tucson, AZ 85721, U.S.A.
mueller@math.arizona.edu
Charles Patton
MathTech Services
1120 Fir Acres Dr.
Eugene, Oregon 97401, U.S.A.
blister0@nic.cerf.net
David A. Smith
Department of Mathematics
Duke University
Box 90320
Durham, NC 27708-0320, U.S.A.
das@math.duke.edu
Franklin A. Wattenberg
Department of Mathematics
Montana State University
Bozeman, MT 59717, U.S.A.
frankw@math.montana.edu
(on leave at the National Science
Foundation)
Abstract
The Connected Curriculum Project is producing innovative interactive computer-based materials in
a range of mathematical areas from precalculus to linear algebra and differential equations as well
as materials that illustrate the role of mathematics in other disciplines. These materials can be
used as integral parts of courses or as free-standing reference modules for review and enrichment.
The authors are participants in the Connected Curriculum Project, CCP, an interactive Web-based
mathematics project with home page at:
http://www.math.arizona.edu/ccp
and with materials available on servers at Cal Poly San Luis Obispo, Duke University, and Montana
State University. The project is supported by National Science Foundation grant DUE-9752421.
The Connected Curriculum Project
At the basis of CCP is the integration of new technological mediums with the following goals for
students: engage in active learning, study mathematics in the context of real problems, break
down the barriers between disciplines, and develop a sense of ownership of the concepts and
techniques discussed. Examples of our materials include placing trigonometric identities in the
context of sound and music, estimating the time it will take to clear Lake Wobegon of pollutants
using Euler's method, and the study of the Canadian Lynx and Snowshoe Hares as an example of
a predator-prey system.
The architecture of the World Wide Web is ideally suited for accomplishing these goals. The
hypertext structure of Web material emphasizes links and connections rather than
compartmentalization. Students starting with material in one subject will find themselves
following links to other subjects. Hypertext also emphasizes choice. By choosing applications and
examples that interest them, and by selecting the background material needed, students
construct individualized learning paths tailored to their own interests and background.
The malleability of Web-based material encourages multiple authorship and, most importantly,
multiple ownership. Web-based courses are living courses, evolving as our experience evolves.
Our goal is to create and maintain a large volume of highly interconnected material that will
support learning across the curriculum.
Design, Implementation, and Learning Issues
A crucial consideration in the development of computer-based learning materials is the
effectiveness of the interface that the student will see and use. The developer must consistently
compare the intended content of a particular lesson plan to the content that the student, in fact,
receives. This is a complicated business determined by many factors, and, as a result, the
interface design of many computer-based learning materials is based solely on the author's
personal experiences as a teacher and his/her best guesses about how to adapt those
experiences to a new medium. The CCP, however, has endeavored to address the question of
effectiveness in a much more systematic, scientific manner. We have gathered together
information from diverse sources in psychology, education, skills-training, industry, and art and
design, and we have distilled from these sources what seem to be the most common, well-tested,
and widely used principles of effective interface design. We have collected these principles in an
interactive text titled Design Principles for Interactive Texts, which is available on our Web site
and in which issues such as optimal use of color; placement, font type, and size of text; and
appropriate introduction of graphics are discussed. By applying these principles throughout our
development process, we are attempting to produce a group of materials that presents to the
student a uniform look and feel and an interface that incorporates sound principles of effective
pedagogy that are appropriate to the medium.
Web browsers are designed to encourage both active and interactive engagement with material.
We use a browser as a conductor, which orchestrates a mix of text, graphics, movies, and sound
with helper applications (e.g., Mathematica, Maple, Mathcad, and TI Graph Link), Java-based
interactions, and CBL data gathering. In a typical session, students go back and forth between
their browser window and their CAS window exploring real phenomena, mathematical models,
and the mathematics underlying the models at the same time.
Uses of CCP Materials
Our materials are being and will be used in various ways: as supplements to existing courses that
use currently available textbooks; to support interdisciplinary courses that draw material from
several different fields; by students on their own to supplement and complement material in their
courses, and to help them see connections between courses and fields that are often overlooked
in a departmentalized university.
These materials can also be used in different settings: in regularly scheduled laboratory
components for traditionally structured classes; in self-scheduled laboratory components for
traditionally structured classes, with work at various sites on campus or at home or in dorms
wherever students have Web access, plus a helper application and (if needed) lab equipment; in
courses where some lecturing is replaced by group work, with students at workstations that
include computers and lab equipment, and with an instructor circulating to work with students in
their groups; and in individual sessions in which students choose to use CCP as an additional
resource, working alone or in groups at home, in dorms, or in open labs.
Contributing Authors, Participating Sites, and Resources
In addition to the authors of this paper, participants in and contributors to CCP include:
William Barker (Bowdoin College, ME),
Lewis Blake (Duke University, NC),
Jack Bookman (Duke University, NC),
Robert Cole (Evergreen State College, WA),
Leonard Lipkin (University of North Florida, FL),
James Peters (Weber State University, UT),
Richard Schori (Oregon State University, OR).
For the time being, our materials reside on three separate (but linked) sites, each with a
special focus.
At the Cal Poly Site the focus is on interdisciplinary projects, student-directed investigations
of extensions and applications of classroom material. These projects draw on mathematical
problems from agriculture, architecture and environmental design, business, engineering,
liberal arts, various sciences, and mathematics itself. The mathematical level ranges from
precalculus to differential equations. Each project contains links to support modules in the
relevant areas of mathematics.
The Duke Site focuses on interactive modules, self-contained lessons for use as laboratory
activities, classroom demonstrations, or self-study. Mathematical topics come from
precalculus, single- and multivariable calculus, differential equations, linear algebra,
engineering math, and probability and statistics. The modules also cover a wide range of
applications of interest to students and teachers across disciplines. This site is a descendant of
the NSF-sponsored Project CALC reform calculus project. In particular, it will eventually
contain Web-based versions of all the Project CALC labs.
The focus of the Montana State Site is on interactive texts featuring detailed, full-length
expositions of mathematical subjects with frequent opportunities for reader participation and
investigation. Subjects include precalculus, calculus, modeling, linear algebra, differential
equations, and probability and statistics. The texts are cross-referenced, linked to a library of
supplementary help material, and tied together by a number of recurring case studies.
Through links to many applications, the texts seek to break down barriers between disciplines
and to encourage student and teacher ownership of individual courses.
The library of materials already developed can also be used by faculty as a model for creating
their own interactive projects. The Connected Curriculum Project has recently been awarded a
grant by the NSF to continue development of a Web site for high-quality, peer-reviewed,
professionally edited, interactive materials. We strongly encourage submissions to this library
from other authors.