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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.

William J. Mueller
Department of Mathematics
University of Arizona
Tucson, AZ 85721, U.S.A.

Lester N. Coyle
Department of Mathematical Sciences
Loyola College in Maryland
4501 N. Charles St.
Baltimore, MD 21210, U.S.A.

Charles Patton
MathTech Services
1120 Fir Acres Dr.
Eugene, Oregon 97401, U.S.A.

Donald Hartig
Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407 U.S.A.

David A. Smith
Department of Mathematics
Duke University
Box 90320
Durham, NC 27708-0320, U.S.A.

Lawrence C. Moore
Department of Mathematics
Duke University
Box 90320
Durham, NC 27708-0320, U.S.A

Franklin A. Wattenberg
Department of Mathematics
Montana State University
Bozeman, MT 59717, U.S.A.
(on leave at the National Science Foundation)



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:

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.