The Connected Curriculum Project - Overview and Philosophy of the CCP Materials

David Smith and Lang Moore

CCP is a collection of learning materials primarily for lower-division undergraduate mathematics. Each CCP learning unit uses at least some of these powerful tools:

  • hypertext links,
  • Java applets,
  • sophisticated graphics,
  • a computer algebra system,
  • realistic scenarios,
  • thought-provoking questions that require written answers,
  • summary questions that enable students to see the forest as well as the trees.

Our purpose is to challenge students to engage with important mathematical concepts in meaningful contexts -- to experiment, to conjecture, to test their ideas, (sometimes) to discover relationships, to check their work until they are convinced that it makes sense. In particular, we do not (in general) provide answers -- rather we provide tools by which students can decide for themselves whether their answers are correct.

Most of our experiences using the CCP materials have been in interactive classroom environments -- a setting in which students begin the work under the eye of the instructor. However, the materials can also be used wherever students have access to the Internet on a computer with one of our supported computer algebra systems.

One of us has recently published an article on the interactive classroom environment in which we currently use the CCP materials. The article also links design features of the materials to recent research on teaching and learning.

There are many tools available for creating interactive learning environments -- and hence many ways to do the same thing. Our principle for deciding whether to create the interaction in a web page (with a Java applet, say) or in the CAS worksheet is this: If we don't need to give the student total control over the interaction -- if we can get the job done from a menu of possibilities, say -- then we do it in the web page, and it doesn't matter which CAS is preferred or available. (A few modules are entirely in web pages and don't need a CAS at all.) But if we want to go beyond the limitations of applets and let students explore in directions we have not completely prescribed, then the CAS environment, guided by a web-based common set of instructions, gives us and the students the freedom and flexibility to do this. A side benefit of this approach is that students learn to work with a modern general-purpose calculational tool. This capability will always be a part of their working environment. We discuss our uses of CAS at greater length in Section 4.

Most of the CCP units are modules, that is, single-topic units that can be used for a two-hour lab, or for a shorter supervised period with follow-up on the student's own time, or for self-study. Most of our modules are class-tested with students working in two-person teams in a lab environment. Some modules use an application to stimulate learning of mathematics, and others go straight to the mathematics.

CCP also contains two projects (and more to come), longer units that may be completed by small groups of students over a period of one or more weeks. Each project involves a significant application of mathematics and is intended to demonstrate the process by which mathematics is used by working scientists and engineers.

The site has additional resources for teachers and developers. The teacher resources will be described in a later section of this article. An important resource for developers is the textbook Design Principles for Interactive Texts, by Julie Jacobs and William Mueller, which we will not discuss here.

The modules -- approximately 100 in number -- that make up the majority of the learning materials at the Duke site were developed for use in undergraduate mathematics courses including

Each module consists of several HTML pages containing discussion and guidance for exploring a topic, generally using Java and/or a computer algebra system. Nearly all modules have downloadable worksheets currently available for Maple, Mathematica, and Matlab, and some also have Mathcad worksheets.

In addition to the undergraduate materials, there is a collection of modules designed specifically for a guided or independent study course for high school students who have completed a year of calculus. These modules are part of the Post CALC Project.