Calculus, Concepts, Computers, and Cooperative Learning (C4L)

Introduction

The Calculus, Concepts, Computers and Cooperative Learning (C4L) program is the result of a National Science Foundation funded research and development project begun at Purdue University under the direction of Ed Dubinsky and Keith Schwingendorf. The emphasis of the C4L program is a pedagogical approach based on a constructivist theoretical perspective of how mathematics is learned.

According to this emerging theory, students need to construct their own understanding of each mathematical concept. Hence, we believe that the primary role of teaching is not to lecture, explain, or otherwise attempt to "transfer" mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of our approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept.

Guiding Principles

  1. Research into how students learn is primary.
  2. Conceptual understanding is the most important, but calculations play a major role.
  3. Technology can be valuable, and some ways of using it can be more valuable than others.
  4. Cooperative learning is the right context for a mathematics course.
  5. Lecturing should be replaced by a task-oriented interactive classroom.
  6. Textbooks and course structure must support the pedagogical strategy.

The ACE Cycle

Activities
Each unit begins with students performing computer activities in a laboratory. In the lab, we insist that students attempt to discover most important mathematical results by performing certain carefully selected computer tasks that are designed to foster the mental construction of mathematical concepts.
Class
Laboratory periods are followed by class meetings in which a modified Socratic approach is used in conjunction with cooperative problem solving in small groups to help the students to build upon their mathematical experiences from the computer laboratory.
Exercises
Finally, relatively traditional exercises are assigned to reinforce the knowledge students are expected to have constructed during the first two steps of the cycle.

For more information about the C4L Program please contact one of the following:


Professor Ed Dubinsky

edd@mcs.kent.edu

or

Professor Keith Schwingendorf
(Preferred Contact)

kschwingendorf@pnc.edu

Phone: (219) 785-5449

FAX: (219) 785-5507

If you are interested in purchasing a copy of one of our textbooks or are interested in getting a copy of ISETL 3.0 (ISETL for Macintosh) or ISETLW (ISETL for Windows) for your platform, check our distribution page.


Maintained by: Keith Schwingendorf
kschwingendorf@pnc.edu
Last modified Tuesday, May 11, 2004