Laboratories in Mathematical Experimentation:
A Bridge to Higher Mathematics
Published, 1997, by Springer-Verlag, now Key College Publishing
ISBN 0-387-94922-4 Introduction and Chapters 1 and 2 are reproduced with the permission of Springer-Verlag New York, Inc.
Table of Contents
This laboratory text and accompanying instructor's manual are based on an unusually effective, sophomore level course developed and taught in the Mathematics and Statistics Program of Mount Holyoke College over the last eight years.
The "Lab," as it is called, serves as a bridge between first year courses (often college geometry or number theory as well as calculus) and more sophisticated upper level mathematics courses. Students explore ideas that they will encounter later and more formally in advanced courses. They learn to experiment, to describe patterns, to generalize, to conjecture, and to argue with different degrees of certainty.
The course is required of all mathematics majors and is central to our mathematics curriculum. The Lab is the key element in allowing us to offer students a number of alternative entries (that is, entries other than the standard calculus sequence) to the study of mathematics. It has also helped us develop an interactive, conversational mode of mathematics teaching that we have found effective in other courses. We have observed that the Lab improves the performance of students in real analysis and abstract algebra.
The student text consists of sixteen modules drawn from a wide range of mathematical and statistical contexts, and each introducing an idea or ideas that the student is likely to encounter in later courses. In a typical offering of the course, the instructor will choose six or seven modules. Each begins by placing the topic in context and providing some background. Then students respond to questions which invite them to examine examples, first by hand and then by computer. The student is encouraged to find and describe patterns, to generalize from observations, to formulate conjectures, and to support conjectures with analysis and sometimes proof. Each project requires a carefully written laboratory report describing the student's findings, conjectures and conclusions.
The course has worked far better than our initial expectations and would, we think, be easy to adapt to a variety of institutions. It is cheap to implement, could be run on calculators, and succeeds wonderfully in engaging students in doing mathematics. It is also easy to teach (although grading it is no picnic), and several sabbatical visitors have thoroughly enjoyed teaching the Lab.
With the advice of participants in our NSF-funded Undergraduate Faculty Enhancement workshops in 1997 and 1999, we have prepared some corrections and clarifications for the student text and suggestions for the instructor's manual .
We invite you to download the software for the course. Currently, the complete package is available for Windows 3.x and Windows 95/98/XP. If you want to download the files for a Windows system, click here: download the files.