At a recent mathematics conference I witnessed a computer algebra system do in minutes what, with pencil and paper, took me weeks in the 1960s. When as a young teacher I abandoned the slide-rule and square-root tables for hand-held calculators and simple programming languages, I could not have foreseen the wealth of technological aids available today.
I have incorporated technology into my classroom ever since I began teaching college classes in 1970. My fascination with technology as a medium for education has accompanied me through a 27-year career in the two-year college system, from which I recently retired, and continues in my current position teaching undergraduate mathematics and statistics.
Graphing calculators and computer algebra systems are - contrary to the assertions of a few backward thinkers - remarkable innovations. They put within our grasp, neophytes and old pros alike, the ability to solve our equations, and then to see those solutions come alive before our eyes.
The capacity to visualize answers to complicated abstract and real-world problems, to graph slope fields for systems of differential equations, to immerse oneself in the twists and turns of three-dimensional surfaces and curves - these are no mere tricks of the trade. They are profound breakthroughs.
Think of aviation without modern navigational techniques. No serious pilot would do without radar, and no one expects apprentice pilots to learn how to fly using only the tools that were available to the previous generation. The mathematics educator who refuses to teach the use of graphing calculators because they were not around when he or she went to school is like the pilot who refuses to exploit modern instrumentation because of a reluctance to rely on newfangled gadgets.
In my doctoral research I spent many hours in search of solutions to complex systems of partial differential equations. Would reliance on the computer have made me a less accomplished mathematician? On the contrary; it would likely have made me more productive.
What of the criticism that students who are allowed (or encouraged) to use technology will never develop the basic mathematical skills necessary to survive in the modern world? This argument has been used to resist every technological advance since the Industrial Revolution. Somehow, we are intelligent enough to survive technological innovation, to acclimatize ourselves to our strange new environment and to bend it to our needs.
The mathematics reform movement struggles with the issues created by the rapid progress of technology. We adapt curricula to the new capabilities that are, literally, at our fingertips. We redefine examinations to exercise old skills and enhance new ones.
Math organizations at all levels - serving K-12 educators, two-year-colleges, and universities - offer sessions on innovative and appropriate use of the new technologies. Conscientious teachers enthusiastically present their ideas and report on their successes.
Incorporating technology into math has breathed new life into my lectures and generated a sense of discovery that exhilarates teacher and student alike. I am gratified that the new technologies permit me and my students to see the world anew.
* Brian Smith teaches mathematics and statistics at the Faculty of Management at McGill University in Montreal. He is the author of 'Simplifying Mathematics using the TI-82/83 or TI-85/86,' (Mathware, Urbana. Ill.).