For the most part, college calculus has been taught pretty much the same way for the past century. Technology, in the form of the graphing calculator, is changing that. According to David Keck, associate professor of mathematics, the use of calculators in some precalculus and calculus courses is beginning to affect the way courses are taught. "The new state-of-the-art calculators are a very useful tool to include in calculus courses," Dr. Keck said. "But change in teaching with calculato rs should happen gradually and conservatively. We should experiment to see what’s useful and what’s not useful, rather than try for something radically different."
The calculating instruments being used by the Department of Mathematics are the TI82 and the TI83, made by Texas Instruments. Besides numerical calculations the machines graph, perform calculus functions, and have statistical packages. A new TI82 costs ab out $90, but they are also available used for about $50 at bookstores. "If a student will use a TI82 for several quarters, the price is comparable to a textbook," Dr. Keck noted.
Technology, pedagogy, and content all influence one another, according to Dr. Keck.
Actually, the so-called calculus reform movement was going on before calculators came along, with the idea of not stressing the intricate computational details as much, but emphasizing concepts and problem-solving more. Technology has helped u s go in that direction and can influence the way a calculus course is built. A lot of the old traditional computation we used to do by hand can be enhanced with the new calculators. But we don’t want students to rely on the machines as a crutch. We want t hem to think of technology as helping them be able to do more elaborate things. Students still have to learn the material, but they can perform calculations much more quickly now.
We are also introducing more investigation in the classroom. The calculators give students the opportunity to try an idea before they are told the answer. We can challenge them to discover for themselves,"Is there a principle here and wha t is it?" Sometimes we have small group projects in the classroom and we’ve also experimented with group projects outside of class. We give students a relevant project—a real-world type issue. It can allow them to see what the engineering world might do with such a project, for example.
In addition, we encourage writing in the classroom. That’s part of a university-wide goal. Many students think of mathematics as only computation. We ask them to describe in writing what they are doing with their project. I tell students to th ink of me as their employer—they have to explain their project to me in writing. That gets them to understand the concept. Many students can compute something, but they can’t quite tell you clearly why they’re doing it.
Students using calculators will also encounter problems they didn’t have before. They may get an answer that obviously isn’t correct and that they need to question. "Students need to recognize an incorrect answer and be able to ask what went wrong. I t makes them realize that some of the things they thought were trivial—such as parentheses—aren’t so trivial after all. The machine is very unforgiving; it will do what you told it to do, not what you wanted it to do." Since technology affects the teaching approach, how does it affect the content? "Although calculators are changing the way we teach, I see course content as remaining fairly stable," Dr. Keck said. " We want the content to be much the same, while recognizing that calculators allow you to have more real world data and to do more modeling. Where students used to have to draw graphs by hand, now they very quickly graph all sorts of things. But we don’t try for exotica at the expense of the mai n core of material, which is calculus."
About one-half of first-year precalculus courses are taught using calculators. The course catalog indicates if a calculator is needed for the course. Students who take the calculator-oriented Mathematics 115, " Precalculus," then go on to a fou
r-quarter series, Mathematics 263, " Analytic Geometry and Calculus." Dr. Keck said the traditional calculus courses are still available for those who want it.
Trevor Lanham, a first-year student majoring in mechanical engineering, said using the calculators enables him to more easily visualize graphs." Often, it is too cumbersome to actually write out a graphing sequence," Mr. Lanham said. " Thi s class is giving me skills I’ll use often in my career."