Often times I hear my students asking: “Can I employ a calculator?” My invariable answer is “No”, and now that I consider it, it is because the normal teaching philosophy implies that you do not want a calculator when you need to compute an integral. Also, as teachers, we use to think instantly that it’s all about “mental laziness”.
Well, I must admit that times have changed, and it appears it is now the right time to be in tune with the wonders that science and technology have to give. The arrival of enormously tough PC Algebra Systems (CAS) is giving us more and more reasons to change out teaching styles to a new paradigm, where the concepts are presented together with real visual computer-generated representations, and where the stress is put on the concepts rather than the symbolic manipulation.
For example, in a typical first year varsity Calculus class, it takes a great deal of effort to go over a series of systems that help the students to grasp integration. Those techniques are obviously mechanical and repeated, but yet students have a tough time understanding the main ideas. Nowadays, software like Mathematica and others are able to clear up symbolically some very complicated integrals, which go way beyond what an excellent first year calculus student can do.
Shouldn’t we make an emphasis on the concepts instead of on the calculations? In mathematics, it is hard to separate because the 2 go tightly together. But I definitely believe that we might benefit by introducing systematically the application of CAS in the classroom. There’s a trend in most of the schools to introduce computer assignments, as a part of the curricula, but from my experience, students are not getting the majority of it. They continue to don’t see the PC as a friendly ally at the time of learning math. But yet, they might gladly accept a calculator.
The future of CAS should also include a technique to use all this “intelligence” used to unravel complex issues to also being able to “explain” how to arrive to the answer.
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