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Often times I hear my scholars asking : “Can I employ a calculator?” My invariable answer is “No”, and now that I consider it, it is because the traditional teaching philosophy implies that you don’t need a calculator when you should 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 supply. The arrival of enormously strong 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 ideas instead of the symbolic manipulation.

For example, in a typical first year school Calculus class, it takes a large amount of effort to go over a chain of methods that help the students to appreciate integration. Those techniques are obviously mechanical and repeated, but yet scholars have a hard time understanding the main ideas. These days , software like Mathematica and others are capable to clear up symbolically some terribly complicated integrals, which go way beyond what a skilled first year calculus student can do.

Shouldn’t we make a stress on the ideas instead of on the calculations? In mathematics, it is tough to separate as the two go firmly together. But I actually believe that we would benefit by introducing methodically the application of CAS in the study room. There’s a trend in almost all of the schools to introduce PC assignments, as a part of the curricula, but from my experience, are not getting most of it. They continue to don’t see the computer as a friendly ally at the time of learning maths. But yet, they would gladly settle for a calculator.

The future of CAS should also include a technique to use all this “intelligence” used to clear up complex problems to also being able to “explain” how to arrive to the answer.

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