Often times I hear my students asking: “Can I use a calculator?” My invariable answer is “No”, and now that I think about it, it is because the traditional teaching philosophy indicates that you dont need a calculator when you have to compute an integral. Also, as teachers, we use to assume immediately that its all about “mental laziness”.
Well, I must admit that times have changed, and it seems it is now the right time to be in tune with the wonders that science and technology have to offer. The advent of immensely powerful Computer Algebra Systems (CAS) is giving us more and more reasons to switch out teaching styles to a new paradigm, where the ideas are presented together with real visual computer-generated representations, and where the emphasis is put on the concepts rather than the symbolic manipulation.
For example, in a typical first year college Calculus class, it takes a great deal of effort to go over a series of techniques that help the students to understand integration. Those techniques are clearly mechanical and repetitive, but yet students have a hard time understanding the main ideas. Nowadays, software like...
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