By Murray Bourne, 13 Jun 2005
The discussion usually goes something like this...
Me: Good to see you! What are you teaching this semester?
Lecturer: Advanced Technical Difficult Engineering Stuff.
Me: Sounds like an interesting topic. Does it include a lot of mathematics?
Lecturer: Oh yes, it has some differential equations, some matrix work and some finite element analysis.
Me: Sounds like the students should explore the application of these topics with a Computer Algebra System (like Scientific Notebook). Then they won't be spending 99% of their time grappling with the algebra and instead, they can think about the concepts, what it all means and how to apply it.
Me: It is no longer necessary for students to do mountains of algebra to solve problems. With a CAS, let the computer do what computers are good at (crunching numbers and algebra, drawing graphs) and let humans do what they should be doing (thinking, solving problems, learning, solving harder problems, etc).
Lecturer: But what about the steps in the middle?
Me: In the Dark Ages, before we started using calculators, we had to do things like find the logarithm of secant 25° using tables. Do we want to go back to doing that? Of course, the calculator could do all that for us. But now, a CAS (computer algebra system) can do so much more than a calculator ever could - and we are missing out on the huge potential of this in mathematics education.
It's no wonder students hate mathematics - they think it is just moving letters and numbers around. We need to leverage on the power of CASs to free up time from algebra and to devote it to the important and interesting stuff - problem solving.
Software is used extensively in engineering now - we need to prepare our students for this reality. Very rarely do engineers use any of the algebraic tricks that they learned in school. What they need to be able to do is solve real problems.
Lecturer: Yes, but what about the steps in the middle?
Me: [Sighs inwardly, and awaits another opportunity at a later date...]
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