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...]
See the 5 Comments below.
1 Nov 2007 at 5:59 am [Comment permalink]
I agree with you - CAS systems should be used a lot more in teaching but which one should we choose? Out of the 3 packages I know of, I know Mathematica best and so if I were asked to come up with a syllabus for mathematics with CAS packages I would be tempted to base it around Mathematica but deep down I would feel it was the wrong thing to do. Matlab, Mathcad, Maple or SNB are not viable choices either IMHO.
Quite simply I would not want to tie the mathematics education of anyone to a commercial product or even a group of commercial products. One argument might be that you would be teaching principles and so the choice of CAS should not matter but in my experience people really do get tied to one package or another and it can take a long time to re skill in a new package. People also build up a body of code that would need to be ported should they ever lose access to their system of choice.
There are open source systems such as Octave or Maxima but unfortunately they are nowhere near as powerful as their commercial counterparts. Should we teach these open but weaker systems or should we teach the more powerful systems that will cost our students money?
1 Nov 2007 at 6:05 am [Comment permalink]
One of the reasons I like Scientific Notebook (SNB) for use with students (and I am mostly talking secondary or polytechnic level here) is that the GUI is approachable and what the user sees throughout is mathematics, rather than code. But I am just proving your point - we get locked into a commercial package and that is a problem. (But you could say that the world is locked into Casio or Ti calculators...)
But I think we do students a disservice if we don't teach them to use a CAS of some kind.
I tried Maxima recently but it didn't even open on my PC. You have inspired me to take a look at Octave.
2 Nov 2007 at 1:44 am [Comment permalink]
I agree - some sort of CAS is essential. Wouldn't it be nice if a few institutions (schools, universities, private individuals, governments, whatever) lent some financial support to some of the open source products?
7 Feb 2010 at 11:56 pm [Comment permalink]
[...] 7 febbraio, 2010 in Insegnanti, Matematica, Scuola, Società | Tags: computer algebra, Matematica, software | by bobcarr Un ipotetico dialogo fra la prof. Morena De Poli e il sottoscritto, liberamente tratto dal questo post. [...]