RE: Re: Re: Mathematica and Education

*To*: mathgroup at smc.vnet.net*Subject*: [mg65102] RE: [mg65075] Re: [mg64957] Re: [mg64934] Mathematica and Education*From*: "King, Peter R" <peter.king at imperial.ac.uk>*Date*: Wed, 15 Mar 2006 06:28:14 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

David, I think actually we are possibly talking at cross purposes. Although I also think this leads to some interesting points. I was responding in the first instance to a post from a student who had proudly proclaimed that he had done all of his assigments without using pen and paper at all and only in Mathematica. My view is that this is dangerous for the reasons outlined. And in fact my concern is not for the professional technical expert (or the prospective ones). In my experience a good student who is capable and motivated to understand the material will do so and tools like Mathematica can make this an even more exciting experience. For them I would agree 100% with what you have said. However, poorer students will simply learn how to use the tool as a black box. Superficially they will look as skilled as the others because they can produce a glossy presentation and they can end up causing alot of trouble (I am absolutely serious about this I have seen it - not with Mathematica but with other commercial software, which is where my fool with a tool quote came from). for weak students they will think that learning how to do something substitutes for learning how to understand something. As for education for the masses actually I do think there is a point. As well as learning about Shakespeare, Bach, Beethoven, Michealangelo, Cezanne and so on every civilised person should know Newton's laws (with Einstein's amendments), thermodynamics, trigonmetry, algebra, calculus and the principles of scientific study. My anology with calculators is to show that reliance on using a tool can weaken the more traditional skills. Not in itself a problem. As you very eloquently pointed out I cannot sharpen a spear and hunt for my own food, it is easier to go down to the supermarket. If shops ceased to exist I would be stuck! The point being that there are some cirucmstances when we don't have calculators about us or when it is easier or even better not to use them (I think it is a great skill that is underestimated and lost to be able to estimate answers to problems without doing an "exact" calculation). I make this analogy, not because I think that Mathematica is a glorified calculator (it is much more than that) but because I remember the discussions 20-30 years ago when calculators were first introduced. Many people in education argued that they would enable students to do more calcuations, more quickly and get on to the "more interesting stuff" because they weren't being held back by "boring" caclulations. In fact I think for weaker students the opposite has happened. They do the caclulations but don't understand them - as I said they don't really understand the concept of numbers at all. This hasn't happened with more advanced mathematics (yet?) because the tools haven't really been available for so long but the same arguments are being made. My concern is that the same mistakes will be made and we will end up with a less mathematically literate population then before. Now this is not inevitable and so this is the real challenge. How can we ensure that these tools are used appropriately to improve mathematical skills and not used lazily to reduce them. There have been some excellent and thought provoking examples of how people on this list have done this. My fear as that these few sites of excellence will be outnumbered by rather lazy teachers (& students) for whom Mathematica will used as a black box. I hope I am proved wrong. I must also confess that I have another sneaking fear. I first learnt progamming by writing FORTRAN IV on punched cards on mainframes. I could probably still do it tomorrow if such things existed. However, the energy barrier to learning more modern languages has meant that I haven't bothered. OK so I'm a dinosaur and therefore out of touch. My worry is for people who have only learnt how to use MAthematica, when that is superceded (and again I am sure that it will) will they have the ability to move on to something else if they haven't learnt the underlying mathemtics properly. However, the mathematics is much more enduring. Anyway I don't really want to keep batting this around, I am sure everyone knows my point of view by now. I hope the message I have got across and that I suspect we would agree on is: anyone claiming to use mathematics must really understand the basic maths (however they are taught it); there is no doubt that modern technologies have an essential and deep rooted part to play in education, research and practical application in mathematical science; the challenge is to ensure that this is done thoughtfully and carefully to ensure best practice and maintainence of fundamental skills (rather than erosion as I feel has happened in some sectors with numeracy skills). I would be very pleased and interested to hear about how this can be done (and perhaps I can sneakily take advantage of some of these ideas in my own teaching). Best wishes, Peter