I ask everyone to read attentively what John Conway wrote. I think that this is very important.
Andrei Toom firstname.lastname@example.org
---------- Forwarded message ---------- Date: Sun, 19 Nov 1995 11:47:30 -0500 (EST) From: John Conway <conway@math.Princeton.EDU> To: 26@math.Princeton.EDU, Pat Ballew <email@example.com> Cc: Jim LaCasse <firstname.lastname@example.org>, email@example.com Subject: Re: Are humans...(a better way to teach stats?) (fd)
On Sun, 19 Nov 1995 firstname.lastname@example.org wrote:
> Why do I have the distinct feeling that if someone HAD taken MR. Griffin out > to collect real world data when he was in high school, and maybe into those > first few years of college, he would have screamed about the choice of data? > One mans "real world experinces" is another mans mindless drivel. > He found a shortcut to avoid really learning the material that someone, > i suspect, tried very hard to make meaningful to him, and in the end it was > essential to his career. Essential in a different way from that of a future > carpenter, or a future chemical engineer, yet it is the same data, and the > STUPID teachers didn't realize that they should construct their classes to > promote the development of a single interest (his) over all the other > applied areas they could use. Poor idiots, they fell back on cards and dice > and defective light bulbs (which NO ONE is interested in). Things that were part of t > he experience of a wide group of students, and had a wide range of > applications. > To all the teachers out there, press on, > or as the gyoji says: > > Hakke Yoi! > Pat Ballew > Edgren HS > Misawa, Japan > email@example.com
This raises once again what I think is a very important point. There seems to be a lot of pressure from everyone for "real-world" applications. I think this is because of the perennial student's question "But what is all this good for?", which makes teachers feel that they must respond with ways that mathematics actually is used in the real world.
The trouble with this is frankly that lots of these real-world (or "real-world" - I don't think it makes much difference!) problems, are, frankly, BORING. As Pat Ballew says, no student is actually interested in problems about defective light-bulbs, even though one or two of the people who make light-bulbs might be very interested in the answers.
I saw this in action at a meeting of school-teachers. They themselves pressed for real-world applications, but when the speaker gave them one, they all started to yawn, whereas in the previous part of the talk they'd been very lively.
You DON'T really need to give your students real-world problems, even if they tell you that that's what they want. What you DO need to do, is give them interesting mathematics.
So what do you do when they ask that perennial question? I think, really, that you should train them NOT to ask it. I don't mean that you should have beaten them to a pulp the first time they asked - that would have been unkind, because they really didn't know - no, you should have told them that just about every interesting piece of mathematics has LOTS of applications (and named a few). Also, that applying the mathematics, though often very useful, can be a bit dull (say no more!), and that sometimes the closer you get to a real-life application, the harder the mathematics gets (it may either get more OR less interesting).
I remember that when someone asked for a real real-life problem, Johnny responded with a long thing, about something like redecorating a corridor that went for 53 feet in one direction, then turned through such and such an angle before going for 76 feet in another direction, the second part being smaller and having a guard-rail 2 feet 8 inches above the ground for 48 feet of its length. You had to work out how much paint ... .
I noticed no throng of eager solvers for Johnny's problem. That's often what real-world problems can be like - both complex and boring, unless perhaps you actually ARE decorating a corridor that's exactly like that. The only genuine real-world problems that kids should be asked to face are the ones that actually face them! By all means get your kids out surveying the school grounds and using their mathematics to plan or build something. But otherwise teach them stuff that's interesting rather than applicable, and TELL them that's what you're doing.