In article <firstname.lastname@example.org>, Paul Tanner <email@example.com> writes >And Mark, it is always the case that we can find a problem that >baffles a group of students (or people in general) that are not Ph.D's >in mathematics with a specialty in the area of the problem. The way I >see it, sooner or later we'll have to be satisfied with a certain >measured performance level.
I know that this first statement is true, but I chose this particular question with intent. It tests understanding of the concepts of mean and s.d., rather then the ability to calculate them. If you don't understand what mean and s.d *are*, what use is the ability to calculate them?
Why do you think that British children, who are able to calculate these quantities, can't demostrate that they understand what they mean? One answer is this: in selecting the appropriate bits of knowledge to impart, teachers have seen, from experience that the "important" thing to teach (ie the one that will pass tests) is the calculation. And, as far as this goes, they are right.
Suddenly, the exam board asks a (very good, I think) question, and students who in any other year "understood" statistical measures, now don't. This shows one of the difficulties ofusing standardized tests as a "scientific measure of knowledge".
I was interested in what you had to say about innate "mathematical talent". I do think that's an interesting area of discussion - and very problematic. But "mathematical talent" begs for a definition.
I'd really like to have the time to discuss your post in full, as it raises so many interesting points, but as I'm trying to move countries ATM, there are just a couple of things more I'd like to probe.
First, by what mechanism do you think that "science [can] set some of our goals"? This seems an odd concept. Kind of like letting a hammer design a house ;-)
Finally, I don't think that anyone here is arguing that memorization is bad, or wrong. The question is how to *achieve* memorization (and, Brian, don't you think that capital cities which you've visited are easier to remember than those you once read in a list at school ;-).
The quibble is with "rote". M. -- Mark Houghton firstname.lastname@example.org