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        riddles >> general problem-solving / chatting / whatever >> he writes nicely.
        
(Message started by: Noke Lieu on Jul 7^th, 2008, 7:27pm)

Title: he writes nicely.
Post by Noke Lieu on Jul 7^th, 2008, 7:27pm

http://www.guardian.co.uk/commentisfree/2008/jun/06/maths.alevels

not entirely sure I agree with the sentiment.

Title: Re: he writes nicely.
Post by ThudanBlunder on Jul 8^th, 2008, 12:04am

on 07/07/08 at 19:27:39, Noke Lieu wrote:

http://www.guardian.co.uk/commentisfree/2008/jun/06/maths.alevels

Been there, read that (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_general;action=display;num=1094528977;start=12#12). :P Pity he doesn't understand what maths is all about. In this country too many decision makers and opinion formers like Jenkins studied PPE (http://en.wikipedia.org/wiki/Philosophy%2C_Politics%2C_and_Economics) or Classics at Oxbridge and do not understand or care about Science. (Having said that, Thatcher graduated in Chemistry and look how she turned out.) And the average person believes that an engineer walks around with a spanner/wrench sticking out of his pocket.

I like this (http://blogs.guardian.co.uk/sport/2008/07/05/ice_cream_and_cushions_that_ho.html) recent article about Wimbledon.

Title: Re: he writes nicely.
Post by NightBreeze on Jul 8^th, 2008, 4:30am

"In the age of computers, maths beyond simple and applied arithmetic is needed only by specialists. Ramming it down pupils' throats in case they may one day need it is like making us all know how to recalibrate a carburettor on the offchance that we might become racing drivers. Maths is a "skill to a purpose", and we would should ponder the purpose before overselling the skill."

---

Hmmm.

---

Anyways, very much liked the Wimbledon article. I am not a big tennis fan, but did watch Wimdledon this year. The peculiar rituals struck me as odd as well and after some research, I found that it went much deeper than I initially suspected. Every aspect of that stadium and the rules of conduct are so deeply ingrained in tradition, it really does resemble a religion. For example, it took a very long time before ball girls were allowed, an even longer time before they were allowed to collect balls alongside boys and even longer before they could perform on the centre court. Crazy stuff.

Title: Re: he writes nicely.
Post by Eigenray on Jul 8^th, 2008, 6:48am

Here's an interesting article about the state of maths education in the US: [link=http://www.maa.org/devlin/devlin_03_08.html]Lockhart's Lament[/link]. Based on my experience, it's pretty accurate:

Quote:

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. "We are helping our students become more competitive in an increasingly sound-filled world." Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made - all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the "language of music." It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

But I think basic arithmetic is more important than he makes it out to be. It's pretty depressing to see just how little it takes to make a whole room full of college freshmen get out their calculators.

Not really related to the above, but I just had a thought for an integration video game. The monsters are functions, and your attacks would be like: split a monster f+g into two; select an expression to do a u-substitution, converting one monster into another, or an integration by parts, popping out dv that you have to kill before you can fight vdu, etc. As you gain experience, the integrals get more complicated, and your character learns to do more basic things automatically.

Well, it doesn't have to be set up that way, but some way of getting you to experiment with different things yourself to get a feel for what works and what doesn't, because that's really the only way to learn. A program would be nice because once you master one trick, you can use it without actually doing it (not to mention step-by-step error checks).

But then of course none of that will teach you what an integral actually is.

Title: Re: he writes nicely.
Post by rmsgrey on Jul 8^th, 2008, 9:24am

Here (http://www.themathlab.com/writings/short%20stories/feeling.htm) is Isaac Asimov's take on the obsolescence of mathematics education...

Myself, I regard basic numeracy like I regard basic literacy and basic IT skills - I accept that it's possible for someone to live without them, but it always astonishes me when I meet someone who needs a calculator to, say, work out what a sixth of six times four is...

Of course, as the article points out, it's to the advantage of those who wish to shape public policy if there's widespread ignorance of maths and science because then it's easy to come up with impressive sounding numbers or facts that carry undue weight - granted, you don't need to know calculus to spot some dodgy assumptions, but I'd be astounded if economists didn't use calculus at some point...

Title: Re: he writes nicely.
Post by rmsgrey on Jul 8^th, 2008, 10:19am

on 07/08/08 at 06:48:34, Eigenray wrote:

Here's an interesting article about the state of maths education in the US: [link=http://www.maa.org/devlin/devlin_03_08.html]Lockhart's Lament[/link]. Based on my experience, it's pretty accurate

As the guy himself points out, he's arguing against an extreme position - that of regimented and standardised rote-learning. On the other hand, some of his examples failed to carry his point - at least with me, though I can see where non-mathematicians would glaze over rather than being able to see the idea being expressed - and he totally neglects the twin problems of large class sizes and mobile populations - the former making it hard to devote the time and resources needed to overcome the problems the latter creates in a non-standardised environment, where a student can cover the same material three times in three different schools and miss out entirely on a whole bunch of other stuff.

On the gripping hand, standardised teaching is turning out a whole bunch of students who rote-memorise templates for the exams and promptly forget them having never seen any sort of point to them in the first place.

Title: Re: he writes nicely.
Post by Eigenray on Jul 8^th, 2008, 12:34pm

on 07/08/08 at 10:19:00, rmsgrey wrote:

On the gripping hand, standardised teaching is turning out a whole bunch of students who rote-memorise templates for the exams and promptly forget them having never seen any sort of point to them in the first place.

Tell me about it. We pretend to teach them, and they pretend to learn, but really are just associating keywords with formulas.

In a multivariable calc class (I just taught section/recitation) I gave a question on a quiz:

Find the maximum possible value of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gifhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gif_R (1-x²-y²) dA, where R is a region in the plane.

(Actually, it was phrased in terms of work done along a simple closed ccw curve. We had just done Green's theorem, and the circulation/curl form of Green's theorem was the only thing written on the blackboard, nice and big right in the middle. Still, about half of them did not try converting it to an area integral, and mostly just wrote a bunch of nonsense.)

(Argh, the nonsense! You give them an area integral where the integrand is like f(y)e^{x^2}dxdy so they have to change the order of integration because they can't integrate wrt x first. But they don't know that they can't, and so they 'integrate' it anyway: e^{x^2}/(2x), e^{x^2}/(x²), e^{x^2}, whatever they feel like. And they fill up a whole page, line after line, errors compounding upon errors, trying to make you feel bad about giving them a 0.)

But I digress. Only a handful decided that the region should be where the integrand is positive. A bunch of them integrated over a circle of radius r centered at the origin (they didn't give any justification; I should have made it centered somewhere else but I wanted to keep it simple), and then left it as a polynomial in r (they didn't even try to differentiate it). And they had just had a very similar problem on their homework. But it wasn't phrased in exactly the same way!!

And this was in a course for engineers. Taking multivariable calculus. So I had to spend the class time on iterated integrals and directional derivatives, even though they didn't understand the one dimensional cases. If you tried explaining why a formula works, they'd just stare at you blankly and wait for you to finish. Of course I held office hours but nobody came, even though they were doing miserably on the exams. But thanks to curving, only a small percentage of them actually failed (the median was about 55%).

Anyway, my point is: if we're going to teach people math just so we can say we did, why calculus? At that level, calculus is just a bunch of meaningless formulas to be memorized. Elementary number theory or combinatorics would be a better introduction to mathematical thought, wouldn't it?

Title: Re: he writes nicely.
Post by TenaliRaman on Jul 8^th, 2008, 2:32pm

on 07/08/08 at 12:34:44, Eigenray wrote:

Anyway, my point is: if we're going to teach people math just so we can say we did, why calculus? At that level, calculus is just a bunch of meaningless formulas to be memorized. Elementary number theory or combinatorics would be a better introduction to mathematical thought, wouldn't it?

I presume that you are talking of bachelor students in engineering. In that case, if some of the students are inspired to take up higher studies, then calculus does prove useful to them.

Most people in engineering tend to find it hard to think in abstractions. Many people who go to higher studies in engineering, normally tend to take more application oriented courses. These may require use of calculus (seeing as it is more pervasive in several applications) without understanding its exact nature.

I am not saying elementary number theory and combinatorics need not be taught. Infact, some amount of combinatorics is already dealth with when studying probability. All I am saying is that there is a decent enough reason to learn calculus.

-- AI

Title: Re: he writes nicely.
Post by Sir Col on Jul 20^th, 2008, 5:03am

As a teacher of mathematics I share Lockhart's Lament:
http://www.manchestereveningnews.co.uk/news/s/1022757_cool_cash_card_confusion

In one sense I find that article amusing, but equally it saddens me greatly, as it represents how we, as educators, have failed. It epitomises perfectly the fruits of eleven years of inappropriate education in England. Through no fault of her own I imagine that the lady in this article has half an understanding of almost every fundamentally important concept, like multiplication, fractions, working with negative numbers, percentage calculations, and so on. The tragedy is that she probably has an equal knowledge of topics that are utterly irrelevant to her life, such as solving linear equations, finding the circumference of a circle, sketching quadratic graphs, et cetera.

I earnestly believe that everyone needs Mathematics but it should have tiers of delivery depending on aptitude. Most people should be taught, re-taught, and constantly have basic concepts consolidated throughout their schooling years. Those who show interest and ability should be granted access to higher concepts; the inept or idlers should be transferred to the "basic" programme so that the rest can learn. The best way to make children want something is tell them that they can't have it!

I am sure that England is not alone, but we humiliate those without a natural inclination for Mathematics by forcing them to sit in classes and try to learn concepts that they are incapable of learning. Equally, to accommodate this majority, we have watered down the curriculum so much that those with a real ability are insulted by the inadequate diet.

Title: Re: he writes nicely.
Post by Noke Lieu on Jul 20^th, 2008, 9:15pm

I mostly agree with you there, Sir Col.
Streaming of maths, IMhO, is a great plan, but I am uncertain when is the best time to introduce the streaming. I believe, possibly arrogantly, that of all the subjects one typically learns at school, maths takes the most intellectual maturity to grasp.
A level of maturity that most people don't possess until their mid 20's, by which time their attitude towards maths- and techniques they'd have developed for avoiding- would prevent them from wanting to start learning maths all over again.

The two major catches are school sizes, and a shortage of good maths teachers. Australia isn't alone in that regard.

I was fortunate enough to have a series of wonderful teachers, but since I've returned to school I've found just how lucky I was. That's been a major part of my job for the past 8 years, trying to ignite the interest of "the lagging teacher"- and trying to get the spark going in some kids along the way.

I've encountered high school maths teachers who couldn't choose three numbers, ANY three numbers to add up to 24. I've met MANY primary school teachers who got into teaching because they "liked P.E."

Combined with the population density of Aus (as opposed to the density of the population of Aus :P ) we have a fair few small schools (typically single or two teacher) scattered around.

Oddly enough though, these small schools, through natural processes- and I suppose something akin to the original Madras system- produce highly competent Maths students. Not exclusively, mind you.

It's entirely possible that it's also due to the extent that maths gets used at homes- typically farms and homesteads.