Mathematician's Lament: An essay on math education and on how we view math(scottaaronson.com)
scottaaronson.com
Mathematician's Lament: An essay on math education and on how we view math
http://scottaaronson.com/blog/?p=410
8 comments
I have friend who had something similar written on an algebra assignment because he used Zorn's Lemma when it wasn't needed.
"Math" is the activity you perform when you don't know what to do next. If you already know what to do next, it's arithmetic.
This is the comment I just left on the blog:
I will have to read the paper in more detail, but I have an extremely simple reason why math education in the US is so hard: We use the English system of measurement. Most students in grade school associate math with this horrific measurement system, and once that happens, there is almost no chance to engage students in what math is really all about.
You want people in the US to embrace math? Then start on a campaign to scrap our horrific measurement system, a system to which logic and simple math can not be applied. In the metric system all you need to know is it is base 10. With the English system you must know that there are 12 inches in a foot, and that there are 3 feet in a yard. How many feet in a mile? There is NO WAY to logically derive this information, one must KNOW it! How may teaspoons in a tablespoon? Can math help us with that? Nope, one must know the answer.
Sorry, I hope I am not ranting, but this has been a burr in my side for years. Yet it seems that no one ever talks about this aspect when talking about why people in the US are so adverse to math. I guess I should just write my own article about it…
I will have to read the paper in more detail, but I have an extremely simple reason why math education in the US is so hard: We use the English system of measurement. Most students in grade school associate math with this horrific measurement system, and once that happens, there is almost no chance to engage students in what math is really all about.
You want people in the US to embrace math? Then start on a campaign to scrap our horrific measurement system, a system to which logic and simple math can not be applied. In the metric system all you need to know is it is base 10. With the English system you must know that there are 12 inches in a foot, and that there are 3 feet in a yard. How many feet in a mile? There is NO WAY to logically derive this information, one must KNOW it! How may teaspoons in a tablespoon? Can math help us with that? Nope, one must know the answer.
Sorry, I hope I am not ranting, but this has been a burr in my side for years. Yet it seems that no one ever talks about this aspect when talking about why people in the US are so adverse to math. I guess I should just write my own article about it…
I think you are doing exactly what Lockhart talked about. It doesn't matter what system one needs to memorize (although only knowing the metric system I can imagine the English system being harder to learn) what matters is that students are given the intellectual freedom to develop their intuition and reasoning capabilities, while current math education is all about needless, rigid formalism that needs to be learned by heart, then applied. Even the few proofs that are shown are presented in such a formalized way that they are a big turnoff.
Neither the English nor the metric system allow you to logically derive much about it (maybe Hertz = 1/second), the metric system is only more consistent and therefore easier to learn.
At least that's my take on that.
Neither the English nor the metric system allow you to logically derive much about it (maybe Hertz = 1/second), the metric system is only more consistent and therefore easier to learn.
At least that's my take on that.
While I agree that the US would be better served moving over to the metric system, this has nothing at all to do with the article.
The article was about focusing on math as art and on problem solving, not on any particular system and not on rote memorization.
The article was about focusing on math as art and on problem solving, not on any particular system and not on rote memorization.
The problem is that 10 is not an especially divisible number. It only divides evenly by 2 and 5. English measurements have lots of 12's and 60's and so forth not out of malice, but so we can precisely determine what 1/3 or 1/4 of a foot is without using decimals.
Likewise, Fahrenheit temperatures are perfect for weather since the 0-100 scale consistently matches the spectrum from "especially cold day" to "especially hot day".
Likewise, Fahrenheit temperatures are perfect for weather since the 0-100 scale consistently matches the spectrum from "especially cold day" to "especially hot day".
And this was of great value when decimal notation was unknown in Europe and even retained some value when it was known only by a select few elite. Now most people are as (or more, especially when equipped with a calculator) using decimal notation as they are dealing with fractions.
Now that the decimal system predominates the metric system is generally easier to use, once you get used to it. Moreover, it will bring us into line with virtually all of the rest of the world which simplifies international communications, not to mention that most technical/scientific work is done in the metric system anyway. This means that most school children are burdened with learning 2 separate systems of measurement and their conversions for very little reason now.
While this is completely off topic from the main article, I think that overall America would be best served by the metric system.
Now that the decimal system predominates the metric system is generally easier to use, once you get used to it. Moreover, it will bring us into line with virtually all of the rest of the world which simplifies international communications, not to mention that most technical/scientific work is done in the metric system anyway. This means that most school children are burdened with learning 2 separate systems of measurement and their conversions for very little reason now.
While this is completely off topic from the main article, I think that overall America would be best served by the metric system.
You're probably right, at least for most things. But justifying the English system is still worthwhile, if only to better understand its rationale in the first place.
I still maintain that Fahrenheit is an exceptionally good temperature scale for weather, though. It's beautifully simple.
I still maintain that Fahrenheit is an exceptionally good temperature scale for weather, though. It's beautifully simple.
Link to the original article: http://www.maa.org/devlin/LockhartsLament.pdf
Every time I read this is causes me physical pain to think that I'd have to take more than a 50% pay cut to become a math teacher. If only I were independently wealthy...
We have issues with physics in our local high school. I've decided to apply for the job. If I get it, I'll be scrambling to keep up the biz; but it's a workload I feel I need to accept because we'll lose the kids if I don't.
Thanks! That made me stop watching The Wire and continue working my way through Practical Foundations of Mathematics.
Every single time this is posted I read it and it is still as good as I remember. Thank you for reposting this, volodia.
The scenario at the beginning is real - at least in Germany
Nobody in Germany listens to or plays music until grad school?
Well, in some elementary schools you may learn to play a bit of the flute - Also we sang sometimes but the focus was clearly on music theory and music history.
Right, but there's radio stations and street musicians and concerts and stuff, right?
"At no time are students let in on the secret that mathematics, like any literature, is created by human beings for their own amusement; that works of mathematics are subject to critical appraisal; that one can have and develop mathematical taste. A piece of mathematics is like a poem, and we can ask if it satisfies our aesthetic criteria: Is this argument sound? Does it make sense? Is it simple and elegant? Does it get me closer to the heart of the matter?"
I remember once in some math class at Berkeley doing a sloppy rush job on a proof assigned as an exercise. The TA grading the assignment gave me credit, but wrote: "Isn't this using an H-bomb to kill a fly?" I was embarrassed, but also kind of glad to know that elegance (or lack thereof) did matter.