Sunday, July 29, 2012

article post (math ed): in which i rant for a bit.

so i ran into an article titled "Is Algebra Necessary?" in the new york times, just now. the author writes, among other things:
Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers.

Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
so based from this paragraph, you'd think that this article would be a defense in favor of mathematics and a critique of the american educational system .. but there's more:
This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources ..
.. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.
to be fair, proficiency in mathematics is a sufficient condition, but not necessary. if you are adept at it, then it shows a minimal level of skill, that you are smart enough to beat the system ..

.. like, say, earning a college degree. strictly speaking, that kind of accreditation is not necessary for earning a well-paying job. hard reality, however, suggests otherwise.

as for the next paragraph:
It’s not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better. [1]

say: i think i just missed something, because i could swear that the author had just written that ..

Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship.
i'm trying to be fair here: maybe the author realises that statistics is important, and maybe maths could be important, but not the algebra taught in schools.

i think, though, that most statisticians will tell you that that algebra is important.

there seems to be a disagreement here: to me, there is no difference between the mechanical methods of algebra and general numeracy, but i think there is a difference to the author of the article.

as for something that really upsets me, though:
I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet.
this could make sense .. if mathematics were a liberal art, which it is not. i don't think that i am alone in thinking this.

on the other hand, i wouldn't call maths a science, but i wouldn't refer to macroeconomics or psychology as sciences either, because actual experiments play no role in their epistemology. yes, they crunch a lot of data, but to be called a science, shouldn't you be able to demonstrate that your disciple uses, say, the scientific method and show the capacity to run control experiments?

in general, i don't like the consistency (or lack thereof) in this article:
It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.
If we rethink how the discipline is conceived, word will get around and math enrollments are bound to rise. It can only help. Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics.
so do standardised test scores mean nothing, while college enrollments mean everything? does this author have a good litmus test as to which statistics are important and which are not?

i'd rather that this author stop arguing sideways and avoid this pseudo-intellectual sleight of hand.

the author makes some good points, independent of his motives or mine:
maths education in the states could be vastly improved; right now, i think it's substandard. many, many teachers stress the mechanical aspect of algebra, without explaining what it really means ..

.. and some lines of computation don't really mean anything that's directly relevant to the world that we see, hear, and measure. that's a fair point ..

.. but i can say the same about a line of code in javascript that makes your web browser run: there is no analogue in physical reality that simplifies it. does it mean, however, that the syntax in which it functions is useless?

the author would argue that not everyone needs to learn how to code: true enough. also, very very few people really need any understanding of history to do their job .. nor literature and sociology, for that matter.

come to think of it, why educate people at all?
i don't agree with the author's vision. i don't see maths as how he sees it; then again, i'm just a mathematician and he's a social scientist, which suggests that we both live in the same bubble that academicians live.

i happen to see maths as, among other things, a kind of language and skill. i make no difference between the proficiency of algebra, the ability of being given data and checking the extent of correlation, and knowing the illogic of good people have a good life; rich people have a good life, ergo rich people are good.

to say that we shouldn't teach young people these skills, especially as they are important for society, means that we shouldn't have capable future citizens that can hold government and other agents of society responsible for their roles in our society.

added later: yes, i'm reaching a bit in the final paragraph. it's what i believe, not what is probably true. also, having looked around the blogosphere and parts of the internet, i feel like i'm saying essentially what everyone else is saying. (this post by mathbabe isn't bad, though.)

[1] accounting for symmetry, then that means that math and physic majors should be exempt from freshman writing courses .. because if they work with data and equations all the time, then they don't need to write essays, right?

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