(no subject)

[rivka]

I just read an interesting article by a mathematician, lamenting the way his subject is tortured and murdered in schools. (Article is here, in a PDF.) Here's his basic thesis:

All this fussing and primping about which "topics" should be taught in what order, or the use of this notation instead of that notation, or which make and model of calculator to use, for god’s sake— it’s like rearranging the deck chairs on the Titanic! Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion— not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it. Remove this from mathematics and you can have all the conferences you like; it won’t matter. Operate all you want, doctors: your patient is already dead.

The saddest part of all this "reform" are the attempts to “make math interesting” and "relevant to kids’ lives." You don’t need to make math interesting— it’s already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives.

He's passionate, furious, despondent, and very funny, producing gems along the lines of:

All metaphor aside, geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum. Other math courses may hide the beautiful bird, or put it in a cage, but in geometry class it is openly and cruelly tortured. (Apparently I am incapable of putting all metaphor aside.)

The article is long, but I found it a quick read. It's worth reading to the end, if only to get his truth-in-advertising summary of the K-12 math curriculum ("TRIGONOMETRY. Two weeks of content are stretched to semester length by masturbatory definitional runarounds.") I was one of those people who was very good at plugging numbers correctly into formulas but never felt like I had a good conceptual grasp of math. This article makes me feel sad about what I missed.

Comments

[naomikritzer]

OK, I'm reading a bit further in. I love his ideas about teaching geometry. Some of my thoughts on his commentary are colored by the fact that I've volunteered in an elementary school for three years, and my older kid is not in high school yet (or anywhere near it). He clearly WANT to apply his ideas to grade school, but I don't think he's actually taught in one.

There are kids who come to grade school not knowing how to count. Or who start first grade unable to do addition problems like 3+1. Part of the purpose of teaching early grade school arithmetic is to teach kids things like how to make change, or know if they were given the correct change. This is important stuff.

[naomikritzer]

Well, I stand corrected; I googled, and he teaches K-12, all grades.

That implies he does enrichment, though, rather than being the only math teacher these kids get. So it's someone else who makes sure they can count, add, multiply, etc.

High school math has been in the news here (in MN) a bit, because we had this test that all the high school kids were supposed to pass in order to graduate. However, very few (like less than a third, IIRC) were passing it. They ran some questions from the test in the paper, and there is no way in hell most of the adults I know could pass this test, which raises the question, why are we requiring these students to do so? It's really not clear to me why we have set mathematics (rather than music theory, say, or formal logic, or Classical Greek, or some other not-wide-applicable intellectual exercise) up as one of the major things that all kids should study. Basic arithmetic is useful. Fractions are useful. Basic algebra is useful. Beyond that, you might just as well have everyone do discovery-style math with a teacher like Lockhart because while they might not master trig that way, they will never ever use trig for anything so who really care? and with Lockhart's approach, they'll at least learn a lot about exploring ideas and thinking about problems. There's very little inclination to question why we think students need to learn this stuff -- what the point of it is, whether it's mental calisthenics or if it's just in case they become mechanical engineers or something.

[green-knight.livejournal.com]

Statistics is useful. An understanding of statistics will give you a life tool: can you expect to win the lottery? Do pyramid schemes work? How valuable are newspaper statistics that say '75% of all the people we questioned' when they don't tell you whether they questioned four or four hundred?

One skill they don't tend to teach in school but which is the most useful of all is the kind of mental arithmetic that in German is known as 'pi times thumb' - you round numbers and get an idea of the size of the number you expect to get from any calculation. So when you're asked to pay a supermarket bill that's fifty dollars higher than what you thought was in your trolley, you'll question it immediately, and you'll spot that something went wrong when your bank statement or tax return don't look right. In order to do that, you need multiplication tables up to twelve - and a few mental tricks.

[naomikritzer]

Statistics is very useful and is hardly ever taught in school beyond the most rudimentary level.

They do usually teach some estimation in younger grades.

[almeda.livejournal.com]

The problem I had with estimation as taught in the schools is that they only ever taught us to estimate AFTER we already had the basic math we were estimating down pat ... so I thought it was a huge, useless waste of time and energy, and didn't bother even trying. Much, much later it became clear to me that estimation is very useful (in the 'how to tell if your calculator is lying to you' department -- does this answer look like the sort of answer you ought to get?), but the way it was TAUGHT caused me to instantly write it off.

[panacea1.livejournal.com]

See, I'm one of those weirdoes that thinks a solid general education should include, among other things, music theory, formal logic, and if not classical Greek then at least a riding-the-subway-and-reading-the-newspaper functional proficiency in a language not spoken in one's home. A general education should be a sampling of everything - the useful and the intriguing both - not just a "crank 'em through" process. I'd like to see number theory and intro to prob & stat at the high school level as an alternative to the trig/calculus sequence, though. Most people won't use a whole lot of calculus, it's true. Geometry, otoh, is widely applicable to the visual arts - if you let it be. But I digress and am about to rant in a stranger's journal, so I'd better stop now. ;-)

[almeda.livejournal.com]

My Freshman Comp II english class in college (at a community college, actually) was basically Classical Rhetoric. It was awesome. Stuff like the different kinds of fallacies should totally be taught in 4th or 5th grade English, both as a way of teaching kids to calibrate their b*llsh*t meters, and to help them figure out how to structure a paper.

[almeda.livejournal.com]

I use trig for craft projects (if I want to make something x high at the peak, with a slanty top, and y high at the edge, and it's z wide between those two verticals, (a) what angles are involved for the structural members, and (b) what's the length of the third side I need in materials?

Etc. Anything crafty involving angles can be aided by application of trig, though it's not necessarily REQUIRED.