# "Your argument has to be beautiful."

July 31, 2012 10:48 AM Subscribe

Paul Lockhart, author of the famous Mathematician's Lament, has a new book coming out called Measurement, which tries to discuss mathematics "as an artful way of thinking and living". Lockhart discusses his passion for math and motives for writing the book in this video.

The Mathematician's lament was posted previously by my brother a while ago and the discussion is still relevant, but this is a great post!

posted by Blasdelb at 11:22 AM on July 31, 2012

posted by Blasdelb at 11:22 AM on July 31, 2012

Yeah, that is a great essay (I'm not yet finished with). I've always done poorly with math, and always been interested in it, but when I would ask a teacher 'why' something was so, I'd get the answer: 'it just is' shutting down my interest. I started reading up on sacred geometry, gematria and astrology, which at least treat math as an art, and introduced me to some math principles and ideas in a context that made sense to me.

posted by not_that_epiphanius at 11:24 AM on July 31, 2012

posted by not_that_epiphanius at 11:24 AM on July 31, 2012

There are a lot of problems facing the United States in the next 20 years, but if I were pressed hard, I think the state of K-12 math education is chief among them on the list.

Why? Because we're facing this huge problem of global warming, and it's a problem that'll be solved to whatever extent by climatologists, physicists, chemists, biologists, engineers, economists, urban planners and architects - not to mention financiers and businesspeople. And every single one of those professions, at a very minimum, requires fairly advanced mathematical training.

Even the students who can get through this training often don't really

I was that kid. My pathological difficulty with math began as early as third grade, when we had to memorize hundreds of multiplication facts and I was among the last kids in the class able to do it. From then on math was a nightmare of teachers teaching algorithms and almost never ideas, insistence on perfect notation and symbols (the use of the Greek alphabet is particularly cruel when not paired with an explanation of what those symbols actually mean). It's like they all wanted kids to think of math as this weird rune-like language full of mystical power, instead of a shorthand way of expressing ideas that we encounter in life all the time.

For some reason, in my mid-20's, I got over my math phobia and I've since gone back to school, completed all those prerequisite classes and am applying to applied math and finance programs (still not sure which I want to do). But I wasted an awful lot of time being irrationally scared of the subject, and I think a lot of it has to do with the way math is taught by American teachers.

posted by downing street memo at 11:27 AM on July 31, 2012 [7 favorites]

Why? Because we're facing this huge problem of global warming, and it's a problem that'll be solved to whatever extent by climatologists, physicists, chemists, biologists, engineers, economists, urban planners and architects - not to mention financiers and businesspeople. And every single one of those professions, at a very minimum, requires fairly advanced mathematical training.

Even the students who can get through this training often don't really

*learn*the math, they grind it out via memorization and promptly forget it. Meanwhile, people who don't have the patience (or have other, more immediately-gratifying interests) to grind out the years of boring rote-learning are quickly told that they are not "math people" and develop an almost pathological fear of any and all numbers.I was that kid. My pathological difficulty with math began as early as third grade, when we had to memorize hundreds of multiplication facts and I was among the last kids in the class able to do it. From then on math was a nightmare of teachers teaching algorithms and almost never ideas, insistence on perfect notation and symbols (the use of the Greek alphabet is particularly cruel when not paired with an explanation of what those symbols actually mean). It's like they all wanted kids to think of math as this weird rune-like language full of mystical power, instead of a shorthand way of expressing ideas that we encounter in life all the time.

For some reason, in my mid-20's, I got over my math phobia and I've since gone back to school, completed all those prerequisite classes and am applying to applied math and finance programs (still not sure which I want to do). But I wasted an awful lot of time being irrationally scared of the subject, and I think a lot of it has to do with the way math is taught by American teachers.

posted by downing street memo at 11:27 AM on July 31, 2012 [7 favorites]

*(the use of the Greek alphabet is particularly cruel when not paired with an explanation of what those symbols actually mean)*

The use of the Greek alphabet is particularly cruel, full stop. I've seen more people (myself included) become utterly frustrated with math because of an debilitating lack of penmanship experience with Greek letters. Nothing elicits more rage and contempt for every mathematician who ever lived than a malformed γ that morphs into an r after several pages of work.

posted by RonButNotStupid at 12:04 PM on July 31, 2012

*There are a lot of problems facing the United States in the next 20 years, but if I were pressed hard, I think the state of K-12 math education is chief among them on the list.*

When it comes to math instruction, this country is slowly committing suicide, one student at a time, when someone can ask with a straight face if math classes are really needed, because it is

*too hard*.

posted by Blazecock Pileon at 12:14 PM on July 31, 2012 [5 favorites]

I love that essay and link to it almost every time any discussion about the nature of mathematics instruction comes up on the blue. Thanks for the post.

posted by King Bee at 12:15 PM on July 31, 2012

posted by King Bee at 12:15 PM on July 31, 2012

It's like they all wanted kids to think of math as this weird rune-like language full of mystical power ...

That was like crack for me.

posted by benito.strauss at 12:47 PM on July 31, 2012

That was like crack for me.

posted by benito.strauss at 12:47 PM on July 31, 2012

*It's like they all wanted kids to think of math as this weird rune-like language full of mystical power, instead of a shorthand way of expressing ideas that we encounter in life all the time.*

In the class I'm teaching right now, we started talking about probability last week. Now, shh don't tell anyone what I've decided to do is not use any symbols at all, at least not for the first week. I told them to close the textbook and not open it for a week. (For a class that meets 100 minutes a day, 5 days a week for 5 weeks, that's a significant chunk of time.) We can do, and have done, an awful lot without having to resort to crazy formulas and runes all over the joint. We're getting away from that now, because we are starting to talk about continuous probability distributions (and it is much more difficult to avoid some of the symbology).

Surprise surprise, this class has actually done the best of any class I've ever had, in regards to the subject of probability.

The problem you encountered is likely due to the fact that mathematics "teachers" in third grade don't know

*why*anything is what it is, and they couldn't do the mathematics without the formal symbol-pushing. To those people, that's all mathematics is.

posted by King Bee at 12:59 PM on July 31, 2012 [3 favorites]

*When it comes to math instruction, this country is slowly committing suicide, one student at a time, when someone can ask with a straight face if math classes are really needed, because it is too hard.*

Wow, that article is awful. Can you imagine anyone saying, "We should teach students how to write sentences, but not paragraphs, since so few of them will end up as professional writers"? And when they describe math as a collection of formulas to be remembered, all I can think is, "Well,

*there*'s your problem!"

posted by samw at 1:16 PM on July 31, 2012 [1 favorite]

*TRIGONOMETRY. Two weeks of content are stretched to semester length by masturbatory definitional runarounds.*

So this is what I have to look forward to in the Fall in class.

Excellent. *steeples fingers*

posted by spinifex23 at 1:24 PM on July 31, 2012 [1 favorite]

I just showed the Lockhart video to my class of middle-school math students. I plan to call arguments

posted by Wulfhere at 1:36 PM on July 31, 2012

*reason poems*from here on out. Beautiful.posted by Wulfhere at 1:36 PM on July 31, 2012

My friend teaches in the same department as Paul. I was lucky enough to get to read the manuscript and the book is completely awesome. I don't really know of any book like it.

posted by mathtime! at 4:59 PM on July 31, 2012 [1 favorite]

posted by mathtime! at 4:59 PM on July 31, 2012 [1 favorite]

I just want to know what kind of creative paradise that author went to school at. The "nightmares" he describes were exactly my experience in music and arts classes. Lots of rote, small doings and copywork and not a whole lot of actual creating. I get what he's saying about math classes though. The part about "a triangle is always half of the box its in" was news to me.

For me math got a lot more interesting when we did the logic unit. I wish we had done that sooner, and more of it.

posted by bleep at 5:44 PM on July 31, 2012

For me math got a lot more interesting when we did the logic unit. I wish we had done that sooner, and more of it.

posted by bleep at 5:44 PM on July 31, 2012

Geometry -> Computational Geometry -> Algebra, that would have worked better for me than the other way a round. Then I would have welcomed the algebra, because it would have had some point, for solving the details of the geometries.

posted by StickyCarpet at 7:52 PM on July 31, 2012

posted by StickyCarpet at 7:52 PM on July 31, 2012

*Geometry -> Computational Geometry -> Algebra*

Mmmhmmm. Along that same vein, interested folks may wish to consider these so-called "algebra tiles", which I have used in lower level classes with varying degrees of success. "Completing the square" ceases to be a meaningless catchphrase (as it may seem to the uninitiated) when you use these to factor polynomials.

The online tool is nice, but it helps if you have physical ones to play with also.

posted by King Bee at 8:06 PM on July 31, 2012

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TRIGONOMETRY. Two weeks of content are stretched to semester length by masturbatory definitional runarounds.

Quoted for pure truth.

posted by chavenet at 11:09 AM on July 31, 2012 [1 favorite]