A Mathematician's Lament — an Indictment of US Math Education

Scott Aaronson recently had "A Mathematician's Lament" [PDF], Paul Lockhardt's indictment of K-12 math education in the US, pointed out to him and takes some time to examine the finer points. "Lockhardt says pretty much everything I've wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet. If you like math, and more so if you think you don't like math, I implore you to read his essay with every atom of my being. Which is not to say I don't have a few quibbles [...] In the end, Lockhardt's lament is subversive, angry, and radical ... but if you know anything about math and anything about K-12 'education' (at least in the United States), I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth."

Comments

The way math is structured is disconnected from...

[blahplusplus]

... interesting things kids want to do.

Lets face it a minority of people will like math, but matehmaticians have done a lot to make mathematics overly complicated.

I struggled with the symbolic format math was presented in highschool because it was so disconnected from the world, only as I got older did I realize how arbitrary and how that was only one way to present mathematics. To really teach math one must learn how to observe first before one even gets into symbolic computation, math at it's most basic is about observing relationships, patterns of : Size, ratio, proportion, etc. It's really a language invented to systematize structure and relationships of the real world, therefore how math is represented and structured and is taught matters a hell of a lot.

I've learned over the years that many mathematical systems are totally arbitrary are are more obtuse then they need to be, math comes from the simplest observations. Math has built up a lot of cruft and wasteful jargon disconnecting math from the world.

For instance I had no idea for a long time that the way math is structured could be restructured when I was young and it was one group of peoples perspective on mathematical principles, I came across debates and alernative systems like:

http://www.symmetryperfect.com/

And it showed me how arbitrary mathematical systems and their structures really are and they are built to suit particular kinds of minds or cultures.

For instance the ancient mayans used shapes for numbers, instead of 1, 2, 3

See here:
http://en.wikipedia.org/wiki/Maya_numerals

Math is a very rich subject which unfortunately has a lot of cultish like people who think themselves the gatekeepers of mathematics.

I've thought about writing a book in my spare time about how badly mathematicians and the academia has blinded themselves to simplifying mathematics by focusing too much on symbolic jargon and not teaching children how 'mathematical' relationships are related to our simplest observations of the world: Size, shape, form, color, motion, etc.

Eh.

[gbarules2999]

Found it here: http://plato.asu.edu/LockhartsLament.pdf

The whole idea behind his essay is that he liked playing with numbers and shapes as if it's an art, but he doesn't seem to realize most people don't share this love for math, like pretty much 90% of any student population. This is me speaking as a just-graduated senior: the things he suggests is beyond the ability of most math students in high school.

An allegedly true story from a professor

[thirty-seven]

While I was in university, a computer science professor in the faculty of mathematics told me (and the rest of the class) a cute and funny story about what happens "when the children of math professors get together". He and a colleague, who each had a young daughter at that time, were walking together in a park with their daughters. The children were old enough to have picked up some math-related words and phrases from their fathers, but young enough to have no idea what they really meant - six or seven years old, maybe? The daughters went off to play and their fathers overheard them arguing about who had seen the most flowers in the park.

My professor's daughter said, "I saw five flowers!"

"And I saw... six!", the other girl replied.

Not to be outdone, my professor's daughter said, "I saw a million flowers."

"Oh yeah? I saw infinity flowers."

This, according to my professor, caused his daughter to pause - she had never heard of "infinity" before. How could she top "infinity flowers", especially since she didn't know what it meant?

But after thinking for a few seconds, she said, "Well, I saw all the flowers."

Re:tl;dr

[Fallingcow]

Bingo, and that's one of the big problems with trying to do anything about the issues the paper raises: there are only so many people with the 1) ability, 2) knowledge, and 3) inclination, to do the kind of real mathematics he's talking about.

We'd have to re-vamp our teacher training along the lines of what's talked about in the paper to try to increase the number of people who could do it, and hope Lockhart's right about this being an art with universal appeal so that enough of the teacher candidates "get" it. Even if elementary schools began using dedicated math teachers (some already do, but many don't) we'd still need a shitload of people trained in this "math as an art/math as play" style, and we currently have approximately zero in elementary education.

Re:Several Proxies

[eldavojohn]

Bah, like we're going to RTFA on a Friday when there are much better ...

I know you're mostly joking but this was a pretty interesting albeit lengthy opinion piece. In fact, he even busts into dialogue between two fictional characters named Simplicio & Salviati to illustrate his point. It's a very Plato/Caroll/Hofstadter sort of way to illustrate his point. Hell, I love this format so much, half my posts are in it!

Anyway, after reading this, I am really eager for vdash.org to get its wiki up and running so that can be used to build engines and homework for students. Maybe even provide a hub for teachers to discuss interesting assignments? I'm sure the discussion pages will prove interesting if real academics get in arguments about proofs and math. I don't think the real payoff would be reinstitutionalizing the teachers but instead giving the students the free online resources to go the extra mile if they so desire. Save your Turings and Erdoses if you can't help everyone!

Lockhart is definitely a dreamer and this isn't going to change public schools. But it might change how you as a parent get involved with your children and math.

Re:It starts with the textbooks. . .

[geobeck]

You start by having someone like the gentleman who wrote that paper create a new textbook and teachers' manual to go along with it (or, really, a 'series' of textbooks that go through the different grades) that implements the different way of teaching mathematics which he is espousing. It then dies in state and local education department when there is resistance from comittees on doing things differently than they've been done before, and anyhow there is no funding for new textbooks anyhow.

And you get around the economic obstacles by subverting the system: Crowdsource the textbook to a group of interested mathematicians. Publish it online for free, with printed copies available for a price far below what a crooked textbook publisher would charge. Add value by posting demonstrations by mathematicians, math historians, and math professors on YouTube, linked to the relevant chapter of this comprehensive, global mathematics resource.