Lockhart's Lament: On Mathematics at School • Hacker News Board

Re: Lockhart's Lament: On Mathematics at School

#11

Post by phaedrus » Fri, Mar 07, 2008, 4:14 AM UTC

My high school algebra/trig teacher was a real drone; every problem had to be done by rote and she cared more about your handwriting and placing the numbers the same way she did than whether you actually knew what you were doing. She had the imagination of a four-function calculator; to her it "math" meant "mechanical". I made C's and D's in her classes, because I'd see shortcuts that got the right answers faster but she'd mark right answers wrong if we didn't use her methods to get them.

Meanwhile I was writing my own 3-d graphics engine at home, working all the math out from observation of the real world with yardsticks and using graph paper, because I didn't have internet at home to look up the answers or the math education to know . Every time I'd try to ask her if anything from algebra or trig connected in some way to what I was doing, or if she knew of some math tools that would help me, she'd shut my questioning down and belittle me. I actually worked out sine/cosine and rotation matrices out on my own before we covered them in class, because she wouldn't point anything out to me.

To this day I still don't know if she was such an unimaginative rock that she really didn't make any cognitive connection between math and real world applications, or if she just hated me for being a nonconformist.

Re: Lockhart's Lament: On Mathematics at School

#12

Post by Spyckie » Fri, Mar 07, 2008, 7:30 AM UTC

This is a beautiful article. I hated math during high school, but was very good at it. I even skipped a grade of math so I could free up my schedule to do more interesting classes! It's such a shame - I love math puzzles but really hate math class.

Even the introductory math courses in college are terrible.

Re: Lockhart's Lament: On Mathematics at School

#13

Post by palish » Fri, Mar 07, 2008, 7:55 AM UTC

phaedrus wrote: post #11

My high school algebra/trig teacher was a real drone; every problem had to be done by rote and she cared more about your handwriting and placing the numbers the same way she did than whether you actually knew what you were doing. She had the imagination of a four-function calculator; to her it "math" meant "mechanical". I made C's and D's in her classes, because I'd see shortcuts that got the right answers faster but…

What are you working on now? Just curious.

Re: Lockhart's Lament: On Mathematics at School

#14

Post by comatose_kid » Fri, Mar 07, 2008, 8:23 AM UTC

Man, what a great article. Thanks.

I love Lockhart's definition of Trigonometry: "Two weeks of content are stretched to semester length by masturbatory definitional runarounds".

Reading this article makes me understand why people home-school their children.

Re: Lockhart's Lament: On Mathematics at School

#15

Post by newt0311 » Fri, Mar 07, 2008, 10:57 AM UTC

huherto wrote: post #3

Very interesting. Does any one have any suggestions to interest an 11 year old about Math?

Given said 11 year old interesting problems from mathematics competitions. The AMC10/12 and AIME competitions are good sources. Some others are USAMTS and for the really good ones, USAMO and Putnam. Note: Do NOT give the UIL competitions. Those aren't much better than advanced high school arithmetic.

Re: Lockhart's Lament: On Mathematics at School

#16

Post by musiciangames » Fri, Mar 07, 2008, 11:44 AM UTC

It struck me while reading this that we should rename the subject we teach as maths to puzzles.

Just about everybody likes having a go at puzzles, and people are pretty good at selecting puzzles with the right amount of challenge. I'm sure as a student I'd have a more positive expectation going into a puzzles class than the current experience.

Re: Lockhart's Lament: On Mathematics at School

#17

Post by optimal » Fri, Mar 07, 2008, 3:36 PM UTC

Is this specific to math, or is all standardized (bastardized?) education this way?

I can't remember doing any creative writing in elementary school, but I do remember diagramming sentences, much like the musician's nightmare in the article.

Re: Lockhart's Lament: On Mathematics at School

#18

Post by wisernow » Fri, Mar 07, 2008, 5:17 PM UTC

The PDF was painful so here is a converted HTML link http://viewer.zoho.com/docs/xdLbwd

Re: Lockhart's Lament: On Mathematics at School

#19

Post by hhm » Fri, Mar 07, 2008, 5:39 PM UTC

musiciangames wrote: post #16

It struck me while reading this that we should rename the subject we teach as maths to puzzles. Just about everybody likes having a go at puzzles, and people are pretty good at selecting puzzles with the right amount of challenge. I'm sure as a student I'd have a more positive expectation going into a puzzles class than the current experience.

I don't know. I think maths can be fun and can be very interesting without having to hide it as puzzles. I'd prefer to call the things by their name, but to show them as they truly are: interesting, fun, and even quite addicting.

Re: Lockhart's Lament: On Mathematics at School

#20

Post by optimal » Fri, Mar 07, 2008, 6:05 PM UTC

Did anybody read _King of Infinite Space_, the biography of Donald Coxeter?

I noticed the article used lots of drawings, and I believe this and the general discussion fits into Coxeter's thinking on mathematics, versus the Bourbaki school's more rigid and less intuitive approach.

"GEOMETRY. Isolated from the rest of the curriculum, this course will raise the hopes of students who wish to engage in meaningful mathematical activity, and then dash them."