Lockhart's Lament: On Mathematics at School(maa.org)
maa.org
Lockhart's Lament: On Mathematics at School
http://www.maa.org/devlin/devlin_03_08.html
15 comments
The bit about finding the area of a triangle was great -- a quick, simple example of what math is and why anyone would enjoy it.
K-12 public school math education burned me so bad that I didn't realize how much I love math until my mid-20s. (These days I'm reading about abstract algebra for fun!)
K-12 public school math education burned me so bad that I didn't realize how much I love math until my mid-20s. (These days I'm reading about abstract algebra for fun!)
As a mathematics major and having gone through some seriously crappy math courses in highschool (and even freshman college courses) including AP Calculus classes, I just want to say that I truely recommend reading this article.
It really cannot be stated any better than this, folks. Even as a math major, reading this reinspires me and refuels my passion for mathematics.
Simply lovely. :)
It really cannot be stated any better than this, folks. Even as a math major, reading this reinspires me and refuels my passion for mathematics.
Simply lovely. :)
I'm a graduate student in mathematics.
This article made me cry. Really powerful.
This article made me cry. Really powerful.
Yes, it's a very very nice article. Actually, you put it better: very, very powerful.
I wish I could upmod this so many times... Amazing article, everyone should read the entire thing.
I hated math throughout school, although I was told I was "good at it", even though I had no clue what was going on. Now I know why!
What can we do about this?!
I hated math throughout school, although I was told I was "good at it", even though I had no clue what was going on. Now I know why!
What can we do about this?!
Great article! I've always thought that having math education focusing on formulas is having poetry and literature focus on grammar and spelling -- the painting and music analogies are dead-on.
But that's exactly what happens: Formulas and equations (grammar) are one way to express a beautiful idea. Unfortunately we end up focusing on the syntax and not the semantics, the underlying meaning.
Shameless plug, but I try to do my part to make math intuitive at betterexplained.com.
What a great essay.
But that's exactly what happens: Formulas and equations (grammar) are one way to express a beautiful idea. Unfortunately we end up focusing on the syntax and not the semantics, the underlying meaning.
Shameless plug, but I try to do my part to make math intuitive at betterexplained.com.
What a great essay.
It always struck me how my math classess seemed to focus on the mechanical exercises and never let us glimpse at the true genius of what we were brainlasly repeating with them.
However, I think I could say the same for many of my classes. As an Engineering student, I'm sure most of my physics classes are way beyond what I will ever use when I leave university (trig btw, heavily used for most of this classes). I think the same reasoning could be applied here, instead of repeating painful exercises consisting basically of memorizing and rearranging formulas, let the student wonder at the context and history behind each of the subjects and the problems that were solved with them.
This is a problem affecting education systems in a deeper level than the math curriculum, it comes down, I think, to something the author points at, which is this widespread notion that education is supposed to be something that "prepares tomorrow's workforce" instead of it being a source for inspiration and enlightenment.
However, I think I could say the same for many of my classes. As an Engineering student, I'm sure most of my physics classes are way beyond what I will ever use when I leave university (trig btw, heavily used for most of this classes). I think the same reasoning could be applied here, instead of repeating painful exercises consisting basically of memorizing and rearranging formulas, let the student wonder at the context and history behind each of the subjects and the problems that were solved with them.
This is a problem affecting education systems in a deeper level than the math curriculum, it comes down, I think, to something the author points at, which is this widespread notion that education is supposed to be something that "prepares tomorrow's workforce" instead of it being a source for inspiration and enlightenment.
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.
Even the introductory math courses in college are terrible.
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.
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.
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."
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."
The PDF was painful so here is a converted HTML link
http://viewer.zoho.com/docs/xdLbwd
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.
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.
Very interesting. Does any one have any suggestions to interest an 11 year old about Math?
Let them find a way to use it.
When I was in high school, I played Robot Battle, a game in which you scripted behaviors for automated tanks. This gave me immediate reason to use and learn much of what I learned in math at school. The day we were taught basic trigonometry, I was on the edge of my seat, because I knew that what I was learning would be useful several hours later when I got back to coding my robots.
Of course, you can't force an interest on a child, but you can certainly introduce them to new ones.
When I was in high school, I played Robot Battle, a game in which you scripted behaviors for automated tanks. This gave me immediate reason to use and learn much of what I learned in math at school. The day we were taught basic trigonometry, I was on the edge of my seat, because I knew that what I was learning would be useful several hours later when I got back to coding my robots.
Of course, you can't force an interest on a child, but you can certainly introduce them to new ones.
I think you have to show interest about it yourself. If you aren't curious about it, he/she probably won't either.
From time to time I talk children in my family about mathematical subjects I myself find interesting, and I know something about, such as strange stuff about infinite, mathematical logic, or crazy and counter-intuitive mathematical theorems. And they keep interested about it as long as I do. So I think that can be a way.
From time to time I talk children in my family about mathematical subjects I myself find interesting, and I know something about, such as strange stuff about infinite, mathematical logic, or crazy and counter-intuitive mathematical theorems. And they keep interested about it as long as I do. So I think that can be a way.
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.
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.
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.
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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.