Math for Math's sake

Current Events Domestic United States Politics
1

A math expert/teacher advocates in the following article that math should be done for math’s sake regardless of practical applications. People are too stupid to use the practical applications of math anyway! (Sort of ad lib here, I don’t actually think this) Children should play games instead of learning addition! Reason is useless! The only interesting questions in math are the kind that have no answer!

This is just great. I can’t even imagine how stupid the products of such an education would be. *shivers* Dr. Simon Pritchett anyone? Behold American public schools can get worse:

http://www.maa.org/devlin/LockhartsLament.pdf

2

A math expert/teacher advocates in the following article that math should be done for math’s sake regardless of practical applications. People are too stupid to use the practical applications of math anyway! (Sort of ad lib here, I don’t actually think this) Children should play games instead of learning addition! Reason is useless! The only interesting questions in math are the kind that have no answer!

This is just great. I can’t even imagine how stupid the products of such an education would be. *shivers* Dr. Simon Pritchett anyone? Behold American public schools can get worse:

http://www.maa.org/devlin/LockhartsLament.pdf

Archimedes, Euler, Laplace, Gauss, Newton, Fourier, et.al., were very practical mathematicians and they were the most brilliant mathematicians in history. It is the practical worth of their ideas that makes them so damned worthwhile and cool.

I have no use for ivory tower “thinkers”.

3

I think Lockhart correctly identifies the problem in today’s math curriculum, which is that students are taught to shuffle symbols around by rote so they can pass the test without learning what any of it really means. However, the solution is to motivate the subject material, not to throw out systematic instruction and have the students reinvent the wheel as they go along. In particular, this requires math teachers that themselves actually know what it means and why the methods taught are efficient, not just teachers with education degrees reading out of the textbook as we have now.

Also, his argument seems to appeal to an intrinsic/subjective dichotomy. He discards the intrinsic approach of “apply these formulas in the gray boxes to these story problems because we said so” with the subjective “just explore the ideas at whim and if we never get to long division it couldn’t have been that useful or interesting anyway.” His whole “ladder myth” is a rejection of hierarchical knowledge and further suggests subjectivism is involved in his reasoning.

4

I didn’t interpret it that way at all.

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The author of the article is advocating a return to problem solving and Socratic-style teaching (in some cases) to re-kindle a love for mathematics by inducing students to reason rather than pounding rote formulas into their heads. “Formula-pounding” might be appropriate for a college-level engineering course, but certainly not for elementary school. Here is evidence for my claim:

The main problem with school mathematics is that there are no problems. Oh, I know what

passes for problems in math classes, these insipid “exercises.” “Here is a type of problem. Here

is how to solve it. Yes it will be on the test. Do exercises 1-35 odd for homework.” What a sad

way to learn mathematics: to be a trained chimpanzee.

But a problem, a genuine honest-to-goodness natural human question— that’s another thing.

How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a

number? How many ways can I symmetrically tile a surface? The history of mathematics is the

history of mankind’s engagement with questions like these, not the mindless regurgitation of

formulas and algorithms (together with contrived exercises designed to make use of them).

A good problem is something you don’t know how to solve. That’s what makes it a good

puzzle, and a good opportunity. A good problem does not just sit there in isolation, but serves as

a springboard to other interesting questions. A triangle takes up half its box. What about a

pyramid inside its three-dimensional box? Can we handle this problem in a similar way?

p.9

Now I will address your post:

People are too stupid to use the practical applications of math anyway!

http://www.maa.org/devlin/LockhartsLament.pdf

CITATION NEEDED

Reason is useless!

CITATION NEEDED

The only interesting questions in math are the kind that have no answer!

CITATION NEEDED.

Here is the next paragraph from the essay:

I can understand the idea of training students to master certain techniques— I do that too.

But not as an end in itself. Technique in mathematics, as in any art, should be learned in context.

The great problems, their history, the creative process— that is the proper setting. Give your

students a good problem, let them struggle and get frustrated. See what they come up with.

Wait until they are dying for an idea, then give them some technique.

Ranger, you’re obviously very angry about something. I suggest you take a long, deep breath before responding, if you’re considering doing so.