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This is nauseating. Not to say arithmetic is a useless skill, but we should not be focusing on teaching kids things that computers can easily do. At a certain

by sz 17y ago

This is nauseating. Not to say arithmetic is a useless skill, but we should not be focusing on teaching kids things that computers can easily do. At a certain point, "higher math" becomes about coming up with original arguments and explaining them clearly, not about performing computations. Consider a typical higher math problem, like: "Let C denote the unit circle in the complex plane. Suppose f:C->C is a map which is not homotopic to the identity. Prove that f(x)=-x for some point x of C." I fail to see how years spent on tedious factorization and fraction manipulation would help anyone solve that type of problem. Look up the essay "Lockhart's Lament" for a real mathematician's perspective.

tokenadult 17y ago
Look up the essay "Lockhart's Lament" for a real mathematician's perspective. I have read the Lockhart's Lament essay already years ago. http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf I like his point, "The saddest part of all this 'reform' are the attempts to 'make math interesting' and 'relevant to kids’ lives.' You don’t need to make math interesting--it’s already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives. That’s why it’s so fun!" But there are various kinds of real mathematicians, and various kinds of activities that real mathematicians find fun, or at least strictly necessary for doing the fun things. "Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York." http://www.maa.org/devlin/devlin_03_08.html http://www.maa.org/devlin/devlin_03_08.html So I regard Mr. Lockhart's opinion, but I also consider the opinion of Fields medalist William P. Thurston. http://arxiv.org/PS_cache/math/pdf/0503/0503081v1.pdf http://arxiv.org/PS_cache/math/pdf/0503/0503081v1.pdf "Addition of fractions is a very boring topic to someone who already knows it, but it is an essential skill for algebra, which in turn is essential for calculus. It is not so hard, when talking with students individually, to find out what parts of the structure need shoring up and to deal with those parts individually." And I consider the opinion of professor of homotopy theory W. Stephen Wilson http://www.math.jhu.edu/~wsw/guide/node19.html http://www.math.jhu.edu/~wsw/guide/node19.html "We memorize in order to facilitate learning, so we can function with the demands of the field. Memorization is not an end in itself, and it does not constitute learning. But when you use this information, you won't forget it. Every field requires memorization, and most fields -- biology, history, physics, political science, languages -- require far more. We are only able to solve problems if we are familiar with the necessary terms and laws. To improve your memory, don't trust your recognition memory when it comes to a test. Practice writing out the definitions and theorems, and make outlines of the major points of the theory. Check back to your text for accuracy. It is easy to think we know something until we attempt to put it in writing. By practicing studying continuously in this way, rather than cramming at the last minute, you will find memorization will feel more naturally like part of the learning process." Anyway, can't learning the content of the preliminary course mentioned in the submitted article be fun for someone who recognizes beautiful consistent patterns for the first time?
- sz 17y ago
  Yes I agree completely that elementary concepts and techniques of arithmetic (the concepts behind which may not even be so elementary) are essential and must be understood by any math student, but I distinguish strongly between learning said concepts/techniques and repeating them ad nauseam in frivolous repetitive exercise that demand no originality in reasoning whatsoever. I love math and would be considered by most to be a decent student, but just looking at those problems gives me a headache, and never have I encountered a circumstance in which carrying out those types of calculations by hand was remotely necessary. I will note that the memorization quote is particularly true with more abstract topics where definitions are crucial to understanding ideas and writing proofs.

by sz 17y ago

tokenadult 17y ago

Look up the essay "Lockhart's Lament" for a real mathematician's perspective. I have read the Lockhart's Lament essay already years ago. http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf I like his point, "The saddest part of all this 'reform' are the attempts to 'make math interesting' and 'relevant to kids’ lives.' You don’t need to make math interesting--it’s already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives. That’s why it’s so fun!" But there are various kinds of real mathematicians, and various kinds of activities that real mathematicians find fun, or at least strictly necessary for doing the fun things. "Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York." http://www.maa.org/devlin/devlin_03_08.html http://www.maa.org/devlin/devlin_03_08.html So I regard Mr. Lockhart's opinion, but I also consider the opinion of Fields medalist William P. Thurston. http://arxiv.org/PS_cache/math/pdf/0503/0503081v1.pdf http://arxiv.org/PS_cache/math/pdf/0503/0503081v1.pdf "Addition of fractions is a very boring topic to someone who already knows it, but it is an essential skill for algebra, which in turn is essential for calculus. It is not so hard, when talking with students individually, to find out what parts of the structure need shoring up and to deal with those parts individually." And I consider the opinion of professor of homotopy theory W. Stephen Wilson http://www.math.jhu.edu/~wsw/guide/node19.html http://www.math.jhu.edu/~wsw/guide/node19.html "We memorize in order to facilitate learning, so we can function with the demands of the field. Memorization is not an end in itself, and it does not constitute learning. But when you use this information, you won't forget it. Every field requires memorization, and most fields -- biology, history, physics, political science, languages -- require far more. We are only able to solve problems if we are familiar with the necessary terms and laws. To improve your memory, don't trust your recognition memory when it comes to a test. Practice writing out the definitions and theorems, and make outlines of the major points of the theory. Check back to your text for accuracy. It is easy to think we know something until we attempt to put it in writing. By practicing studying continuously in this way, rather than cramming at the last minute, you will find memorization will feel more naturally like part of the learning process." Anyway, can't learning the content of the preliminary course mentioned in the submitted article be fun for someone who recognizes beautiful consistent patterns for the first time?

sz 17y ago
Yes I agree completely that elementary concepts and techniques of arithmetic (the concepts behind which may not even be so elementary) are essential and must be understood by any math student, but I distinguish strongly between learning said concepts/techniques and repeating them ad nauseam in frivolous repetitive exercise that demand no originality in reasoning whatsoever. I love math and would be considered by most to be a decent student, but just looking at those problems gives me a headache, and never have I encountered a circumstance in which carrying out those types of calculations by hand was remotely necessary. I will note that the memorization quote is particularly true with more abstract topics where definitions are crucial to understanding ideas and writing proofs.