Difference between revisions of "Memorization in mathematics"

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Broadly speaking, there seem to be two "schools of thought" regarding memorization in mathematics, as well as a third "default position":
 
Broadly speaking, there seem to be two "schools of thought" regarding memorization in mathematics, as well as a third "default position":
  
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! Name !! Description !! People who hold this position
 
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| Default position/status quo (often implicitly held) || Memorization is not just necessary to learn mathematics, but it is the primary means through which to learn mathematics. Mathematics is the study of memorizing algorithms for solving problems. Mathematics pretty much consists of rote memorization. || School teachers
 
| Default position/status quo (often implicitly held) || Memorization is not just necessary to learn mathematics, but it is the primary means through which to learn mathematics. Mathematics is the study of memorizing algorithms for solving problems. Mathematics pretty much consists of rote memorization. || School teachers
 
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| Reactionary position || The point of mathematics isn't to just memorize things; the point is the understand why things are true and to appreciate the beauty of mathematics. One should eschew memorization in favor of trying to deeply understand the concepts. || Richard Feynman, [[wikipedia:A Mathematician's Lament|Paul Lockhart]]
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| Reactionary position || The point of mathematics isn't to just memorize things; the point is the understand why things are true and to appreciate the beauty of mathematics. One should eschew memorization in favor of trying to deeply understand the concepts. || Richard Feynman, [[wikipedia:A Mathematician's Lament|Paul Lockhart]], smart teenagers
 
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| Revised status quo position || Memorization is pretty important for learning mathematics, and understanding comes from having fluency/competency. Understanding is the real goal, but memorization for the purpose of gaining fluency and storing facts in long-term memory (so as to free up working memory) is actually an essential part of the learning process. || Tim Gowers, Michael Nielsen
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| Revised status quo position || Memorization is pretty important for learning mathematics, and understanding comes from having fluency/competency. Understanding is the real goal, but memorization for the purpose of gaining fluency and storing facts in long-term memory (so as to free up working memory) is actually an essential part of the learning process. || Tim Gowers,<ref>Tim Gowers. [https://gowers.wordpress.com/2018/12/22/how-craig-barton-wishes-hed-taught-maths/ "How Craig Barton wishes he’d taught maths"]. December 22, 2018. ''Gowers's Weblog''. "Of particular importance, he claims, is the fact that we cannot hold very much in our short-term memory. This was music to my ears, as it has long been a belief of mine that the limited capacity of our short-term memory is a hugely important part of the answer to the question of why mathematics looks as it does, by which I mean why, out of all the well-formed mathematical statements one could produce, the ones we find interesting are those particular ones. I have even written about this (in an article entitled Mathematics, Memory and Mental Arithmetic, which unfortunately appeared in a book and is not available online, but I might try to do something about that at some point)." and "A prejudice that was strongly confirmed was the value of mathematical fluency. Barton says, and I agree with him (and suggested something like it in my book Mathematics, A Very Short Introduction) that it is often a good idea to teach fluency first and understanding later. More precisely, in order to decide whether it is a good idea, one should assess (i) how difficult it is to give an explanation of why some procedure works and (ii) how difficult it is to learn how to apply the procedure without understanding why it works."</ref> Michael Nielsen<ref>Michel Nielsen. [http://augmentingcognition.com/ltm.html "Augmenting Long-term Memory"]. July 2018.</ref>
 
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==See also==
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* [[Spaced repetition]]
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* [[Retention]]
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* [[Remembering mathematics]]
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==References==
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<references/>
  
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]

Latest revision as of 21:58, 7 January 2019

Broadly speaking, there seem to be two "schools of thought" regarding memorization in mathematics, as well as a third "default position":

Name Description People who hold this position
Default position/status quo (often implicitly held) Memorization is not just necessary to learn mathematics, but it is the primary means through which to learn mathematics. Mathematics is the study of memorizing algorithms for solving problems. Mathematics pretty much consists of rote memorization. School teachers
Reactionary position The point of mathematics isn't to just memorize things; the point is the understand why things are true and to appreciate the beauty of mathematics. One should eschew memorization in favor of trying to deeply understand the concepts. Richard Feynman, Paul Lockhart, smart teenagers
Revised status quo position Memorization is pretty important for learning mathematics, and understanding comes from having fluency/competency. Understanding is the real goal, but memorization for the purpose of gaining fluency and storing facts in long-term memory (so as to free up working memory) is actually an essential part of the learning process. Tim Gowers,[1] Michael Nielsen[2]

See also

References

  1. Tim Gowers. "How Craig Barton wishes he’d taught maths". December 22, 2018. Gowers's Weblog. "Of particular importance, he claims, is the fact that we cannot hold very much in our short-term memory. This was music to my ears, as it has long been a belief of mine that the limited capacity of our short-term memory is a hugely important part of the answer to the question of why mathematics looks as it does, by which I mean why, out of all the well-formed mathematical statements one could produce, the ones we find interesting are those particular ones. I have even written about this (in an article entitled Mathematics, Memory and Mental Arithmetic, which unfortunately appeared in a book and is not available online, but I might try to do something about that at some point)." and "A prejudice that was strongly confirmed was the value of mathematical fluency. Barton says, and I agree with him (and suggested something like it in my book Mathematics, A Very Short Introduction) that it is often a good idea to teach fluency first and understanding later. More precisely, in order to decide whether it is a good idea, one should assess (i) how difficult it is to give an explanation of why some procedure works and (ii) how difficult it is to learn how to apply the procedure without understanding why it works."
  2. Michel Nielsen. "Augmenting Long-term Memory". July 2018.