Memorization in mathematics - Revision history

Issa Rice: /* Notes */

2020-09-18T00:00:09Z

Notes

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	* "What we do believe is that many people's dislike of rote memorization has led them to a generalized dislike of memory, and consequently to underrate the role it plays in cognition. Memory is, in fact, a central part of cognition. But the right response to this is not immense amounts of dreary rote memorization. Rather, it's to use good tools and good judgment to memorize what truly matters." https://numinous.productions/ttft/		* "What we do believe is that many people's dislike of rote memorization has led them to a generalized dislike of memory, and consequently to underrate the role it plays in cognition. Memory is, in fact, a central part of cognition. But the right response to this is not immense amounts of dreary rote memorization. Rather, it's to use good tools and good judgment to memorize what truly matters." https://numinous.productions/ttft/
			* [https://notes.andymatuschak.org/z5d7PMFhoTTpJfGAXms4H9gSBvUDRHb43pkfn "People underrate the importance of memory because of bad experiences with rote memorization in school"]

	==References==		==References==

Issa Rice at 04:11, 4 October 2019

2019-10-04T04:11:06Z

← Older revision		Revision as of 04:11, 4 October 2019
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	* [[Retention]]		* [[Retention]]
	* [[Remembering mathematics]]		* [[Remembering mathematics]]

			==Notes==

			* "What we do believe is that many people's dislike of rote memorization has led them to a generalized dislike of memory, and consequently to underrate the role it plays in cognition. Memory is, in fact, a central part of cognition. But the right response to this is not immense amounts of dreary rote memorization. Rather, it's to use good tools and good judgment to memorize what truly matters." https://numinous.productions/ttft/

	==References==		==References==

Issa Rice: /* See also */

2019-01-07T21:58:19Z

Issa Rice at 21:53, 7 January 2019

2019-01-07T21:53:20Z

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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		\| 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
	\|-		\|-
	\| 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		\| 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>
	\|}		\|}

Issa Rice at 21:52, 7 January 2019

2019-01-07T21:52:11Z

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	* [[Spaced repetition]]		* [[Spaced repetition]]
	* [[Retention]]		* [[Retention]]

			==References==

			<references/>

	[[Category:Mathematics]]		[[Category:Mathematics]]

Issa Rice at 21:51, 7 January 2019

2019-01-07T21:51:50Z

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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		\| 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
	\|-		\|-
	\| 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		\| 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
	\|}		\|}

Issa Rice at 21:46, 7 January 2019

2019-01-07T21:46:47Z

← Older revision		Revision as of 21:46, 7 January 2019
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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		\| 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
	\|}		\|}

			==See also==

			* [[Spaced repetition]]
			* [[Retention]]

	[[Category:Mathematics]]		[[Category:Mathematics]]

Issa Rice at 21:45, 7 January 2019

2019-01-07T21:45:33Z

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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
	\|-		\|-
	\| 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]]		\| 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
	\|-		\|-
	\| 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		\| 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

Issa Rice at 21:44, 7 January 2019

2019-01-07T21:44:42Z

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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":

	{\| class="sortable ~~table~~"		{\| class="sortable wikitable"
	\|-		\|-
	! Name !! Description !! People who hold this position		! Name !! Description !! People who hold this position

Issa Rice: Created page with "Broadly speaking, there seem to be two "schools of thought" regarding memorization in mathematics, as well as a third "default position": {| class="sortable table" |- ! Name..."

2019-01-07T21:44:26Z

Created page with "Broadly speaking, there seem to be two "schools of thought" regarding memorization in mathematics, as well as a third "default position": {| class="sortable table" |- ! Name..."

New page

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

{| class="sortable table"
|-
! 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, [[wikipedia:A Mathematician's Lament|Paul Lockhart]]
|-
| 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
|}

[[Category:Mathematics]]

← Older revision		Revision as of 21:58, 7 January 2019
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	* [[Spaced repetition]]		* [[Spaced repetition]]
	* [[Retention]]		* [[Retention]]
			* [[Remembering mathematics]]

	==References==		==References==