Spaced proof review is not about memorizing proofs - Revision history

Issa at 01:04, 17 July 2021

2021-07-17T01:04:49Z

Issa at 02:37, 28 March 2021

2021-03-28T02:37:05Z

Issa at 03:07, 6 March 2021

2021-03-06T03:07:21Z

Issa at 02:27, 16 June 2020

2020-06-16T02:27:43Z

Issa at 02:26, 16 June 2020

2020-06-16T02:26:14Z

Issa at 02:25, 16 June 2020

2020-06-16T02:25:43Z

Issa at 02:25, 16 June 2020

2020-06-16T02:25:01Z

Issa at 02:24, 16 June 2020

2020-06-16T02:24:43Z

Issa at 07:26, 14 June 2020

2020-06-14T07:26:31Z

Issa at 07:26, 14 June 2020

2020-06-14T07:26:18Z

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 <references/>
 [[Category:Spaced repetition]]
 [[Category:Claim]]

← Older revision		Revision as of 02:37, 28 March 2021
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	[[Category:Spaced repetition]]		[[Category:Spaced repetition]]
		+	[[Category:Claim]]

← Older revision		Revision as of 03:07, 6 March 2021
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	See also [[Tim Gowers]] on memorizing proofs, e.g. <ref>https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/</ref>, <ref>https://mathoverflow.net/a/3957</ref>		See also [[Tim Gowers]] on memorizing proofs, e.g. <ref>https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/</ref>, <ref>https://mathoverflow.net/a/3957</ref>
		+
		+	==See also==
		+
		+	* [[Spaced repetition isn't about memorization]]

	==References==		==References==

@@ Line 13: / Line 13: @@
 <blockquote><p>I have, on more occasions than I’m willing to admit, run into the following situation. I solve some exercise in a textbook. Sometime later, I am reading about some other result, and I need some intermediate result, which looks like it could be true but I don’t how to prove it immediately. So I look it up, and then find out it was the exercise I did (and then have to re-do the exercise again because I didn’t write up the solution).</p>
 <p>I think you can argue that if you don’t even recognize the statement later, you didn’t learn anything from it. So I think the following is a good summarizing test: ''how likely is the student to actually remember it later?''</p></blockquote>
 using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).

@@ Line 12: / Line 12: @@
 <blockquote><p>I have, on more occasions than I’m willing to admit, run into the following situation. I solve some exercise in a textbook. Sometime later, I am reading about some other result, and I need some intermediate result, which looks like it could be true but I don’t how to prove it immediately. So I look it up, and then find out it was the exercise I did (and then have to re-do the exercise again because I didn’t write up the solution).</p>
-<p>I think you can argue that if you don’t even recognize the statement later, you didn’t learn anything from it. So I think the following is a good summarizing test: how likely is the student to actually remember it later?</p></blockquote>
+<p>I think you can argue that if you don’t even recognize the statement later, you didn’t learn anything from it. So I think the following is a good summarizing test: ''how likely is the student to actually remember it later?''</p></blockquote>
 using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).

@@ Line 9: / Line 9: @@
 And of course, even if you do spaced proof review, you will be adding new proofs all the time, so you're still solving new problems. The difference is thus in whether to invest the time into reviewing the problems you've already seen. I do think that in the future, it would be nice to have something sort of like Anki which would show problems you haven't seen before (and where the problems are selected to be interesting to you/based on your tastes).
-Even extremely competent math grad students seem to forget a lot of problems:
+Even extremely competent math grad students seem to forget a lot of problems:<ref>https://usamo.wordpress.com/2020/06/14/on-choosing-exercises/</ref>
 <blockquote><p>I have, on more occasions than I’m willing to admit, run into the following situation. I solve some exercise in a textbook. Sometime later, I am reading about some other result, and I need some intermediate result, which looks like it could be true but I don’t how to prove it immediately. So I look it up, and then find out it was the exercise I did (and then have to re-do the exercise again because I didn’t write up the solution).</p>
-<p>I think you can argue that if you don’t even recognize the statement later, you didn’t learn anything from it. So I think the following is a good summarizing test: how likely is the student to actually remember it later?<ref>https://usamo.wordpress.com/2020/06/14/on-choosing-exercises/</ref></p></blockquote>
+<p>I think you can argue that if you don’t even recognize the statement later, you didn’t learn anything from it. So I think the following is a good summarizing test: how likely is the student to actually remember it later?</p></blockquote>
 using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).
-See also [[Tim Gowers]] on memorizing proofs, e.g. [https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/], [https://mathoverflow.net/a/3957]
+See also [[Tim Gowers]] on memorizing proofs, e.g. <ref>https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/</ref>, <ref>https://mathoverflow.net/a/3957</ref>
 [[Category:Spaced repetition]]

← Older revision		Revision as of 02:24, 16 June 2020
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	And of course, even if you do spaced proof review, you will be adding new proofs all the time, so you're still solving new problems. The difference is thus in whether to invest the time into reviewing the problems you've already seen. I do think that in the future, it would be nice to have something sort of like Anki which would show problems you haven't seen before (and where the problems are selected to be interesting to you/based on your tastes).		And of course, even if you do spaced proof review, you will be adding new proofs all the time, so you're still solving new problems. The difference is thus in whether to invest the time into reviewing the problems you've already seen. I do think that in the future, it would be nice to have something sort of like Anki which would show problems you haven't seen before (and where the problems are selected to be interesting to you/based on your tastes).
		+
		+	Even extremely competent math grad students seem to forget a lot of problems:
		+
		+	<blockquote><p>I have, on more occasions than I’m willing to admit, run into the following situation. I solve some exercise in a textbook. Sometime later, I am reading about some other result, and I need some intermediate result, which looks like it could be true but I don’t how to prove it immediately. So I look it up, and then find out it was the exercise I did (and then have to re-do the exercise again because I didn’t write up the solution).</p>
		+	<p>I think you can argue that if you don’t even recognize the statement later, you didn’t learn anything from it. So I think the following is a good summarizing test: how likely is the student to actually remember it later?</p><ref>https://usamo.wordpress.com/2020/06/14/on-choosing-exercises/</ref></blockquote>

	using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).		using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).

← Older revision		Revision as of 07:26, 14 June 2020
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	using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).		using anki as a problem bank (with my proofs deck): the spacing is more to make sure seeing the same problem over and over again does not trigger your annoyance threshold, than to memorize optimally. actually you're not even trying to memorize the proofs, but to "absorb the rhythm" of the underlying concepts. When you're proving things, there's a bunch of non-verbal instincts/"mental moves" that go on (which are pretty hard to consciously observe/reason about). The point isn't to do like supervised learning on the text of the proof and be able to reproduce it perfectly. instead, you're training yourself to practice these mental moves, in a spaced out way (spacing it out makes it non-annoying, and verifies that the ability is an instinct rather than a reflex/rote-memorized).
		+
		+	See also Tim Gowers on memorizing proofs, e.g. [https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/], [https://mathoverflow.net/a/3957]

	[[Category:Spaced repetition]]		[[Category:Spaced repetition]]