Concept dependency tracking - Revision history

Issa Rice at 22:58, 24 April 2020

2020-04-24T22:58:25Z

← Older revision		Revision as of 22:58, 24 April 2020
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	<references/>		<references/>

			[[Category:Coinage]]

Issa Rice: /* Emotional stakes */

2020-03-26T06:07:47Z

Emotional stakes

← Older revision		Revision as of 06:07, 26 March 2020
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	If you just crawl the dependency graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your enthusiasm will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?		If you just crawl the dependency graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your enthusiasm will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?

			I think one of the more valuable forms of feedback an [[explainer]] can receive is the specific points of an explanation where the [[learner]]'s attention starts to fade, where it gets boring.

	==Data structures==		==Data structures==

Issa Rice: /* Emotional stakes */

2020-03-26T06:04:42Z

Emotional stakes

← Older revision		Revision as of 06:04, 26 March 2020
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	Sort of related to the logical vs pedagogical distinction, but learning requires some amount of switching back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).		Sort of related to the logical vs pedagogical distinction, but learning requires some amount of switching back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).

	If you just crawl the dependency graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your ~~interests~~ will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?		If you just crawl the dependency graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your enthusiasm will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?

	==Data structures==		==Data structures==

Issa Rice: /* Emotional stakes */

2020-03-26T06:04:06Z

Emotional stakes

← Older revision		Revision as of 06:04, 26 March 2020
Line 40:		Line 40:
	Sort of related to the logical vs pedagogical distinction, but learning requires some amount of switching back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).		Sort of related to the logical vs pedagogical distinction, but learning requires some amount of switching back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).

	If you just crawl the graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your interests will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?		If you just crawl the dependency graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your interests will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?

	==Data structures==		==Data structures==

Issa Rice: /* Emotional stakes */

2020-03-26T06:03:23Z

Emotional stakes

← Older revision		Revision as of 06:03, 26 March 2020
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	==Emotional stakes==		==Emotional stakes==

	Sort of related to the logical vs pedagogical distinction, but learning requires some amount of ~~juggling~~ back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).		Sort of related to the logical vs pedagogical distinction, but learning requires some amount of switching back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).

	If you just crawl the graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your interests will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?		If you just crawl the graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your interests will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?

Issa Rice at 06:02, 26 March 2020

2020-03-26T06:02:59Z

← Older revision		Revision as of 06:02, 26 March 2020
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	A possibly equivalent way to rephrase the above is the following: each concept has many smaller parts or affordances, and these need to be made explicit in a concept dependency tracking system. For example, "Peano axioms" isn't an atomic concept. Instead, the Peano axioms have various affordances (i.e. one can perform various actions using them; "affordance" might not be the best term), like "use the Peano axioms to prove that addition of natural numbers is commutative", "give an informal description of what the Peano axioms are", "explain how the Peano axioms are different from the axioms of Robinson arithmetic", and so on. An informal understanding of the Peano axioms would correspond to knowing fewer of these affordances, while a solid understanding corresponds to knowing more/most of these things.		A possibly equivalent way to rephrase the above is the following: each concept has many smaller parts or affordances, and these need to be made explicit in a concept dependency tracking system. For example, "Peano axioms" isn't an atomic concept. Instead, the Peano axioms have various affordances (i.e. one can perform various actions using them; "affordance" might not be the best term), like "use the Peano axioms to prove that addition of natural numbers is commutative", "give an informal description of what the Peano axioms are", "explain how the Peano axioms are different from the axioms of Robinson arithmetic", and so on. An informal understanding of the Peano axioms would correspond to knowing fewer of these affordances, while a solid understanding corresponds to knowing more/most of these things.

	===Emotional stakes===		==Emotional stakes==

	Sort of related to the logical vs pedagogical distinction, but learning requires some amount of juggling back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).		Sort of related to the logical vs pedagogical distinction, but learning requires some amount of juggling back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).

Issa Rice at 06:02, 26 March 2020

2020-03-26T06:02:41Z

← Older revision		Revision as of 06:02, 26 March 2020
Line 29:		Line 29:

	In mathematics, logically speaking some axiomatic system (such as Peano axioms or ZFC) comes before everything else, and is thus a dependency. However, pedagogically speaking, it does not make any sense to start one's mathematical education with ZFC.		In mathematics, logically speaking some axiomatic system (such as Peano axioms or ZFC) comes before everything else, and is thus a dependency. However, pedagogically speaking, it does not make any sense to start one's mathematical education with ZFC.


	===Soft vs hard dependency===		===Soft vs hard dependency===
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	A possibly equivalent way to rephrase the above is the following: each concept has many smaller parts or affordances, and these need to be made explicit in a concept dependency tracking system. For example, "Peano axioms" isn't an atomic concept. Instead, the Peano axioms have various affordances (i.e. one can perform various actions using them; "affordance" might not be the best term), like "use the Peano axioms to prove that addition of natural numbers is commutative", "give an informal description of what the Peano axioms are", "explain how the Peano axioms are different from the axioms of Robinson arithmetic", and so on. An informal understanding of the Peano axioms would correspond to knowing fewer of these affordances, while a solid understanding corresponds to knowing more/most of these things.		A possibly equivalent way to rephrase the above is the following: each concept has many smaller parts or affordances, and these need to be made explicit in a concept dependency tracking system. For example, "Peano axioms" isn't an atomic concept. Instead, the Peano axioms have various affordances (i.e. one can perform various actions using them; "affordance" might not be the best term), like "use the Peano axioms to prove that addition of natural numbers is commutative", "give an informal description of what the Peano axioms are", "explain how the Peano axioms are different from the axioms of Robinson arithmetic", and so on. An informal understanding of the Peano axioms would correspond to knowing fewer of these affordances, while a solid understanding corresponds to knowing more/most of these things.

			===Emotional stakes===

			Sort of related to the logical vs pedagogical distinction, but learning requires some amount of juggling back and forth between "what I care about" and "what I can easily understand given the concepts I already know". The things you emotionally care about are the big results (e.g. Godel's incompleteness theorems, singular value decomposition, how AlphaGo works), while the next thing you can easily understand are much more boring (e.g. understanding the definition of language, understanding what each axiom of Peano arithmetic does, understanding the definition of a normal operator, understanding the ''n''th way to write the Bellman equations).

			If you just crawl the graph by taking the reachable nodes, it might take like 100 serial steps before you actually get to Godel's first incompleteness theorem. Maybe by that time your interests will have faded. Part of what the concept dependency system needs to do is to maintain your curiosity, by showing you interesting things (in some fuzzy/informal form) before you can fully understand them. Some sort of foreshadowing feature, or explaining the interesting idea using the abstractions that you have learned so far, every 5-20 steps of the way, or something like that. As a learner from textbooks, I already naturally do this, by flipping back and forth every chapter or so so that I can test myself: do I understand SVD yet? Am I getting any closer?

	==Data structures==		==Data structures==

Issa Rice: /* Types of dependencies */

2020-03-26T06:02:03Z

Types of dependencies

← Older revision		Revision as of 06:02, 26 March 2020
Line 29:		Line 29:

	In mathematics, logically speaking some axiomatic system (such as Peano axioms or ZFC) comes before everything else, and is thus a dependency. However, pedagogically speaking, it does not make any sense to start one's mathematical education with ZFC.		In mathematics, logically speaking some axiomatic system (such as Peano axioms or ZFC) comes before everything else, and is thus a dependency. However, pedagogically speaking, it does not make any sense to start one's mathematical education with ZFC.


	===Soft vs hard dependency===		===Soft vs hard dependency===

Issa Rice: /* Examples */

2020-03-26T05:50:49Z

Examples

← Older revision		Revision as of 05:50, 26 March 2020
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	==Examples==		==Examples==

	* [[Metacademy]]		* [[Metacademy]] -- I don't think Metacademy distinguishes different levels of a skill/concept
	* [[Arbital]]		* [[Arbital]] -- I think Arbital distinguishes between different levels of a skill/concept
	* David R. MacIver's Current/Pending system		* David R. MacIver's Current/Pending system

Issa Rice: /* See also */

2020-03-18T20:14:05Z

← Older revision		Revision as of 20:14, 18 March 2020
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	==See also==		==See also==

			* [[Importance of struggling in learning]]

	==References==		==References==

	<references/>		<references/>