Category mistake - Revision history

Riegler: -typo

2026-04-02T14:25:20Z

-typo

← Older revision		Revision as of 16:25, 2 April 2026
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	#*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent.		#*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent.
	#*Thinking that a sequence converges in a certain region.		#*Thinking that a sequence converges in a certain region.
	#*Viewing <math>\{4, \{-3,2,-1/7\},\{\{17,5\}\}\}</math> as a set of six elements rather than ~~four~~.		#*Viewing <math>\{4, \{-3,2,-1/7\},\{\{17,5\}\}\}</math> as a set of six elements rather than three.
	#In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See [[Limits]].		#In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See [[Limits]].

Riegler: +further example

2026-04-02T12:55:26Z

+further example

← Older revision		Revision as of 14:55, 2 April 2026
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	===Mathematics===		===Mathematics===
	#Alcock and Simpson<ref>Alcock, L., & Simpson, A. (2008). ''[https://s3.eu-west-2.amazonaws.com/assets.creode.advancehe-document-manager/documents/hea/private/alcocksimpsonbook_1568036775.pdf Ideas from Mathematics Education—An Introduction for Mathematicians]''. </ref> mention ~~three~~ examples for category mistakes in mathematics:		#Alcock and Simpson<ref>Alcock, L., & Simpson, A. (2008). ''[https://s3.eu-west-2.amazonaws.com/assets.creode.advancehe-document-manager/documents/hea/private/alcocksimpsonbook_1568036775.pdf Ideas from Mathematics Education—An Introduction for Mathematicians]''. </ref> mention four examples for category mistakes in mathematics:
			#*Saying that every point in a compact set is compact.
	#*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent.		#*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent.
	#*Thinking that a sequence converges in a certain region.		#*Thinking that a sequence converges in a certain region.

Riegler: +lemma, math

2026-04-02T12:36:54Z

+lemma, math

← Older revision		Revision as of 14:36, 2 April 2026
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	~~{{Hint\|text=~~ '''~~How to use this template~~'''		A '''category mistake''' can be coarsily described as the "error of assigning to something a quality or action which can only properly be assigned to things of another category".<ref>Magidor, O. (2025). [https://plato.stanford.edu/archives/spr2025/entries/category-mistakes/ Category Mistakes]. In E. N. Zalta & U. Nodelman (Ed.), ''The Stanford Encyclopedia of Philosophy'' (Spring 2025). Metaphysics Research Lab, Stanford University. </ref> For instance, a math student saying that "the [[Limits\|limit]] of a function approaches 1" commits a category mistake. The student assigns "approaches 1" which is an attribute of a function to a limit value which is a number.
	~~# Start by describing~~ the ~~bottleneck in the Section '''Description~~ of ~~Bottleneck'''. If you like you~~ can ~~orient yourself on the bottleneck description [[From Derivative~~ to ~~Proportionality]]~~. ~~If you feel able to turn the bottleneck into a~~ (~~positive~~) ~~learning outcome, please do also describe the intended learning outcome~~.
	~~# This wiki also serves to connect people interested in certain bottlenecks~~. ~~If you wish to make yourself known as interested~~, ~~fill in your name under~~ ''~~'People interested in this Bottleneck'~~''.		The purpose of this page is twofold:
	~~# When done editing~~, ~~save page~~.
	~~# When in reading mode, add suitable tags~~/~~categories by pressing the tag symbol on the top of the page.~~ For instance, if the ~~bottleneck~~ is ~~in connection~~ to ~~biology, add "biology" as~~ a ~~tag~~.		*Describing the corresponding bottleneck and the related literature.
	~~# Edit once again~~ and ~~delete~~ the ~~whole Section '''How to use this Template''' and save your changes~~.		*Collecting category mistakes which hinder student learning in various disciplines.
	}}

	==Description of bottleneck==		==Description of bottleneck==
	~~Add description. Please, avoid [[Step_1_-_Identify_a_Bottleneck_to_Learning#Describing bottlenecks\|vague descriptions]]~~.		Students attach properties to the wrong kind of objects.

	==~~Related scholarly work on this bottleneck~~==		==Collection of category mistakes==

	==~~People interested~~ in this ~~bottleneck==~~		===Mathematics===
			#Alcock and Simpson<ref>Alcock, L., & Simpson, A. (2008). ''[https://s3.eu-west-2.amazonaws.com/assets.creode.advancehe-document-manager/documents/hea/private/alcocksimpsonbook_1568036775.pdf Ideas from Mathematics Education—An Introduction for Mathematicians]''. </ref> mention three examples for category mistakes in mathematics:
			#*Considering the first two vectors in <math>\{(1,0),(0,1),(1,1)\}</math> as linearly independent and the third as linearly dependent.
			#*Thinking that a sequence converges in a certain region.
			#*Viewing <math>\{4, \{-3,2,-1/7\},\{\{17,5\}\}\}</math> as a set of six elements rather than four.
			#In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See [[Limits]].

	==References==		==References==
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	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Philosophy]]		[[Category:Philosophy]]

			<references />

Riegler: Changed categories.

2026-03-31T21:05:39Z

Changed categories.

← Older revision		Revision as of 23:05, 31 March 2026
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	[[Category:Bottleneck]]		[[Category:Bottleneck]]
			[[Category:Mathematics]]
			[[Category:Philosophy]]

Riegler: init

2026-03-31T21:05:22Z

init

New page

{{Hint|text= '''How to use this template'''
# Start by describing the bottleneck in the Section '''Description of Bottleneck'''. If you like you can orient yourself on the bottleneck description [[From Derivative to Proportionality]]. If you feel able to turn the bottleneck into a (positive) learning outcome, please do also describe the intended learning outcome.
# This wiki also serves to connect people interested in certain bottlenecks. If you wish to make yourself known as interested, fill in your name under '''People interested in this Bottleneck'''.
# When done editing, save page.
# When in reading mode, add suitable tags/categories by pressing the tag symbol on the top of the page. For instance, if the bottleneck is in connection to biology, add "biology" as a tag.
# Edit once again and delete the whole Section '''How to use this Template''' and save your changes.
}}

==Description of bottleneck==
Add description. Please, avoid [[Step_1_-_Identify_a_Bottleneck_to_Learning#Describing bottlenecks|vague descriptions]].

==Related scholarly work on this bottleneck==

==People interested in this bottleneck==

==References==

[[Category:Bottleneck]]