Decoding the Disciplines - Recent changes [en]

Talk:Language processing

Riegler — Fri, 30 Oct 2026 20:27:54 GMT

Created page with "test --~~~~"

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test --[[User:Riegler|Riegler]] ([[User talk:Riegler|talk]]) 20:27, 30 October 2026 (UTC)

Language processing

Riegler — Fri, 30 Oct 2026 20:27:42 GMT

init

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Test and link to [[Limits]].

Talk:Main Page

Riegler — Fri, 30 Oct 2026 20:26:10 GMT

test

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erster Eintrag --[[User:Riegler|Riegler]] ([[User talk:Riegler|talk]]) 20:26, 30 October 2026 (UTC)

Category talk:Bottleneck

Riegler — Fri, 30 Oct 2026 20:22:46 GMT

test discussion

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Could we have a listing of bottlenecks by topic? --[[User:Riegler|Riegler]] ([[User talk:Riegler|talk]]) 20:22, 30 October 2026 (UTC)

Events

141.41.126.16 — Fri, 30 Oct 2026 19:40:54 GMT

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	Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].		Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
	\|[https://www.bayziel.de BayZiel], Munich, Germany & online		\|[https://www.bayziel.de BayZiel], Munich, Germany & online
	\|		\|Joan
	\|-		\|-
	\|Oct 8, 2 pm UK time		\|Oct 8, 2 pm UK time

Main Page

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EditTogetherTest

141.41.124.131 — Fri, 30 Oct 2026 14:08:02 GMT

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			{{DISPLAYTITLE:Welcome to the Decoding & Disrupting the Disciplines Wiki}}

			<span style="color: #000000">'''[./Decoding_the_Disciplines Decoding the Disciplines]''' is a process for increasing student learning by narrowing the gap between expert and novice thinking. Beginning with the identification of [./Bottleneck bottlenecks] to learning in particular disciplines, it seeks to make explicit the tacit knowledge of experts and to help students master the [./Mental_moves mental actions] they need for success in particular courses.</span> Decoding <span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin">is not complete without</span> [./Disrupting_the_Disciplines Disrupting]<span style="mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin">, which focuses on the bottlenecks of colonialism, racism, identity, bias—the hidden curriculum or issues that disciplines do not address, that make people uncomfortable, or that the people tend to turn away from.</span>

			About this [./Decoding_the_Disciplines_Wiki Wiki ...]
			{\|
			\| width="50%" \|<!-- NEWS --------------------------><div style="margin:0; margin-top:10px; margin-right:10px; border:1px solid #3e5389; padding: 1em; background:#F9F9F9;"><div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">News</div>Volume 18, number 3 (2025) of ''Transformative Dialogues: Teaching and Learning Journal,'' subtitled [https://doi.org/10.59236/td2025vol18iss3 Advancements in Decoding the Disciplines] has been published.
			</div><!-- FEATURED ARTICLE --------------------------><div style="margin:0; margin-top:10px; margin-right:10px; border:1px solid #3e5389; padding: 1em; background:#F9F9F9; overflow: hidden;"><div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Featured Decoding Work</div>[[File:phases-groupwork.png\|alt=graphical illustration of the five phases that commence group work\|left\|thumb\|200x200px\|Five phases which commence group work]]'''Group activities''' are an integral part of teaching. Often they consist of tasks given to students in order to work on them collectively. However, it cannot be assumed that students consciously or subconsciously perform operations that allow them to get started with problem solving in group tasks ([./Group_activities_in_interactive_teaching Full article ...])
			</div><!-- DID YOU KNOW --------------------------><div style="margin:0; margin-top:10px; margin-right:10px; border:1px solid #3e5389; padding: 1em; background:#F9F9F9;"><div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Did you know?</div>When mathematicians think of [./Limits limits], "approaching" has a very nuanced meaning - an amalgam of "dancing" and "getting closer."
			</div>
			\|<!-- RIGHT COLUMN ########################################################--> <!-- UPCOMING EVENTS --------------------------><div style="margin:0; margin-top:10px; border:1px solid #3e5389; padding: 1em; background:#F9F9F9;"><div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Upcoming Events</div>

			* Nov 18-19, 2026: Meeting of the German [./Deoding_working_group_at_BayZiel Decoding working group at BayZiel]
			* Jan 28, 2027: Decoding the Disciplines Virtual [./Decoding_Conference Conference]

			For details, future and past events see [./Events Events].
			</div><!-- FEATURED BOTTLENECKS --------------------------><div style="margin:0; margin-top:10px; border:1px solid #3e5389; padding: 1em; background:#F9F9F9;"><div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Featured Bottlenecks</div>

			* [./Scope_of_formula Scope of formula]: When using a mathematical formula students don’t check whether the prerequisites for the applicability of this formula apply.
			* Students have difficulties distinguishing images like paintings from what they depict. Watch an instructor explaining this bottleneck "[./Artifice_in_representation Artifice in representation]."
			* Students find it difficult to view [./History_of_the_American_Home Home] as a constructed ideal.

			See also the [./Category:Bottleneck list of bottlenecks] collected in this wiki.
			</div><!-- FEATURED PUBLICATION --------------------------><div style="margin:0; margin-top:10px; border:1px solid #3e5389; padding: 1em; background:#F9F9F9;"><div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Featured Publication</div>[./How_Many_Sources_Do_I_Need%3F How many sources do I need?] is an award winning paper by Leah Shopkow. It covers the bottleneck of identifying sources for a History paper.
			</div>
			\|}

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Testuser2 — Fri, 30 Oct 2026 14:02:41 GMT

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User:Testuser2

Testuser2 — Fri, 30 Oct 2026 14:00:34 GMT

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Testuser — Fri, 30 Oct 2026 13:20:25 GMT

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Testuser — Fri, 30 Oct 2026 13:19:11 GMT

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Main Page

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	<div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Featured Decoding Work</div>		<div style="padding: 4px; text-align: center; font-size:120%; border-bottom: solid 1px #3e5389; margin-bottom:5px;">Featured Decoding Work</div>
	[[File:phases-groupwork.png\|alt=graphical illustration of the five phases that commence group work\|left\|thumb\|200x200px\|Five phases which commence group work]]		[[File:phases-groupwork.png\|alt=graphical illustration of the five phases that commence group work\|left\|thumb\|200x200px\|Five phases which commence group work]]

Lehrendenlerngemeinschaften als Ort und Gegenstand von SoTL

Riegler — Tue, 27 Oct 2026 10:26:24 GMT

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Decoding Conference

Riegler — Tue, 27 Oct 2026 09:19:50 GMT

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	==2023: Connecting and ~~expanding~~ the ~~community~~==		==2023: Connecting and Expanding the Community==
	The first conference took place November 6-7, 2023 in Aachen, Germany and was hosted by Fachhochschule Aachen.<ref>https://zhq-blog.fh-aachen.de/decoding-the-disciplines-connecting-and-expanding-the-community/</ref> Presentations have been recorded and made available for participants.<ref>https://zhq-blog.fh-aachen.de/video-documentation/ (Password protected; password has been emailed to participants on Feb 15, 2024)</ref> Proceedings have been published in two volumes.<ref>Barnat, M., Riegler, P., Middendorf, J. & Pace, D. (eds.) (2025). [[Decoding across Disciplines. New Developments from all over the world\|Decoding across disciplines: New Developments from all over the world.]] Special issue of die hochschullehre, Jahrgang 11/2025. DOI: 10.3278/HSL2535W</ref><ref>Walter, C., Riegler, P. & Blotevogel, T. (2025): [[Didaktiknachrichten 07-2025\|Didaktiknachrichten, Issue July, 2025]]</ref>		The first conference took place November 6-7, 2023 in Aachen, Germany and was hosted by Fachhochschule Aachen.<ref>https://zhq-blog.fh-aachen.de/decoding-the-disciplines-connecting-and-expanding-the-community/</ref> Presentations have been recorded and made available for participants.<ref>https://zhq-blog.fh-aachen.de/video-documentation/ (Password protected; password has been emailed to participants on Feb 15, 2024)</ref> Proceedings have been published in two volumes.<ref>Barnat, M., Riegler, P., Middendorf, J. & Pace, D. (eds.) (2025). [[Decoding across Disciplines. New Developments from all over the world\|Decoding across disciplines: New Developments from all over the world.]] Special issue of die hochschullehre, Jahrgang 11/2025. DOI: 10.3278/HSL2535W</ref><ref>Walter, C., Riegler, P. & Blotevogel, T. (2025): [[Didaktiknachrichten 07-2025\|Didaktiknachrichten, Issue July, 2025]]</ref>

	==2024: ~~Connecting and expanding~~ the ~~community~~==		==2024: Adopting Decoding for the Next Generation==
	The second conference took place November 1-2, 2024 in Bloomington, Indiana and was hosted by Indiana University.<ref>https://decodingthedisciplines.org/the-second-decoding-the-disciplines-conference/</ref>		The second conference took place November 1-2, 2024 in Bloomington, Indiana and was hosted by Indiana University.<ref>https://decodingthedisciplines.org/the-second-decoding-the-disciplines-conference/</ref>

MediaWiki:Sitenotice

Riegler — Sun, 25 Oct 2026 13:46:29 GMT

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			We are doing major maintenance work during the last week of October. Expect the wiki be unavailable for some time. </h2>

Question 2: Uncovering the tacit mental moves

Riegler — Sun, 11 Oct 2026 14:51:12 GMT

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	# The interview isn’t always 100’% successful in unpacking the specialist’s thinking into intelligible components and must be revisited several times for success.		# The interview isn’t always 100’% successful in unpacking the specialist’s thinking into intelligible components and must be revisited several times for success.
	# Interviews are arduous, sometimes like mental duels with the specialist making analytical leaps that leave the interviewers adrift in unknown territory without a clear path forward.		# Interviews are arduous, sometimes like mental duels with the specialist making analytical leaps that leave the interviewers adrift in unknown territory without a clear path forward.
	# Interviews are time consuming. When only one specialist can be interviewed at a time and some ''Decoding'' groups as large as 100 needing to uncover their mental moves, there’s not enough time or staff to conduct the interviews. Flash ''Decoding'' offers a potent short-cut to uncover the often-invisible mental moves of educators. Alternate forms of ''Decoding'' give us that “flash” of insight that helps us uncover implicit mental processing so they can be brought to the forefront and scaffolded for the students”<ref name=":0">Middendorf, J., & Mondelli, V. (~~in press~~.~~) "~~[[Flash Decoding with ~~analogies~~ and ~~game mechanics~~: Alternatives to the Decoding ~~interview~~]].” Transformative Dialogues: Teaching and Learning Journal.</ref>		# Interviews are time consuming. When only one specialist can be interviewed at a time and some ''Decoding'' groups as large as 100 needing to uncover their mental moves, there’s not enough time or staff to conduct the interviews. Flash ''Decoding'' offers a potent short-cut to uncover the often-invisible mental moves of educators. Alternate forms of ''Decoding'' give us that “flash” of insight that helps us uncover implicit mental processing so they can be brought to the forefront and scaffolded for the students”<ref name=":0">Middendorf, J., & Mondelli, V. (2025). [[Flash Decoding with Analogies, Game Mechanics, and AI Assistance: Alternatives to the Traditional Decoding Interview]]. ''Transformative Dialogues: Teaching and Learning Journal'', ''18''(3), 61-83.</ref>

	=== Analogies ===		=== Analogies ===

Quick guide

Riegler — Sun, 11 Oct 2026 14:46:47 GMT

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Blinde Flecken der Lehrenden entdecken und beheben mit „Decoding the Disciplines“

Riegler — Sun, 11 Oct 2026 14:34:10 GMT

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	[https://www.hlb.de/fileadmin/hlb-global/downloads/dnh/full/2021/DNH_2021-2.pdf#page=24 https://www.hlb.de/fileadmin/hlb-global/downloads/dnh/full/2021/DNH_2021-2.pdf]		[https://www.hlb.de/fileadmin/hlb-global/downloads/dnh/full/2021/DNH_2021-2.pdf#page=24 https://www.hlb.de/fileadmin/hlb-global/downloads/dnh/full/2021/DNH_2021-2.pdf]
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Blinde Flecken der Lehrenden entdecken und beheben mit „Decoding the Disciplines“

Riegler — Sun, 11 Oct 2026 14:33:43 GMT

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==Abstract==

Lehrende sind Expertinnen und Experten mit selbstverständlich gewordenen, fachspezifi-schen Arbeits- und Denkweisen. Oft stellt das Erlernen dieser Fähigkeiten eine besondereHürde für Studierende dar. Decoding the Disciplines ist eine Methode, die Expertenwissenwieder sichtbar und unterrichtbar macht.
==Bibliographic data==

Niebler, Christine; Foltz, Britta: Blinde Flecken der Lehrenden entdecken und beheben mit „Decoding the Disciplines“. Die NeueHochschule 2/2021, 24–25.
==External source==
[https://www.hlb.de/fileadmin/hlb-global/downloads/dnh/full/2021/DNH_2021-2.pdf#page=24 https://www.hlb.de/fileadmin/hlb-global/downloads/dnh/full/2021/DNH_2021-2.pdf]
[[Category:PublishedWork]]

Bottleneck Lesson - Art History - Visual Analysis

Riegler — Sun, 11 Oct 2026 11:19:57 GMT

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Flash Decoding with Analogies, Game Mechanics, and AI Assistance: Alternatives to the Traditional Decoding Interview

Riegler — Sun, 11 Oct 2026 11:15:43 GMT

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Category:Game based learning

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Category:Game based learning

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Category:Reading

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Category:Reading

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File:Virtual Decoding Conference Call for Papers Final.pdf

Riegler — Sun, 11 Oct 2026 11:07:49 GMT

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	Virtual (Zoom) Conference: Call for Papers		Virtual (Zoom) Conference: Call for Papers
	Theme: (Re)creating Connection & Community		Theme: (Re)creating Connection & Community
	~~[[Category:Conference]]~~

Peter Riegler

Riegler — Sun, 11 Oct 2026 11:06:04 GMT

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User:Benutzerangaben

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User:Riegler

Riegler — Sun, 11 Oct 2026 11:02:18 GMT

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	==Contact==		==Contact==
	In the interest of data protection the email address is not provided here. If you are a human being we trust that you would be able to find out the email address by doing an internet research using e.g. <code>Peter Riegler Ostfalia university</code> as a search string.		In the interest of data protection the email address is not provided here. If you are a human being we trust that you would be able to find out the email address by doing an internet research using e.g. <code>Peter Riegler Ostfalia university</code> as a search string.
	~~[[Category:Person]]~~
	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:People]]		[[Category:People]]

Formula

Riegler — Sun, 11 Oct 2026 11:00:15 GMT

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Decoding the Disciplines – A Roundtrip from Novice to Expert back to Novice

Riegler — Sun, 11 Oct 2026 10:49:39 GMT

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	German translation: [https://www.didaktikzentrum.de/images/cwattachments/493_46f6251eae8bd4aa1f94aeefb28ceea7.pdf Decoding the Disciplines – vom Laien zum Experten und noch einmal zu den Anfängen zurück]		German translation: [https://www.didaktikzentrum.de/images/cwattachments/493_46f6251eae8bd4aa1f94aeefb28ceea7.pdf Decoding the Disciplines – vom Laien zum Experten und noch einmal zu den Anfängen zurück]
	[[Category:PublishedWork]]		[[Category:PublishedWork]]
	~~[[Category:Decoding]]~~
	[[Category:Riegler, P]]		[[Category:Riegler, P]]
	[[Category:2020]]		[[Category:2020]]
	[[Category:Article]]		[[Category:Article]]
			[[Category:General]]

Dekodieren impliziten Wissens – Disziplinäres Wissen und praktische Expertise für Kompetenzentwicklung zugänglich machen

Riegler — Sun, 11 Oct 2026 10:49:20 GMT

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	https://www.nhhl-bibliothek.de/de/handbuch/gliederung/#/Beitragsdetailansicht/297/3881/Dekodieren-impliziten-Wissens-%25E2%2580%2593-Disziplinaeres-Wissen-und-praktische-Expertise-fuer-Kompetenzentwicklung-zugaenglich-machen		https://www.nhhl-bibliothek.de/de/handbuch/gliederung/#/Beitragsdetailansicht/297/3881/Dekodieren-impliziten-Wissens-%25E2%2580%2593-Disziplinaeres-Wissen-und-praktische-Expertise-fuer-Kompetenzentwicklung-zugaenglich-machen
	[[Category:PublishedWork]]		[[Category:PublishedWork]]
	~~[[Category:Decoding]]~~
	[[Category:Barnat, M]]		[[Category:Barnat, M]]
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	*[[Template:Bottleneck]] for adding a bottleneck description. See [[Slip\|Mechanical slip]] for an example. When contributing a bottleneck please avoid [[vague]] descriptions and follow the [[recommendations for bottleneck descriptions]].		*[[Template:Bottleneck]] for adding a bottleneck description. See [[Slip\|Mechanical slip]] for an example. When contributing a bottleneck please avoid [[vague]] descriptions and follow the [[recommendations for bottleneck descriptions]].
	*[[Template:Decoding work]] for adding information on Decoding work which extends the mere description of a bottleneck. See [[Group activities in interactive teaching]] for an example.		*[[Template:Decoding work]] for adding information on Decoding work which extends the mere description of a bottleneck. See [[Group activities in interactive teaching]] for an example.
	*[[Template:PublishedWork]] for adding bibliographical data about published work on Decoding. See [[~~PublishedWork:~~Decoding group activities in interactive teaching\|Decoding group activities in interactive teaching]] for an example.		*[[Template:PublishedWork]] for adding bibliographical data about published work on Decoding. See [[Decoding group activities in interactive teaching (paper)\|Decoding group activities in interactive teaching]] for an example.
	*[[Template:People]] for adding information about a person engaged in Decoding work (usually yourself). See [[David Pace]] for an example.		*[[Template:People]] for adding information about a person engaged in Decoding work (usually yourself). See [[David Pace]] for an example.
	*[[Template:Resource-File]] for sharing research data related to Decoding work. See [[:File:Transcript-groupactivities.pdf]] for an example.		*[[Template:Resource-File]] for sharing research data related to Decoding work. See [[:File:Transcript-groupactivities.pdf]] for an example.
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	*[[:Category:Decoding work]] which sorts Decoding work by discipline,		*[[:Category:Decoding work]] which sorts Decoding work by discipline,
	*[[:Category:PublishedWork]] which sorts literature by authors, discipline and type of publication,		*[[:Category:PublishedWork]] which sorts literature by authors, discipline and type of publication,
	*[[:Category:Person]] which sorts users by discipline.		*[[:Category:People\|Category:Person]] which sorts users by discipline.

	Say, you have created a page describing your Decoding work which relates to the academic discipline of ''Blablaology'' and more specifically to the subfield ''Traxoline''. By adding your page to the categories "Blablaology" and "Traxoline" the page will be listed under the respective categories in [[:Category:Decoding work]].		Say, you have created a page describing your Decoding work which relates to the academic discipline of ''Blablaology'' and more specifically to the subfield ''Traxoline''. By adding your page to the categories "Blablaology" and "Traxoline" the page will be listed under the respective categories in [[:Category:Decoding work]].
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	Also note that in the categorization scheme used here a category can have more than one parent. For instance,[[:Category:History\|Category:History]] is a child of (among others) [[:Category:Decoding work]] and [[:Category:Person]]. [[:Category:Group theory\|Group theory]] might be a child of both [[:Category:Mathematics\|Mathematics]] and [[:Category:Physics\|Physics]], [[:Category:Thermodynamics\|Thermodynamics]] might be a child of both [[:Category:Mechanical Engineering\|Mechanical Engineering]] and [[:Category:Physics\|Physics]].		Also note that in the categorization scheme used here a category can have more than one parent. For instance,[[:Category:History\|Category:History]] is a child of (among others) [[:Category:Decoding work]] and [[:Category:People\|Category:Person]]. [[:Category:Group theory\|Group theory]] might be a child of both [[:Category:Mathematics\|Mathematics]] and [[:Category:Physics\|Physics]], [[:Category:Thermodynamics\|Thermodynamics]] might be a child of both [[:Category:Mechanical Engineering\|Mechanical Engineering]] and [[:Category:Physics\|Physics]].

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← Older revision		Revision as of 11:00, 11 October 2026
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	===Step 1: Identification of [[bottleneck]]===		===Step 1: Identification of [[bottleneck]]===
	Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between e^(x^2) which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.		Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between <math>e^(x^2)</math> which can be collapsed to e^t and <math>(e^x)^2</math> which can be collapsed to <math>t^2</math>. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.

	Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K ~~R_1R~~/( ~~R_1−R~~) with respect to R is like 1=2x/(3-x) with respect to x.		Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. <math>(a+b)/(2x)</math> is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. <math>{C=4 \pi K R_1 R / (R_1 - R) }</math> with respect to <math>R</math> is like <math>1=2x/(3-x)</math> with respect to <math>x</math>.

	===Step 2: Description of [[Mental moves\|mental tasks]] needed to overcome the [[bottleneck]]===		===Step 2: Description of [[Mental moves\|mental tasks]] needed to overcome the [[bottleneck]]===
	The experts is able to see the structure by zooming in and out into the formula to blend out the details.		The experts is able to see the structure by zooming in and out into the formula to blend out the details.

	He encapsulates the result of one operation as an element which will be an input to the next operation. Thus he sees the operation sign as important ones e.g while reading "a+bs" he doesnt compare the letters a,b,s but the operation signs + and because he has to make a decision that the * goes first. This results in reading the formula as a sum of two elements.		He encapsulates the result of one operation as an element which will be an input to the next operation. Thus he sees the operation sign as important ones e.g. while reading "a+bs" he doesnt compare the letters a,b,s but the operation signs + and because he has to make a decision that the * goes first. This results in reading the formula as a sum of two elements.

	===[[Step 3 - Modeling Mental Operations\|Step 3: Modelling the tasks]]===		===[[Step 3 - Modeling Mental Operations\|Step 3: Modelling the tasks]]===
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	An important outcome of decoding is the recognition that students must first master reading and writing mathematical formulas before they can successfully engage with tasks that depend on these skills, such as applying the chain rule or rearranging formulas. Consequently, explicit practice in reading and interpreting mathematical expressions is essential.		An important outcome of decoding is the recognition that students must first master reading and writing mathematical formulas before they can successfully engage with tasks that depend on these skills, such as applying the chain rule or rearranging formulas. Consequently, explicit practice in reading and interpreting mathematical expressions is essential.

	A good starting point is "confrontation" exercise: " Paul says to his teacher, "I calculated ''a'' plus ''b'' divided by two times ''c''." Write a mathematical expression that matches his statement."		A good starting point is "confrontation" exercise: " Paul says to his teacher, "I calculated <math>a</math> plus <math>b</math> ' divided by two times <math>c</math> ." Write a mathematical expression that matches his statement."

	Students quickly realise that the Paul's statement is ambiguous because it does not specify how the operations are grouped. That allows to stress the role and importance of structuring and brackets.		Students quickly realise that the Paul's statement is ambiguous because it does not specify how the operations are grouped. That allows to stress the role and importance of structuring and brackets.
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	The third student must reconstruct the handwritten mathematical notation from the typed expression and compare it with the original formula. Differences between the original and reconstructed expressions can then be discussed to reinforce the importance of correct notation which mathes the structure of the formula.		The third student must reconstruct the handwritten mathematical notation from the typed expression and compare it with the original formula. Differences between the original and reconstructed expressions can then be discussed to reinforce the importance of correct notation which mathes the structure of the formula.

	===Step 5: Anticipate and lessen resistance===		=== Step 5: Anticipate and lessen resistance===
	Because typing mathematical formulas is an integral part of programming and prompting, the ''telephone game'' provides authentic practice and is therefore typically well received by students.		Because typing mathematical formulas is an integral part of programming and prompting, the ''telephone game'' provides authentic practice and is therefore typically well received by students.