Decoding the Disciplines - User contributions [en]

Step 4: Give Students Practice and Feedback

2026-04-11T16:37:18Z

Riegler: fixing page

Creating opportunities for students to practice essential mental operations and receive feedback is fourth step within the seven steps of Decoding the Disciplines.

To help students overcome most bottlenecks to learning, it is necessary to augment modeling ([http://decodingthedisciplines.org/step-3-modeling-mental-operations/ Step 3]) with opportunities for them to practice these steps and to receive feedback on the extent to which they have mastered each. Here are some things to bear in mind when creating occasions for practice:

*This practice can come in a wide variety of forms — brief in-class assignments or Classroom Assessment Techniques, on-line exercises, collaborative tasks, etc. Just-in-Time Teaching and Team-Based Learning have proven to be particular useful approaches to consider for this step.
*It is important that the exercises initially be focused on a particular mental operation that is problematic for many students. Complex tasks, which require the simultaneous application of multiple skills, can confuse students and do not provide them specific feedback on their mastery of particular operations. Once individual skills are clearly mastered, then an instructor can give them more complex assignments that allow them to practice the integration of multiple operations.
*With challenging operations it may be necessary to give students multiple opportunities for practice in a variety of forms.
*Practice exercises should be arranged in logical order and integrated with modeling, so that the two steps reinforce one another.
*Practice can often be integrated with crucial content from the course, so that the work on skills also increases student understanding of the particular material that is used as examples in the exercise.
*Students should generally receive some form of information about the extent to which they are succeeding at the essential task that they are practicing. This can come in the form of specific comments on their individual attempts to do the tasks that they have been assigned, or the instructor may discuss typical examples of successful or unsuccessful student work using techniques of Just-in-Time teaching.
*Students need to understand the reason for the practice. They should understand that it offers them a chance to find out where they have gained mastery of essential steps and where they still need work with minimal negative impact on their grade.[http://decodingthedisciplines.org/step-4-creating-opportunities-for-students-to-practice-essential-mental-operations/

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2026-04-04T20:25:12Z

Riegler: banner for AK Decoding

[[File:decoding-goes-schnuedel.png]]

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2026-04-04T20:23:58Z

Riegler:

Category mistake

2026-04-02T14:25:20Z

Riegler: -typo

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.

The purpose of this page is twofold:

*Describing the corresponding bottleneck and the related literature.
*Collecting category mistakes which hinder student learning in various disciplines.

==Description of bottleneck==
Students attach properties to the wrong kind of objects.

==Collection of category mistakes==

===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.
#*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 three.
#In an Decoding interview on students' difficulties with limits the interviewee mentions the example described at the beginning of this page. See [[Limits]].

==References==

[[Category:Bottleneck]]
[[Category:Mathematics]]
[[Category:Philosophy]]

<references />

Category mistake

2026-04-02T12:55:26Z

Riegler: +further example

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.

The purpose of this page is twofold:

*Describing the corresponding bottleneck and the related literature.
*Collecting category mistakes which hinder student learning in various disciplines.

==Description of bottleneck==
Students attach properties to the wrong kind of objects.

==Collection of category mistakes==

===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.
#*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==

[[Category:Bottleneck]]
[[Category:Mathematics]]
[[Category:Philosophy]]

<references />

Category mistake

2026-04-02T12:36:54Z

Riegler: +lemma, math

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.

The purpose of this page is twofold:

*Describing the corresponding bottleneck and the related literature.
*Collecting category mistakes which hinder student learning in various disciplines.

==Description of bottleneck==
Students attach properties to the wrong kind of objects.

==Collection of category mistakes==

===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==

[[Category:Bottleneck]]
[[Category:Mathematics]]
[[Category:Philosophy]]

<references />

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2026-04-02T11:35:31Z

Riegler: delete banner for call for papers

Editorial to the special issue: Decoding across disciplines: New Developments from all over the world

2026-04-02T10:28:09Z

Riegler: -typo

==Bibliographic data==

Barnat, M., Riegler, P., Middendorf, J. & Pace, D. (2025). Editorial to the special issue: Decoding across disciplines: New Developments from all over the world. die hochschullehre, Jahrgang 11/2025. DOI: 10.3278/HSL2535W
==External source==
https://dx.doi.org/10.3278/HSLT2535W
[[Category:PublishedWork]]
[[Category:2025]]
[[Category:Barnat, M]]
[[Category:Middendorf, J]]
[[Category:Pace, D]]
[[Category:Riegler, P]]

Category mistake

2026-03-31T21:05:39Z

Riegler: Changed categories.

{{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]]
[[Category:Mathematics]]
[[Category:Philosophy]]

Category mistake

2026-03-31T21:05:22Z

Riegler: init

Recursion

2026-03-08T18:24:35Z

Riegler: Changed categories.

'''Recursion''' is a core concept in computer science and programming. Recursively solving a problem involves solving a simpler or previous version of the problem.

==Decoding work done==
In a [https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E video] Suzane Menzel reports on the process of decoding recursion:

#Identify Bottleneck: recursion in algorithms 0.00
#Uncover the Mental Moves of the expert 1.26-2.16 Uncover the tacit knowledge of experts about recursion. Recursion can be about structure and occurs when one of the parts looks like the whole; There’s a process part of recursion –building recursion.
#Modeling (1.12) uses analogies; an Alice Through the Looking Glass image shows how the parts look like the whole; also 2:18 Collecting back the Russian Nesting Dolls as an analogy for the process of collecting the pieces in a recursion that is so difficult for students to understand.
#Practice the recursion structure through code reviews 4.20 AND TBL quizzes on several kinds of algorithms. (5.20)
#Motivation 5.56 Team-based learning: students work in teams of 4-7
#Assessment 7.17 n=190 students final test scores were compared with students in previous semesters (non-Decoding methodology) to with Decoding and found significant results on both the list and tree recursion programming. List recursion in semester w/out Decoding B grade avg; in semester with Decoding, A-. Tree recursion from C to B-. As well, student commented that they enjoyed the Decoding approach, because their brains were being trained which “…challenges you to think in a completely new way.” They also enjoyed working in teams.
#Share 8.41: analyze results of the several assessments and Go public with them as in the attached video.

==Researchers involved==
Suzanne Menzel

==Related Work==
* [[Algorithm Design]]

==Available resources==
*[https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E Suzanne Menzel - Decoding Recursion in Computing] (Youtube video)
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=iNvQlm9phEI</embedvideo>
[[Category:Computer Science]]
[[Category:Decoding work]]
[[Category:Decoding Interview]]
[[Category:Bottleneck]]
[[Category:Menzel, S]]

Recursion

2026-03-08T18:23:59Z

Riegler: Changed categories.

Recursion

2026-03-08T18:23:33Z

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Submit your Decoding and Disrupting work to the 2026 volume of [https://journals.psu.edu/td/about/ Transformative Dialogues: Teaching and Learning Journal]. Deadline is April, 1st. </h2>

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Submit your Decoding and Disrupting work to the 2026 volume of [https://journals.psu.edu/td/about/ Transformative Dialogues: Teaching and Learning Journal]. Deadline is April, 1st. </h1>

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2026-03-08T14:20:54Z

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Submit your Decoding and Disrupting work to the 2026 volume of [https://journals.psu.edu/td/about/ Transformative Dialogues: Teaching and Learning Journal]. Deadline is April, 1st. </h1>

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Submit your Decoding and Disrupting work to the 2026 volume of [https://journals.psu.edu/td/about/ Transformative Dialogues: Teaching and Learning Journal]. Deadline is April, 1st. </h1>

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Call for contributionsSubmit your Decoding and Disrupting work to the 2026 volume of [https://journals.psu.edu/td/about/ Transformative Dialogues: Teaching and Learning Journal]. Deadline is April, 1st. </h1>

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2026-03-08T13:58:06Z

Riegler: Decoding journal

Submit your Decoding and Disrupting work to the 2026 volume of [https://journals.psu.edu/td/about/ Transformative Dialogues: Teaching and Learning Journal]. Deadline is April, 1st.

Main Page

2026-03-08T13:52:49Z

Riegler: adding event

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

<span style="color: #000000">'''[[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 ...]]

{|

|- style="vertical-align:top"
| width="50%" |

<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>

<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;">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 ...]])
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<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]], "approaching" has a very nuanced meaning - an amalgam of "dancing" and "getting closer."
</div>

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<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>

*Mar 10, 2026: [[Decoding SIG]] online meeting on "Decoding Outside the SoTL Box: Is Decoding More than Scholarship"

For details, future and past events see [[Events]].
</div>


<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]]."
*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.
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<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>
|}

Events

2026-03-08T13:51:28Z

Riegler: +SIG meeting

<br />
==2026==
{| class="wikitable"
!Time
!
!Title
!Description
!Location
!Guest/Speaker
|-
|Nov, 19-20
|
|[[Decoding working group at BayZiel|AK Decoding]]
|Meeting of the German [[Deoding working group at BayZiel|Decoding working group at BayZiel]].

Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
|[https://www.bayziel.de BayZiel], Munich, Germany & online
|
|-
|Jul, 16-17
|
|[[Decoding working group at BayZiel|AK Decoding]]
|Meeting of the German [[Deoding working group at BayZiel|Decoding working group at BayZiel]].

Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
|TH Würzburg-Schweinfurg, Schweinfurt, Germany & online
|
|-
|Mar, 10, 11 am EST
|
|'''Decoding Outside the SoTL Box: Is Decoding More than Scholarship'''
|Decoding the Disciplines clearly plays a major role in the scholarship of teaching and learning. But that fact can blind us to other benefits that can arise from this practice. In this webinar we will collectively explore the non-scholarly dimensions of Decoding, focusing particularly on the ways in which the interview process in itself can be a transformative experience for teachers.
|[[Decoding SIG]] online meeting
|David Pace
|-
|Feb, 16-17
|
|[[Decoding working group at BayZiel|AK Decoding]]
|Meeting of the German [[Deoding working group at BayZiel|Decoding working group at BayZiel]].

Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
|[https://www.bayziel.de BayZiel], Munich, Germany & online
|
|}

==2025 ==
{| class="wikitable"
!Time
!
!Title
!Description
!Location
!Guest/Speaker
|-
|Dec, 9, 18:00 German time
|
| '''Decoding and Student as Partners'''
|In this session, we will describe several Decoding projects that we have conducted within the framework of "student as partners". We will provide both student and faculty perspectives and will encourage session attendees to consider ways in which they might include students as partners in their Decoding work.
|[[Decoding SIG]] online meeting
|Leslie Cameron, Temple Burling, Sophia Choronzuk, and Holly Pelnar
|-
|Nov, 20-21
|
| [[Decoding working group at BayZiel|AK Decoding]]
|Meeting of the German [[Deoding working group at BayZiel|Decoding working group]] at Darmstadt University of Applied Sciences.

Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
|Darmstadt, Germany & online
|
|-
|Nov, 18, 18:00 German time
|
| '''Decoding and Action Cards'''
|In this session, we will describe how ''action cards'' can be used within the Decoding-the-Disciplines framework to surface metacognitive bottlenecks in real time. Drawing on a case study of novice programmers, it will illustrate how action cards reveal students’ planning, monitoring, and evaluation strategies, highlighting where they get stuck and why.
|[[Decoding SIG]] online meeting
|Liezel Nel & Karabo Matabane (South Africa)
|-
|Nov, 18, 18:00 German time
|
| Using AI for the decoding interview
|
|[[Decoding SIG]] online meeting
|Miriam Barnat, Britta Foltz (Germany)
|-
|Sep, 22 13:00 p.m UTC-0, 15:00 German time
|
|HFDlocal
|[[David Pace]] speaks about Decoding at the German Forum for Digitalisation in Higher Ed
|see https://hochschulforumdigitalisierung.de/hfdlocal/hfdlocal-themenwoche-2025/
|David Pace
|-
|Jul, 10-11
|
|[[Decoding working group at BayZiel|AK Decoding]]
|Meeting of the German [[Deoding working group at BayZiel|Decoding working group]]
Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
|[https://www.bayziel.de BayZiel], Munich, Germany & online
|
|-
|July, 8th, 2025
|
|Decoding Beyond the University
|This installment of the Decoding the Disciplines webinar series will move outside the confines of the university and examine the ways that the approach can increase learning in high schools and can create a basis for communication and collaboration across different educational systems. The Indiana University Decoding the Transitions to College program brought together teachers from both high school and college to identify bottlenecks to learning that prevent students from progressing from one level to the next in particular disciplines. Sharing Decoding interviews helped teachers from the two groups work together to create new strategies for helping more students make a successful transition to college.

In this webinar teachers involved in this program will describe how their encounters with Decoding reshaped their own teaching at the same time that collaboration across the high school/college frontier helped them better understand the longer trajectory of student learning. Then the program will be opened up for discussion of how Decoding can be expanded into new pedagogical contexts.
|[[Decoding SIG]] online meeting
|David Pace and Guests
|-
|June, 18-20
|
|[https://www.rug.nl/about-ug/organization/service-departments/teaching-academy-groningen/activities/eurosotl-2025/ EuroSoTL 2025]
|Meet Decoding enthusiasts at EuroSoTL
|Groningen, The Netherlands
|
|-
|June, 17
|
|Meeting of the EuroSoTL Collaborative Writing Group on Decoding
|
|Groningen, The Netherlands
|
|-
|May, 19th, 2025
16:00 GMT
|
|Disrupting: Can You Imagine Doing Something Different?
|For background we will explain why a group of Canadian researchers realized the need to repurpose the Decoding interview—to draw attention to the unaddressed bottlenecks of colonialism, racism, and implicit bias that result, in part, in the hidden curriculum. We will attempt to give participants a sense of Disrupting and how it draws on yet differs from Decoding: Disrupting takes a turn from a focus on knowledge within the discipline to unsettle our relationship to the discipline itself (Lindstrom, et. al, 2022). Session participants will explore where they see colonial structures, racism or implicit bias in our home disciplines, educational development, and SoTL. In addition to providing a taste of Disrupting, we hope to point to resources so that our colleagues can lead Disrupting inquiry in their own contexts.
|[[Decoding SIG]] online meeting
|Joan Middendorf,
Michelle Yeo
|-
|Apr 23rd, 2025, 16:00 GMT
|
|Decoding Institutions
|In this session, we will discuss our attempt to adapt the DtD framework from its traditional classroom context to the broader institutional arena as well as share lessons learned/implications for DtD practitioners and researchers interested in decoding contexts outside of the classroom.
|[[Decoding SIG]] online meeting
|Alex Arreguin and Stacey Wilson
|-
|March, 11<sup>th</sup> 17:00 GMT
|
|Decoding Debugging: A Case Study in Overcoming Learning Bottlenecks through Growth Mindsets
|This presentation will showcase how the Decoding the Disciplines (DtD) framework was used to make the ‘invisible’ mental processes of expert programmers visible to novices. We will highlights how a tailored instructional strategy (grounded in explicit modelling, collaborative inquiry, and mindset theory) helped undergraduate programming students overcome critical debugging bottlenecks. While the focus is on Computer Science, the methods and findings offer practical insights for educators in any discipline seeking to address learning bottlenecks by fostering a growth mindset and translating expert thinking into effective teaching practices.
|[[Decoding SIG]] online meeting
|Liezel Nel, Tipson Maleti
|-
|Feb, 17-18
|
|[[Decoding working group at BayZiel|AK Decoding]]
|Meeting of the German [[Deoding working group at BayZiel|Decoding working group at BayZiel]].
Sign up at [https://www.didaktikzentrum.de www.didiaktikzentrum.de].
|[https://www.bayziel.de BayZiel], Munich, Germany & online
|
|-
|Feb 12
|
|[[Feb 12 2025 Event Modeling|What Comes after the Interview? An Exploration of the Modeling and Practice Steps of Decoding]]
|If you are interested in joining the session: send E-Mail to barnat@fh-aachen.de
|[[Decoding SIG]] online meeting
|
*Nana Amoah-Ramey
*Megan Dunn
*David Pace
|-
|January, 14 17:00-18:0 [[wikipedia:Greenwich_Mean_Time|GMT]]
|
|'''Learning about and collectively working on the Decoding wiki'''
|At this meeting participants will work collectively on adding content to this wiki. Participants unfamiliar with contributing to a wiki will be introduced to the (few) skills needed. Feel free to bring your breakfast/lunch/dinner or to have your 5 o'clock tea parallel to the meeting.
For details see [[User:Riegler/Decoding SIG on wiki|agenda]].
|[[Decoding SIG]] online meeting
|Peter Riegler
|}

==2024==

*November 19, 17:00-18:00 [[wikipedia:Greenwich_Mean_Time|GMT]], Joan Middendorf: Decoding and Curriculum, [[Decoding SIG]] online meeting

*November, 1-2: [[Decoding Conference|Decoding the Disciplines Conference]], Bloomington, Indiana
*Decoding student services & expertise beyond the classroom (Christian Briggs, Bloomington, USA; Lauren Crane, Mesa, USA) [[Decoding SIG]] online meeting
*September, 9th: Decoding AI prompts – What is still humanly possible? (Earle Abrahamson, Herfortshire, UK) [[Decoding SIG]] online meeting
*June, 12th: Decoding and newcomers to teaching: (Peter D’Sena, Hertfordshire, UK), [[Decoding SIG]] online meeting
*May, 7th: Alternatives to the interview: (Joan Middendorf, Bloomington, USA), [[Decoding SIG]] online meeting
*April, 5th: Possibilities to integrate decoding in academic development courses (Petra Weiß, Zürich, Switzerland), [[Decoding SIG]] online meeting
*March, 1st: Curriculum Development (Michelle Yeo, Calgary, Canada), [[Decoding SIG]] online meeting

==2023==

*November, 6-7: [[Decoding Conference|Decoding the Disciplines Conference]], Aachen, Germany

Recursion

2026-03-07T15:18:12Z

Riegler:

Recursion

2026-03-07T15:17:21Z

Riegler:

'''Recursion''' is a core concept in computer science and programming. Recursively solving a problem involves solving a simpler or previous version of the problem.

==Decoding work done==
In a [https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E video] Suzane Menzel reports on the process of decoding recursion:

#Identify Bottleneck: recursion in algorithms 0.00
#Uncover the Mental Moves of the expert 1.26-2.16 Uncover the tacit knowledge of experts about recursion. Recursion can be about structure and occurs when one of the parts looks like the whole; There’s a process part of recursion –building recursion.
#Modeling (1.12) uses analogies; an Alice Through the Looking Glass image shows how the parts look like the whole; also 2:18 Collecting back the Russian Nesting Dolls as an analogy for the process of collecting the pieces in a recursion that is so difficult for students to understand.
#Practice the recursion structure through code reviews 4.20 AND TBL quizzes on several kinds of algorithms. (5.20)
#Motivation 5.56 Team-based learning: students work in teams of 4-7
#Assessment 7.17 n=190 students final test scores were compared with students in previous semesters (non-Decoding methodology) to with Decoding and found significant results on both the list and tree recursion programming. List recursion in semester w/out Decoding B grade avg; in semester with Decoding, A-. Tree recursion from C to B-. As well, student commented that they enjoyed the Decoding approach, because their brains were being trained which “…challenges you to think in a completely new way.” They also enjoyed working in teams.
#Share 8.41: analyze results of the several assessments and Go public with them as in the attached video.

==Researchers involved==
Suzanne Menzel

==Available resources==

*[https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E Suzanne Menzel - Decoding Recursion in Computing] (Youtube video)
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=iNvQlm9phEI</embedvideo>

==Related Work==

* [[Algorithm Design]]

Recursion

2026-03-07T15:16:53Z

Riegler: + related work

'''Recursion''' is a core concept in computer science and programming. Recursively solving a problem involves solving a simpler or previous version of the problem.

==Decoding work done==
In a [https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E video] Suzane Menzel reports on the process of decoding recursion:

#Identify Bottleneck: recursion in algorithms 0.00
#Uncover the Mental Moves of the expert 1.26-2.16 Uncover the tacit knowledge of experts about recursion. Recursion can be about structure and occurs when one of the parts looks like the whole; There’s a process part of recursion –building recursion.
#Modeling (1.12) uses analogies; an Alice Through the Looking Glass image shows how the parts look like the whole; also 2:18 Collecting back the Russian Nesting Dolls as an analogy for the process of collecting the pieces in a recursion that is so difficult for students to understand.
#Practice the recursion structure through code reviews 4.20 AND TBL quizzes on several kinds of algorithms. (5.20)
#Motivation 5.56 Team-based learning: students work in teams of 4-7
#Assessment 7.17 n=190 students final test scores were compared with students in previous semesters (non-Decoding methodology) to with Decoding and found significant results on both the list and tree recursion programming. List recursion in semester w/out Decoding B grade avg; in semester with Decoding, A-. Tree recursion from C to B-. As well, student commented that they enjoyed the Decoding approach, because their brains were being trained which “…challenges you to think in a completely new way.” They also enjoyed working in teams.
#Share 8.41: analyze results of the several assessments and Go public with them as in the attached video.

==Researchers involved==
Suzanne Menzel

==Available resources==

*[https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E Suzanne Menzel - Decoding Recursion in Computing] (Youtube video)
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=iNvQlm9phEI</embedvideo>

==Related Work==

* [[Algorithm Design]]

Algorithm Design

2026-03-07T15:15:24Z

Riegler: -typo

==Description of bottleneck==
In their work on algorithm design Yaqoob et al. list and investigate the following bottlenecks related to sorting algorithms:

* Understanding the nested structureand the design approach
* The usefulness of the divide step.
* Understanding recursions to combining solution to sub-problems.
* Dealing with repeated numbers using indices.
* How to transform the algorithm to handle largeand negative numbers.
* Understanding the stable version.

==References==
[[Evaluating the Decoding the Disciplines Paradigm From a Student Perspective in Teaching Algorithm Design]]
[[Category:Bottleneck]]
[[Category:Computer Science]]

Recursion

2026-03-07T15:13:56Z

Riegler: -typo

'''Recursion''' is a core concept in computer science and programming. Recursively solving a problem involves solving a simpler or previous version of the problem.

==Decoding work done==
In a [https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E video] Suzane Menzel reports on the process of decoding recursion:

#Identify Bottleneck: recursion in algorithms 0.00
#Uncover the Mental Moves of the expert 1.26-2.16 Uncover the tacit knowledge of experts about recursion. Recursion can be about structure and occurs when one of the parts looks like the whole; There’s a process part of recursion –building recursion.
#Modeling (1.12) uses analogies; an Alice Through the Looking Glass image shows how the parts look like the whole; also 2:18 Collecting back the Russian Nesting Dolls as an analogy for the process of collecting the pieces in a recursion that is so difficult for students to understand.
#Practice the recursion structure through code reviews 4.20 AND TBL quizzes on several kinds of algorithms. (5.20)
#Motivation 5.56 Team-based learning: students work in teams of 4-7
#Assessment 7.17 n=190 students final test scores were compared with students in previous semesters (non-Decoding methodology) to with Decoding and found significant results on both the list and tree recursion programming. List recursion in semester w/out Decoding B grade avg; in semester with Decoding, A-. Tree recursion from C to B-. As well, student commented that they enjoyed the Decoding approach, because their brains were being trained which “…challenges you to think in a completely new way.” They also enjoyed working in teams.
#Share 8.41: analyze results of the several assessments and Go public with them as in the attached video.

==Researchers involved==
Suzanne Menzel

==Available resources==

*[https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E Suzanne Menzel - Decoding Recursion in Computing] (Youtube video)
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=iNvQlm9phEI</embedvideo>

Recursion

2026-03-07T15:12:11Z

Riegler: -typos

'''Recursion''' is a core concept in computer science and programming. Recursively solving a problem involves solving a simpler or previous version of the problem.

==Decoding work done==
In a [https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E video] Suzane Menzel reports on the process of decoding recursion:

#Identify Bottleneck: recursion in algorithms 0.00
#Uncover the Mental Moves of the expert 1.26-2.16 Uncover the tacit knowledge of experts about recursion. Recursion can be about structure and occurs when one of the parts looks like the whole; There’s a process part of recursion –building recursion.
#Modeling (1.12) uses analogies; an Alice Through the Looking Glass image shows how the parts look like the whole; also 2:18 Collecting back the Russian Nesting Dolls as an analogy for the process of collecting the pieces in a recursion that is so difficult for students to understand.
#Practice the recursion structure through code reviews 4.20 AND TBL quizzes on several kinds of algorithms. (5.20)
#Motivation 5.56 Team-based learning: students work in teams of 4-7
#Assessment 7.17 n=190 students final test scores were compared with students in previous semesters (non-Decoding methodology) to with Decoding and found significant results on both the list and tree recursion programming. List recursion in semester w/out Decoding B grade avg; in semester with Decoding, A-. Tree recursion from C to B-. As well, student commented that they enjoyed the Decoding approach, because their brains were being trained which “…challenges you to think in a completely new way.” They also enjoyed working in teams.
#Share 8.41: analyze results of the several assessments and Go public with them as in the attached video.

==Researchers involved==
Suzanne Menzel

==Available resources==

*[https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E Suzanne Menzel - Decoding Recursion in Computing] (Youtube video)
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=iNvQlm9phEI</embedvideo>

n

Recursion

2026-03-07T15:10:55Z

Riegler: initialize page

'''Recursion''' is a core concept in computer science and programming. Recursively solving a problem involves solving a simpler or previous version of the problem.

==Decoding work done==
In a [https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E video] Suzane Menzel reports on the process of decoding recursion:

#Identify Bottleneck: recursion in algorithms 0.00
#Uncover the Mental Moves of the expert 1.26-2.16 Uncover the tacit knowledge of experts about recursion. Recursion can be about structure and occurs when one of the parts looks like the whole; There’s a process part of recursion –building recursion.
#Modeling (1.12) uses analogies; an Alice Through the Looking Glass image shows how the parts look like the whole; also 2:18 Collecting back the Russian Nesting Dolls as an analogy for the process of collecting the pieces in a recursion that is so difficult for students to understand.
#Practice the recursion structure through code reviews 4.20 AND TBL quizzes on several kinds of algorithms. (5.20)
#Motivation 5.56 Team-based learning: students work in teams of 4-7
#Assessment 7.17 n=190 students final test scores were compared with students in previous semesters (non-Decoding methodology) to with Decoding and found significant results on both the list and tree recursion programming. List recursion in semester w/out Decoding B grade avg; in semester with Decoding, A-. Tree recursion from C to B-. As well, student commented that they enjoyed the Decoding approach, because their brains were being trained which “…challenges you to think in a completely new way.” They also enjoyed working in teams.
#Share 8.41: analyze results of the several assessments and Go public with them as in the attached video.

==Researchers involved==
Suzane Menzel

==Available resources==

*[https://youtu.be/iNvQlm9phEI?si=IwLNg2glIXxs5K-E Suzane Menzel - Decoding Recursion in Computing] (Youtube video)
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=iNvQlm9phEI</embedvideo>
<iframe width="560" height="315" src="https://www.youtube.com/embed/iNvQlm9phEI?si=IwLNg2glIXxs5K-E" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>
<embedvideo service="YouTube" alignment="left">https://www.youtube.com/watch?v=TYpeAtl1SHI</embedvideo>

MediaWiki:Sitenotice

2026-02-26T14:52:35Z

Riegler: Blanked the page

User:Riegler/What has become different

2026-02-17T15:24:57Z

Riegler: (username removed) (log details removed)

#REDIRECT [[User:Riegler/What has become different?]]

User:Riegler/What has become different?

2026-02-17T15:24:57Z

Riegler: (username removed) (log details removed)

* Für Hochschuldidaktiker:innen Einblick in spezifische fachliche Fragestellungen im Kontext Lehre. Nicht nur für Hochschuldidaktiker:innen.
* Einblick und neue Sicht
* Hilfe und Anlaufstelle für konkrete Lehrherausforderungen.
* Auftanken im Lehralltag
* Intellektuelle Herausforderung (durch unterschiedliche Fachkulturen und didaktische Fragen, durch unterschiedliche Fachkulturen wissenschaftstheoretische und -didaktische Fragen). Passiert im Alltag sonst kaum.
* persönliches Interesse an Physik und Mathematik; gewecktes Interesse an andere Diszplinen
* Hineinversetzen in die Denkweisen anderer Disziplinen

User:Riegler/What has become different?

2026-02-17T15:24:46Z

Riegler: init

Quick guide for interviewers

2026-02-17T15:03:10Z

Riegler:

The quick guide for Decoding interviews was initiated by Magda Zarebski and Helen Schneider.
{| class="wikitable"
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!Kommunikation mit Expert:in
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== Downloadble version ==
A printable version for usage in interviews can be downloaded here.

Cheat sheet for Decoding Interview

2026-02-17T15:02:53Z

Riegler: (username removed) (log details removed): renaming page

#REDIRECT [[Quick guide for interviewers]]

Quick guide for interviewers

2026-02-17T15:02:53Z

Riegler: (username removed) (log details removed): renaming page

== The quick guide for Decoding interviews was initiated by Magda Zarebski and Helen Schneider. ==
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== Downloadble version ==
A printable version for usage in interviews can be downloaded here.

Quick guide for interviewers

2026-02-17T15:00:50Z

Riegler:

The cheat sheet for Decoding interviews was initiated by Magda Zarebski and Helen Schneider.

The sheet has been prepared in German and currently is only availble in German. Feel free to translate.
{| class="wikitable"
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!Kommunikation mit Expert:in
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| colspan="2" style="" class="col-blue-light-bg" |Einleitung (Team Up)
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== Downloadble version ==
A printable version for usage in interviews can be downloaded here.

Quick guide for interviewers

2026-02-17T14:58:18Z

Riegler:

The cheat sheet for Decoding interviews was initiated by Magda Zarebski and Helen Schneider.

The sheet has been prepared in German and currently is only availble in German. Feel free to translate.
{| class="wikitable"
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!Kommunikation mit Expert:in
!Im Kopf
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== Downloadble version ==
A printable version for usage in interviews can be downloaded here.

Decoding interview

2026-02-17T14:54:58Z

Riegler: added link to quick guide

[[File:3-abb2.png|thumb|Three educators conducting a Decoding Interview]]
<span>The '''Decoding Interview''' is the second step within the seven steps of [[Decoding the Disciplines]]. The purpose of this step is to uncover the [[Mental moves|mental operations]] students must master to get past the [[Bottleneck]]. Since many of these operations are so automatic to instructors that they have become invisible, a systematic process of deconstructing disciplinary practice is necessary. The most powerful method for becoming clear about the steps that students must master to overcome specific bottlenecks is an interview process in which two interviewers work with instructors to explore how they themselves accomplish the task with which many students have trouble . By interviewing the lecturer as an expert in the field (s)he teaches those mental operations of the expert are revealed.</span>

Generally speaking, a Decoding Interview assumes the following pattern:

# Define and describe the bottleneck in question.
# Articulate the mental operations required to overcome the bottleneck. This step requires that the person conducting the interview probe the subject expert being interviewed in order to push them to clearly outline the operational steps taken to move past the bottleneck. The point of this step is to make the implicit explicit.
# Summarize and reflect on the outlined operations to ensure the steps have been adequately captured. This step may also identify other bottlenecks that need to be addressed in order for a learner to be able to be able to work through the bottleneck being addressed in the interview.
The interview should follow an conversational, exploratory format. An example of a Decoding Interview can be found by [https://iu.mediaspace.kaltura.com/media/t/1_xxqo4gvy clicking on this link].

Detailed descriptions of the process may be found in these resources:

* David Pace, ''[[The Decoding the Disciplines Paradigm: Seven Steps to Increased Student Learning|The Decoding the Disciplines Paradigm]]''<ref>https://iupress.org/9780253024589/the-decoding-the-disciplines-paradigm/</ref> (pp.39-47, 123-125)
* Joan Middendorf and Leah Shopkow, ''[[Overcoming Student Learning Bottlenecks]]''<ref>https://www-routledge-com.uea.idm.oclc.org/Overcoming-Student-Learning-Bottlenecks-Decode-the-Critical-Thinking-of-Your-Discipline/Middendorf-Shopkow/p/book/9781620366653?srsltid=AfmBOopmuDBo9u_39CJnfUrIaOtx35Yype7_J5GR2w5yphtbWKMNJhn3</ref> (pp.48-59)
* Peter Riegler, “[[The Decoding Interview - An Exemplary Insight|The Decoding interview – an exemplary insight]]”'''.''' in ''Decoding the Disciplines'' <ref>https://diz-bayern.de/publikationen/dina-und-tagungsbaende</ref>

== Outcomes of the interview ==
The outcome of the Decoding interview should be a phrase that summarizes the mental moves of the interviewed expert.

== How to do interviews ==
Decoding interviews follow the '''TEACH''' structural model. '''TEACH''' stands for:

* '''Team-up''' - where the lecturer and the interviewers come together and develop a positive, collaborative basis for the interview.
* '''Elucidate''' - where the bottleneck is named and explored by the lecturer and the interviewers for suitability within the context of a Decoding Interview.
* '''Analysis''' - where the interviews ask questions of the lecturer to help them make their knowledge of the bottleneck explicit and explore potential challenges to understanding.
* '''Change'''- where the lecturer and interviewers discuss potential changes to the lecturer's teaching practice that may addresses the bottleneck with students.
* '''Harbour''' - where all interview participants reflect on their discussion and identify next steps and goals.

A more thorough description of the '''TEACH''' structural model can be found in [[Decoding Interviews führen mit dem Strukturmodell TEACH]].

=== Interview participants ===
A Decoding Interview is usually comprised of three participants:

* The lecturer who is trying to decode their bottleneck
* An interviewer who engages the educator in questions
* A second interviewer to support the process

When selecting potential interview partners, the lecturer should consider the knowledge level of the interviewers. If the interviewers are too familiar with the bottleneck and its related discipline, there is the possibility that their shared knowledge will impede them from interrogated the lecturer in a way that challenges them to break down the topic at hand. Likewise, if the interviewers have too little subject knowledge the lecturer may have to spend too much time ensuring they have enough background knowledge to approach the bottleneck. Ideally, the interviewers' knowledge of the bottleneck should approximate the level of the students whom the lecturer usually encounters when teaching the bottleneck. Other configurations may be appropriate for specifics topics and circumstances.

=== Interview process ===
Decoding Interviews begin by having the lecturer name the bottleneck being explored and describing a situation in which students got stuck in the bottleneck (i.e. Team-Up). As the lecturer describes how they understand the bottleneck, the interviewers should probe with questions that push them to describe the bottleneck in as much detail as possible (i.e. Elucidate and Analysis). Important questions include, but are not limited to:

* How exactly do you do that?
* What is the next step?
* What would happen if you didn't do exactly that?

If the interviewers ask a question the lecturer cannot immediately answer, this may indicate that the question relates to an unconscious aspect of the expertise they possess and that impedes students from proceeding through the bottleneck. Interviewers should support the lecturer to make this knowledge explicit in the interview.

Interviewers should make note of any metaphors or physical gestures used by the lecturer when explaining concepts. Metaphors or gestures may need to be unpacked in order to ensure the bottleneck has been explained in such a way that does not rely on interpretations or assumed shared culture or disciplinary knowledge. Creating a video and/or audio recording of the interview may assist in capturing physical elements of a lecturers descriptions.

===== Disrupting the Disciplines =====
[[Disrupting the Disciplines]] is an approach to a Decoding Interview that approaches decoding from a critical, post-colonial and/or Indigenous lens. This approach challenges whether disciplinary knowledges and assumptions are neutral and unbiassed or based within oppressive structures. An example of interview question from the Disrupting the Disciplines approach is to follow-up a question the lecturer cannot answer by pursuing a more imaginative approach: "What can I imagine doing differently?"<ref>Lindstrom, G., Easton, L., Yeo, M., & Attas, R. (2022). The disrupting interview: A framework to approach decolonization. ''International Journal for Academic Development. 1-13.'' https://doi.org/10.1080/1360144X.2022.2103560</ref>

===== In-person versus online interviews =====
Conducting interviews in-person may help facilitate a more dynamic discussion and better allow interviewers to identify physical gestures used by the lecturer in descriptions of the bottleneck. Online interviews, on the other hand, may support participation and accessibility by allowing participants to join from different physical locations. Online communication platforms (e.g. MS Teams, Zoom) may also assist with recording and transcription processes.

== Post-interview activities ==

Once a lecturer and interviewers have reflected on the discussion and identified the lecturer's next steps and goals (i.e. Harbour), the lecturer moves on the [[Step 3 - Modeling Mental Operations|Question 3 of the Decoding Wheel]], where they begin planning how to model the mental moves associated with overcoming the bottleneck discussed in the interview.
== Examples of Decoding Interviews ==

* [https://iu.mediaspace.kaltura.com/media/t/1_xxqo4gvy The Questions in a Decoding the Disciplines Interview]

== See also ==
[[Cheat sheet for Decoding Interview|Quick guide for interviewers]]

==References==
<references />

Quick guide for interviewers

2026-02-17T14:51:17Z

Riegler: initialize page

== The cheat sheet for Decoding interviews was initiated by Magda Zarebski and Helen Schneider. ==
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!Kommunikation mit Expert:in
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== Downloadble version ==
A printable version for usage in interviews can be downloaded here.

Scope of quadratic formula

2026-02-16T08:54:03Z

Riegler:

===Description of Bottleneck===
When using the quadratic formula in the form <math>x=\frac{1}{2} \left(-p \pm \sqrt{p^2-4q}\right)</math>
students don’t check whether the the quadratic equation to be solved is in the form
<math>x^2 + p x + q = 0</math>,
i.e. that the <math>x^2</math>-coefficient is equal to unity.

That is to say, students don't check whether the prerequisites for the applicability of this formula apply.

This bottleneck is a special case of [[Scope of formula]].
[[Category:Mathematics]]
[[Category:Algebra]]
[[Category:Bottleneck]]

Scope of quadratic formula

2026-02-16T08:53:27Z

Riegler: typsetting formulae

===Description of Bottleneck===
When using the quadratic formula in the form <math>x=\frac{1}{2} (-p \pm \sqrt{p^2-4q})</math>
students don’t check whether the the quadratic equation to be solved is in the form
<math>x^2 + p x + q = 0</math>,
i.e. that the <math>x^2</math>-coefficient is equal to unity.

That is to say, students don't check whether the prerequisites for the applicability of this formula apply.

This bottleneck is a special case of [[Scope of formula]].
[[Category:Mathematics]]
[[Category:Algebra]]
[[Category:Bottleneck]]

Scope of quadratic formula

2026-02-12T15:34:16Z

Riegler: + math tags

===Description of Bottleneck===
When using the quadratic formula in the form <math>x=\frac{1}{2} (-p \pm \sqrt{p^2-4q}</math>

students don’t check whether the the quadratic equation to be solved is in the form

<math>x^2 + p x + q = 0</math>,

i.e. that the x^2-coefficient is equal to unity.

That is to say, students don't check whether the prerequisites for the applicability of this formula apply.

This bottleneck is a special case of [[Scope of formula]].
[[Category:Mathematics]]
[[Category:Algebra]]
[[Category:Bottleneck]]

User:Riegler/Community

2026-02-12T15:26:09Z

Riegler:

<DynamicPageList>
category = Bottleneck
category = Mathematics
</DynamicPageList>

Nur Math
<DynamicPageList>
category = Mathematics
</DynamicPageList>

Nur B
<DynamicPageList>
category = Bottleneck
</DynamicPageList>

{{Map||Bloomington, Indiana}}

<math>x^2</math>Text

<iframe src="https://www.google.com/maps/d/embed?mid=1v_RnmYkHlYSVQZiMHoqxLrhrsAVP78E&ehbc=2E312F" width="640" height="480"></iframe>

{{#display_map:center=Brandenburg Gate Berlin | service=google}}

{{Map|München;Flughafen MUC~Munich Airport|München}}

<math>\tfrac{2}{4}</math>

<bs:tagcloud renderer="list" store="category" width="100%" showcount="true" minsize="5" maxsize="30" />