---
_id: '59437'
article_number: '102032'
author:
- first_name: Nicole
full_name: Steib, Nicole
last_name: Steib
- first_name: Theresa
full_name: Büchter, Theresa
last_name: Büchter
- first_name: Andreas
full_name: Eichler, Andreas
last_name: Eichler
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Katharina
full_name: Böcherer-Linder, Katharina
last_name: Böcherer-Linder
- first_name: Markus
full_name: Vogel, Markus
last_name: Vogel
- first_name: Sven
full_name: Hilbert, Sven
last_name: Hilbert
citation:
ama: 'Steib N, Büchter T, Eichler A, et al. How to teach Bayesian reasoning: An
empirical study comparing four different probability training courses. Learning
and Instruction. 2024;95. doi:10.1016/j.learninstruc.2024.102032'
apa: 'Steib, N., Büchter, T., Eichler, A., Binder, K., Krauss, S., Böcherer-Linder,
K., Vogel, M., & Hilbert, S. (2024). How to teach Bayesian reasoning: An empirical
study comparing four different probability training courses. Learning and Instruction,
95, Article 102032. https://doi.org/10.1016/j.learninstruc.2024.102032'
bibtex: '@article{Steib_Büchter_Eichler_Binder_Krauss_Böcherer-Linder_Vogel_Hilbert_2024,
title={How to teach Bayesian reasoning: An empirical study comparing four different
probability training courses}, volume={95}, DOI={10.1016/j.learninstruc.2024.102032},
number={102032}, journal={Learning and Instruction}, publisher={Elsevier BV},
author={Steib, Nicole and Büchter, Theresa and Eichler, Andreas and Binder, Karin
and Krauss, Stefan and Böcherer-Linder, Katharina and Vogel, Markus and Hilbert,
Sven}, year={2024} }'
chicago: 'Steib, Nicole, Theresa Büchter, Andreas Eichler, Karin Binder, Stefan
Krauss, Katharina Böcherer-Linder, Markus Vogel, and Sven Hilbert. “How to Teach
Bayesian Reasoning: An Empirical Study Comparing Four Different Probability Training
Courses.” Learning and Instruction 95 (2024). https://doi.org/10.1016/j.learninstruc.2024.102032.'
ieee: 'N. Steib et al., “How to teach Bayesian reasoning: An empirical study
comparing four different probability training courses,” Learning and Instruction,
vol. 95, Art. no. 102032, 2024, doi: 10.1016/j.learninstruc.2024.102032.'
mla: 'Steib, Nicole, et al. “How to Teach Bayesian Reasoning: An Empirical Study
Comparing Four Different Probability Training Courses.” Learning and Instruction,
vol. 95, 102032, Elsevier BV, 2024, doi:10.1016/j.learninstruc.2024.102032.'
short: N. Steib, T. Büchter, A. Eichler, K. Binder, S. Krauss, K. Böcherer-Linder,
M. Vogel, S. Hilbert, Learning and Instruction 95 (2024).
date_created: 2025-04-08T11:35:09Z
date_updated: 2025-05-17T18:14:24Z
ddc:
- '370'
doi: 10.1016/j.learninstruc.2024.102032
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:13:26Z
date_updated: 2025-05-17T18:13:26Z
file_id: '59927'
file_name: Steib et al 2025 How to train Bayesian reasoning.pdf
file_size: 13811141
relation: main_file
success: 1
file_date_updated: 2025-05-17T18:13:26Z
intvolume: ' 95'
language:
- iso: eng
publication: Learning and Instruction
publication_identifier:
issn:
- 0959-4752
publication_status: published
publisher: Elsevier BV
status: public
title: 'How to teach Bayesian reasoning: An empirical study comparing four different
probability training courses'
type: journal_article
user_id: '83381'
volume: 95
year: '2024'
...
---
_id: '59986'
author:
- first_name: Irene
full_name: Garnelo Abellanas, Irene
id: '93843'
last_name: Garnelo Abellanas
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
citation:
ama: 'Garnelo Abellanas I, Liebendörfer M. Herausforderungen beim Einsatz interaktiver
Theorembeweiser in der Hochschullehre. In: Beiträge Zum Mathematikunterricht
2024. ; 2024.'
apa: Garnelo Abellanas, I., & Liebendörfer, M. (2024). Herausforderungen beim
Einsatz interaktiver Theorembeweiser in der Hochschullehre. Beiträge Zum Mathematikunterricht
2024.
bibtex: '@inproceedings{Garnelo Abellanas_Liebendörfer_2024, title={Herausforderungen
beim Einsatz interaktiver Theorembeweiser in der Hochschullehre}, booktitle={Beiträge
zum Mathematikunterricht 2024}, author={Garnelo Abellanas, Irene and Liebendörfer,
Michael}, year={2024} }'
chicago: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Herausforderungen
Beim Einsatz Interaktiver Theorembeweiser in Der Hochschullehre.” In Beiträge
Zum Mathematikunterricht 2024, 2024.
ieee: I. Garnelo Abellanas and M. Liebendörfer, “Herausforderungen beim Einsatz
interaktiver Theorembeweiser in der Hochschullehre,” 2024.
mla: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Herausforderungen Beim
Einsatz Interaktiver Theorembeweiser in Der Hochschullehre.” Beiträge Zum Mathematikunterricht
2024, 2024.
short: 'I. Garnelo Abellanas, M. Liebendörfer, in: Beiträge Zum Mathematikunterricht
2024, 2024.'
date_created: 2025-05-19T07:24:49Z
date_updated: 2026-01-15T10:34:56Z
language:
- iso: eng
publication: Beiträge zum Mathematikunterricht 2024
status: public
title: Herausforderungen beim Einsatz interaktiver Theorembeweiser in der Hochschullehre
type: conference
user_id: '93843'
year: '2024'
...
---
_id: '59990'
author:
- first_name: Andreas
full_name: Eichler, Andreas
last_name: Eichler
- first_name: Henrik
full_name: Floren, Henrik
last_name: Floren
- first_name: Irene
full_name: Garnelo Abellanas, Irene
id: '93843'
last_name: Garnelo Abellanas
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Raphael
full_name: Müller, Raphael
id: '55246'
last_name: Müller
- first_name: Mirko
full_name: Schürmann, Mirko
id: '59707'
last_name: Schürmann
orcid: 0000-0003-2646-085X
- first_name: Annabelle
full_name: Speer, Annabelle
last_name: Speer
citation:
ama: 'Eichler A, Floren H, Garnelo Abellanas I, et al. Digital STACK tasks and exam
results. In: INDRUM2024 PROCEEDINGS Fifth Conference of the International Network
for Didactic Research in University Mathematics. Escola Univerist`aria Salesiana
de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM; 2024. doi:https://theses.hal.science/INDRUM2024/hal-04944194v1'
apa: Eichler, A., Floren, H., Garnelo Abellanas, I., Liebendörfer, M., Müller, R.,
Schürmann, M., & Speer, A. (2024). Digital STACK tasks and exam results. INDRUM2024
PROCEEDINGS Fifth Conference of the International Network for Didactic Research
in University Mathematics. Fifth conference of the International Network for
Didactic Research in University Mathematics, Barcelona. https://theses.hal.science/INDRUM2024/hal-04944194v1
bibtex: '@inproceedings{Eichler_Floren_Garnelo Abellanas_Liebendörfer_Müller_Schürmann_Speer_2024,
place={Barcelona}, title={Digital STACK tasks and exam results}, DOI={https://theses.hal.science/INDRUM2024/hal-04944194v1},
booktitle={INDRUM2024 PROCEEDINGS Fifth conference of the International Network
for Didactic Research in University Mathematics}, publisher={Escola Univerist`aria
Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM}, author={Eichler,
Andreas and Floren, Henrik and Garnelo Abellanas, Irene and Liebendörfer, Michael
and Müller, Raphael and Schürmann, Mirko and Speer, Annabelle}, year={2024} }'
chicago: 'Eichler, Andreas, Henrik Floren, Irene Garnelo Abellanas, Michael Liebendörfer,
Raphael Müller, Mirko Schürmann, and Annabelle Speer. “Digital STACK Tasks and
Exam Results.” In INDRUM2024 PROCEEDINGS Fifth Conference of the International
Network for Didactic Research in University Mathematics. Barcelona: Escola
Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM,
2024. https://theses.hal.science/INDRUM2024/hal-04944194v1.'
ieee: 'A. Eichler et al., “Digital STACK tasks and exam results,” presented
at the Fifth conference of the International Network for Didactic Research in
University Mathematics, Barcelona, 2024, doi: https://theses.hal.science/INDRUM2024/hal-04944194v1.'
mla: Eichler, Andreas, et al. “Digital STACK Tasks and Exam Results.” INDRUM2024
PROCEEDINGS Fifth Conference of the International Network for Didactic Research
in University Mathematics, Escola Univerist`aria Salesiana de Sarri`a – Univ.
Aut`onoma de Barcelona and INDRUM, 2024, doi:https://theses.hal.science/INDRUM2024/hal-04944194v1.
short: 'A. Eichler, H. Floren, I. Garnelo Abellanas, M. Liebendörfer, R. Müller,
M. Schürmann, A. Speer, in: INDRUM2024 PROCEEDINGS Fifth Conference of the International
Network for Didactic Research in University Mathematics, Escola Univerist`aria
Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, Barcelona, 2024.'
conference:
end_date: 2024-06-14
location: Barcelona
name: Fifth conference of the International Network for Didactic Research in University
Mathematics
start_date: 2024-06-10
date_created: 2025-05-19T08:51:27Z
date_updated: 2025-06-25T07:50:49Z
ddc:
- '510'
doi: https://theses.hal.science/INDRUM2024/hal-04944194v1
file:
- access_level: open_access
content_type: application/pdf
creator: rmuelle2
date_created: 2025-05-19T08:51:19Z
date_updated: 2025-05-19T08:51:19Z
file_id: '59991'
file_name: Poster_Indrum_2024_Digital-STACK-Tasks_Exam-Results.pdf
file_size: 850253
relation: main_file
file_date_updated: 2025-05-19T08:51:19Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- url: https://theses.hal.science/INDRUM2024/hal-04944194v1
oa: '1'
place: Barcelona
publication: INDRUM2024 PROCEEDINGS Fifth conference of the International Network
for Didactic Research in University Mathematics
publication_identifier:
issn:
- 2496-1027 (online)
publication_status: published
publisher: Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona
and INDRUM
status: public
title: Digital STACK tasks and exam results
type: conference
user_id: '55246'
year: '2024'
...
---
_id: '59436'
abstract:
- lang: eng
text: 'BackgroundCommunicating
well with patients is a competence central to everyday clinical practice, and
communicating statistical information, especially in Bayesian reasoning tasks,
can be challenging. In Bayesian reasoning tasks, information can be communicated
in two different ways (which we calldirections of information):
The direction ofBayesian information(e.g., proportion
of people tested positive among those with the disease) and the direction ofdiagnostic
information(e.g., the proportion of people having the disease among
those tested positive). The purpose of this study was to analyze the impact of
both the direction of the information presented and whether a visualization (frequency
net) is presented with it on patient’s ability to quantify a positive predictive
value.Material and methods109
participants completed four different medical cases (2⨯2⨯4 design) that were presented
in a video; a physician communicated frequencies using different directions of
information (Bayesian information vs. diagnostic information). In half of the
cases for each direction, participants were given a frequency net. After watching
the video, participants stated a positive predictive value. Accuracy and speed
of response were analyzed.ResultsCommunicating
with Bayesian information led to participant performance of only 10% (without
frequency net) and 37% (with frequency net) accuracy. The tasks communicated with
diagnostic information but without a frequency net were correctly solved by 72%
of participants, but accuracy rate decreased to 61% when participants were given
a frequency net. Participants with correct responses in the Bayesian information
version without visualization took longest to complete the tasks (median of 106
seconds; median of 13.5, 14.0, and 14.5 seconds in other versions).DiscussionCommunicating with diagnostic
information rather than Bayesian information helps patients to understand specific
information better and more quickly. Patients’ understanding of the relevance
of test results is strongly dependent on the way the information is presented.'
article_number: e0283947
author:
- first_name: Sarah Frederike
full_name: Brose, Sarah Frederike
last_name: Brose
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Martin R.
full_name: Fischer, Martin R.
last_name: Fischer
- first_name: Martin
full_name: Reincke, Martin
last_name: Reincke
- first_name: Leah T.
full_name: Braun, Leah T.
last_name: Braun
- first_name: Ralf
full_name: Schmidmaier, Ralf
last_name: Schmidmaier
citation:
ama: 'Brose SF, Binder K, Fischer MR, Reincke M, Braun LT, Schmidmaier R. Bayesian
versus diagnostic information in physician-patient communication: Effects of direction
of statistical information and presentation of visualization. PLOS ONE.
2023;18(6). doi:10.1371/journal.pone.0283947'
apa: 'Brose, S. F., Binder, K., Fischer, M. R., Reincke, M., Braun, L. T., &
Schmidmaier, R. (2023). Bayesian versus diagnostic information in physician-patient
communication: Effects of direction of statistical information and presentation
of visualization. PLOS ONE, 18(6), Article e0283947. https://doi.org/10.1371/journal.pone.0283947'
bibtex: '@article{Brose_Binder_Fischer_Reincke_Braun_Schmidmaier_2023, title={Bayesian
versus diagnostic information in physician-patient communication: Effects of direction
of statistical information and presentation of visualization}, volume={18}, DOI={10.1371/journal.pone.0283947},
number={6e0283947}, journal={PLOS ONE}, publisher={Public Library of Science (PLoS)},
author={Brose, Sarah Frederike and Binder, Karin and Fischer, Martin R. and Reincke,
Martin and Braun, Leah T. and Schmidmaier, Ralf}, year={2023} }'
chicago: 'Brose, Sarah Frederike, Karin Binder, Martin R. Fischer, Martin Reincke,
Leah T. Braun, and Ralf Schmidmaier. “Bayesian versus Diagnostic Information in
Physician-Patient Communication: Effects of Direction of Statistical Information
and Presentation of Visualization.” PLOS ONE 18, no. 6 (2023). https://doi.org/10.1371/journal.pone.0283947.'
ieee: 'S. F. Brose, K. Binder, M. R. Fischer, M. Reincke, L. T. Braun, and R. Schmidmaier,
“Bayesian versus diagnostic information in physician-patient communication: Effects
of direction of statistical information and presentation of visualization,” PLOS
ONE, vol. 18, no. 6, Art. no. e0283947, 2023, doi: 10.1371/journal.pone.0283947.'
mla: 'Brose, Sarah Frederike, et al. “Bayesian versus Diagnostic Information in
Physician-Patient Communication: Effects of Direction of Statistical Information
and Presentation of Visualization.” PLOS ONE, vol. 18, no. 6, e0283947,
Public Library of Science (PLoS), 2023, doi:10.1371/journal.pone.0283947.'
short: S.F. Brose, K. Binder, M.R. Fischer, M. Reincke, L.T. Braun, R. Schmidmaier,
PLOS ONE 18 (2023).
date_created: 2025-04-08T11:34:41Z
date_updated: 2025-05-17T18:15:35Z
ddc:
- '360'
doi: 10.1371/journal.pone.0283947
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:15:18Z
date_updated: 2025-05-17T18:15:18Z
file_id: '59928'
file_name: Brose, Binder, Fischer, Reincke, Braun, Schmidmaier 2023 Bayesian versus
diagnostic information.pdf
file_size: 2010557
relation: main_file
success: 1
file_date_updated: 2025-05-17T18:15:18Z
intvolume: ' 18'
issue: '6'
language:
- iso: eng
publication: PLOS ONE
publication_identifier:
issn:
- 1932-6203
publication_status: published
publisher: Public Library of Science (PLoS)
status: public
title: 'Bayesian versus diagnostic information in physician-patient communication:
Effects of direction of statistical information and presentation of visualization'
type: journal_article
user_id: '83381'
volume: 18
year: '2023'
...
---
_id: '59988'
author:
- first_name: Raphael
full_name: Müller, Raphael
id: '55246'
last_name: Müller
citation:
ama: Müller R. On the Asymptotics of Wildly Ramified Local Function Field Extensions.;
2023.
apa: Müller, R. (2023). On the asymptotics of wildly ramified local function
field extensions.
bibtex: '@book{Müller_2023, title={On the asymptotics of wildly ramified local function
field extensions}, author={Müller, Raphael}, year={2023} }'
chicago: Müller, Raphael. On the Asymptotics of Wildly Ramified Local Function
Field Extensions, 2023.
ieee: R. Müller, On the asymptotics of wildly ramified local function field extensions.
2023.
mla: Müller, Raphael. On the Asymptotics of Wildly Ramified Local Function Field
Extensions. 2023.
short: R. Müller, On the Asymptotics of Wildly Ramified Local Function Field Extensions,
2023.
date_created: 2025-05-19T08:22:06Z
date_updated: 2025-05-19T08:58:21Z
department:
- _id: '43'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://katalog.ub.uni-paderborn.de/local/r/99372717691706441
oa: '1'
publication_status: published
status: public
title: On the asymptotics of wildly ramified local function field extensions
type: dissertation
user_id: '55246'
year: '2023'
...
---
_id: '59984'
author:
- first_name: Irene
full_name: Garnelo Abellanas, Irene
id: '93843'
last_name: Garnelo Abellanas
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
citation:
ama: 'Garnelo Abellanas I, Liebendörfer M. Introducing mathematics undergraduate
students to the theorem prover lean. In: Thirteenth Congress of the European
Society for Research in Mathematics (CERME13). ; 2023.'
apa: Garnelo Abellanas, I., & Liebendörfer, M. (2023). Introducing mathematics
undergraduate students to the theorem prover lean. Thirteenth Congress of the
European Society for Research in Mathematics (CERME13). Thirteenth Congress
of the European Society for Research in Mathematics Education (CERME13), Budapest.
bibtex: '@inproceedings{Garnelo Abellanas_Liebendörfer_2023, title={Introducing
mathematics undergraduate students to the theorem prover lean}, booktitle={Thirteenth
Congress of the European Society for Research in Mathematics (CERME13)}, author={Garnelo
Abellanas, Irene and Liebendörfer, Michael}, year={2023} }'
chicago: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Introducing Mathematics
Undergraduate Students to the Theorem Prover Lean.” In Thirteenth Congress
of the European Society for Research in Mathematics (CERME13), 2023.
ieee: I. Garnelo Abellanas and M. Liebendörfer, “Introducing mathematics undergraduate
students to the theorem prover lean,” presented at the Thirteenth Congress of
the European Society for Research in Mathematics Education (CERME13), Budapest,
2023.
mla: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Introducing Mathematics
Undergraduate Students to the Theorem Prover Lean.” Thirteenth Congress of
the European Society for Research in Mathematics (CERME13), 2023.
short: 'I. Garnelo Abellanas, M. Liebendörfer, in: Thirteenth Congress of the European
Society for Research in Mathematics (CERME13), 2023.'
conference:
location: Budapest
name: Thirteenth Congress of the European Society for Research in Mathematics Education
(CERME13)
date_created: 2025-05-19T07:19:01Z
date_updated: 2026-01-15T10:36:11Z
department:
- _id: '983'
language:
- iso: eng
publication: Thirteenth Congress of the European Society for Research in Mathematics
(CERME13)
related_material:
link:
- relation: confirmation
url: https://hal.science/hal-04406679v1/file/TWG_14-Garnelo-218.pdf
status: public
title: Introducing mathematics undergraduate students to the theorem prover lean
type: conference
user_id: '93843'
year: '2023'
...
---
_id: '59434'
abstract:
- lang: eng
text: ' Background. Medical students often have problems with Bayesian reasoning
situations. Representing statistical information as natural frequencies (instead
of probabilities) and visualizing them (e.g., with double-trees or net diagrams)
leads to higher accuracy in solving these tasks. However, double-trees and net
diagrams (which already contain the correct solution of the task, so that the
solution could be read of the diagrams) have not yet been studied in medical education.
This study examined the influence of information format (probabilities v. frequencies)
and visualization (double-tree v. net diagram) on the accuracy and speed of Bayesian
judgments. Methods. A total of 142 medical students at different university medical
schools (Munich, Kiel, Goettingen, Erlangen, Nuremberg, Berlin, Regensburg) in
Germany predicted posterior probabilities in 4 different medical Bayesian reasoning
tasks, resulting in a 3-factorial 2 × 2 × 4 design. The diagnostic efficiency
for the different versions was represented as the median time divided by the percentage
of correct inferences. Results. Frequency visualizations led to a significantly
higher accuracy and faster judgments than did probability visualizations. Participants
solved 80% of the tasks correctly in the frequency double-tree and the frequency
net diagram. Visualizations with probabilities also led to relatively high performance
rates: 73% in the probability double-tree and 70% in the probability net diagram.
The median time for a correct inference was fastest with the frequency double
tree (2:08 min) followed by the frequency net diagram and the probability double-tree
(both 2:26 min) and probability net diagram (2:33 min). The type of visualization
did not result in a significant difference. Discussion. Frequency double-trees
and frequency net diagrams help answer Bayesian tasks more accurately and also
more quickly than the respective probability visualizations. Surprisingly, the
effect of information format (probabilities v. frequencies) on performance was
higher in previous studies: medical students seem also quite capable of identifying
the correct solution to the Bayesian task, among other probabilities in the probability
visualizations. Highlights
Frequency double-trees and frequency nets help answer Bayesian tasks not only
more accurately but also more quickly than the respective probability visualizations.
In double-trees and net diagrams, the effect of the information format (probabilities
v. natural frequencies) on performance is remarkably lower in this high-performing
sample than that shown in previous studies. '
article_type: original
author:
- first_name: Alexandra K.
full_name: Kunzelmann, Alexandra K.
last_name: Kunzelmann
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Martin R.
full_name: Fischer, Martin R.
last_name: Fischer
- first_name: Martin
full_name: Reincke, Martin
last_name: Reincke
- first_name: Leah T.
full_name: Braun, Leah T.
last_name: Braun
- first_name: Ralf
full_name: Schmidmaier, Ralf
last_name: Schmidmaier
citation:
ama: Kunzelmann AK, Binder K, Fischer MR, Reincke M, Braun LT, Schmidmaier R. Improving
Diagnostic Efficiency with Frequency Double-Trees and Frequency Nets in Bayesian
Reasoning. MDM Policy & Practice. 2022;7(1). doi:10.1177/23814683221086623
apa: Kunzelmann, A. K., Binder, K., Fischer, M. R., Reincke, M., Braun, L. T., &
Schmidmaier, R. (2022). Improving Diagnostic Efficiency with Frequency Double-Trees
and Frequency Nets in Bayesian Reasoning. MDM Policy & Practice,
7(1). https://doi.org/10.1177/23814683221086623
bibtex: '@article{Kunzelmann_Binder_Fischer_Reincke_Braun_Schmidmaier_2022, title={Improving
Diagnostic Efficiency with Frequency Double-Trees and Frequency Nets in Bayesian
Reasoning}, volume={7}, DOI={10.1177/23814683221086623},
number={1}, journal={MDM Policy & Practice}, publisher={SAGE Publications},
author={Kunzelmann, Alexandra K. and Binder, Karin and Fischer, Martin R. and
Reincke, Martin and Braun, Leah T. and Schmidmaier, Ralf}, year={2022} }'
chicago: Kunzelmann, Alexandra K., Karin Binder, Martin R. Fischer, Martin Reincke,
Leah T. Braun, and Ralf Schmidmaier. “Improving Diagnostic Efficiency with Frequency
Double-Trees and Frequency Nets in Bayesian Reasoning.” MDM Policy &
Practice 7, no. 1 (2022). https://doi.org/10.1177/23814683221086623.
ieee: 'A. K. Kunzelmann, K. Binder, M. R. Fischer, M. Reincke, L. T. Braun, and
R. Schmidmaier, “Improving Diagnostic Efficiency with Frequency Double-Trees and
Frequency Nets in Bayesian Reasoning,” MDM Policy & Practice, vol.
7, no. 1, 2022, doi: 10.1177/23814683221086623.'
mla: Kunzelmann, Alexandra K., et al. “Improving Diagnostic Efficiency with Frequency
Double-Trees and Frequency Nets in Bayesian Reasoning.” MDM Policy &
Practice, vol. 7, no. 1, SAGE Publications, 2022, doi:10.1177/23814683221086623.
short: A.K. Kunzelmann, K. Binder, M.R. Fischer, M. Reincke, L.T. Braun, R. Schmidmaier,
MDM Policy & Practice 7 (2022).
date_created: 2025-04-08T11:33:53Z
date_updated: 2025-05-17T18:22:27Z
ddc:
- '370'
doi: 10.1177/23814683221086623
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:22:12Z
date_updated: 2025-05-17T18:22:12Z
file_id: '59930'
file_name: Kunzelmann Binder Fischer Reincke Braun Schmidmaier_2022_Improving diagnostic
efficiency_MDM_PP.pdf
file_size: 1131713
relation: main_file
success: 1
file_date_updated: 2025-05-17T18:22:12Z
intvolume: ' 7'
issue: '1'
language:
- iso: eng
publication: MDM Policy & Practice
publication_identifier:
issn:
- 2381-4683
- 2381-4683
publication_status: published
publisher: SAGE Publications
status: public
title: Improving Diagnostic Efficiency with Frequency Double-Trees and Frequency Nets
in Bayesian Reasoning
type: journal_article
user_id: '83381'
volume: 7
year: '2022'
...
---
_id: '59432'
abstract:
- lang: eng
text: ZusammenfassungIn stochastischen Situationen
mit zwei dichotomen Merkmalen erlauben weder die schulüblichen Baumdiagramme noch
Vierfeldertafeln die simultane Darstellung sämtlicher in der Situation möglicher
Wahrscheinlichkeiten. Das im vorliegenden Beitrag vorgestellte Netz hat die Kapazität,
alle vier möglichen Randwahrscheinlichkeiten, alle vier Schnittwahrscheinlichkeiten
sowie alle acht bedingten Wahrscheinlichkeiten gleichzeitig
darzustellen. Darüber hinaus ist – aufgrund der Knoten-Ast-Struktur des Netzes –
die simultane Darstellung von Wahrscheinlichkeiten und
absoluten Häufigkeiten mit dieser Visualisierung ebenfalls möglich. Bei der sukzessiven
Erweiterung des typischen Baumdiagramms zunächst zum Doppelbaum und schließlich
zum Netz sinkt der Inferenzgrad (d. h. weniger kognitive Schritte sind erforderlich)
z. B. für Fragen nach bedingten Wahrscheinlichkeiten, aber gleichzeitig steigt
die Komplexität der Darstellung und somit die extrinsische kognitive Belastung.
Im vorliegenden Artikel erfolgt zunächst ein theoretischer Vergleich dieser Knoten-Ast-Strukturen.
Eine anschließende Studie illustriert, dass sich die sukzessive Erweiterung bereits
vollständig ausgefüllter Diagramme positiv auf die Performanz von N = 269 Schülerinnen
und Schülern auswirkt. Obwohl Häufigkeitsdoppelbäume
und Häufigkeitsnetze den Schülerinnen und Schülern
gänzlich unbekannt waren, unterstützten diese Visualisierungen die Schülerinnen
und Schüler bei der Bearbeitung der Aufgaben am meisten.
article_type: original
author:
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Nicole
full_name: Steib, Nicole
last_name: Steib
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
citation:
ama: Binder K, Steib N, Krauss S. Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen –
kognitive Überlastung oder didaktische Unterstützung? Moving from tree diagrams
to double trees to net diagrams—cognitively overwhelming or educationally supportive?
Journal für Mathematik-Didaktik. 2022;44(2):471-503. doi:10.1007/s13138-022-00215-9
apa: Binder, K., Steib, N., & Krauss, S. (2022). Von Baumdiagrammen über Doppelbäume
zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung? Moving
from tree diagrams to double trees to net diagrams—cognitively overwhelming or
educationally supportive? Journal für Mathematik-Didaktik, 44(2),
471–503. https://doi.org/10.1007/s13138-022-00215-9
bibtex: '@article{Binder_Steib_Krauss_2022, title={Von Baumdiagrammen über Doppelbäume
zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung? Moving
from tree diagrams to double trees to net diagrams—cognitively overwhelming or
educationally supportive?}, volume={44}, DOI={10.1007/s13138-022-00215-9},
number={2}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science
and Business Media LLC}, author={Binder, Karin and Steib, Nicole and Krauss, Stefan},
year={2022}, pages={471–503} }'
chicago: 'Binder, Karin, Nicole Steib, and Stefan Krauss. “Von Baumdiagrammen über
Doppelbäume zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung?
Moving from tree diagrams to double trees to net diagrams—cognitively overwhelming
or educationally supportive?” Journal für Mathematik-Didaktik 44, no. 2
(2022): 471–503. https://doi.org/10.1007/s13138-022-00215-9.'
ieee: 'K. Binder, N. Steib, and S. Krauss, “Von Baumdiagrammen über Doppelbäume
zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung? Moving
from tree diagrams to double trees to net diagrams—cognitively overwhelming or
educationally supportive?,” Journal für Mathematik-Didaktik, vol. 44, no.
2, pp. 471–503, 2022, doi: 10.1007/s13138-022-00215-9.'
mla: Binder, Karin, et al. “Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen –
kognitive Überlastung oder didaktische Unterstützung? Moving from tree diagrams
to double trees to net diagrams—cognitively overwhelming or educationally supportive?”
Journal für Mathematik-Didaktik, vol. 44, no. 2, Springer Science and Business
Media LLC, 2022, pp. 471–503, doi:10.1007/s13138-022-00215-9.
short: K. Binder, N. Steib, S. Krauss, Journal für Mathematik-Didaktik 44 (2022)
471–503.
date_created: 2025-04-08T11:32:04Z
date_updated: 2025-05-17T18:37:30Z
ddc:
- '370'
doi: 10.1007/s13138-022-00215-9
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:37:16Z
date_updated: 2025-05-17T18:37:16Z
file_id: '59933'
file_name: Binder Steib Krauss 2023 Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen
- JMD.pdf
file_size: 3105846
relation: main_file
success: 1
file_date_updated: 2025-05-17T18:37:16Z
intvolume: ' 44'
issue: '2'
language:
- iso: ger
page: 471-503
publication: Journal für Mathematik-Didaktik
publication_identifier:
issn:
- 0173-5322
- 1869-2699
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen – kognitive Überlastung
oder didaktische Unterstützung? Moving from tree diagrams to double trees to net
diagrams—cognitively overwhelming or educationally supportive?
type: journal_article
user_id: '83381'
volume: 44
year: '2022'
...
---
_id: '59429'
abstract:
- lang: eng
text: In the present paper we empirically investigate the psychometric properties
of some of the most famous statistical and logical cognitive illusions from the
“heuristics and biases” research program by Daniel Kahneman and Amos Tversky,
who nearly 50 years ago introduced fascinating brain teasers such as the famous
Linda problem, the Wason card selection task, and so-called Bayesian reasoning
problems (e.g., the mammography task). In the meantime, a great number of articles
has been published that empirically examine single cognitive illusions, theoretically
explaining people’s faulty thinking, or proposing and experimentally implementing
measures to foster insight and to make these problems accessible to the human
mind. Yet these problems have thus far usually been empirically analyzed on an
individual-item level only (e.g., by experimentally comparing participants’ performance
on various versions of one of these problems). In this paper, by contrast, we
examine these illusions as a group and look at the ability to solve them as a
psychological construct. Based on an sample ofN= 2,643
Luxembourgian school students of age 16–18 we investigate the internal psychometric
structure of these illusions (i.e., Are they substantially correlated? Do they
form a reflexive or a formative construct?), their connection to related constructs
(e.g., Are they distinguishable from intelligence or mathematical competence in
a confirmatory factor analysis?), and the question of which of a person’s abilities
can predict the correct solution of these brain teasers (by means of a regression
analysis).
author:
- first_name: Georg
full_name: Bruckmaier, Georg
last_name: Bruckmaier
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Sven
full_name: Hilbert, Sven
last_name: Hilbert
- first_name: Martin
full_name: Brunner, Martin
last_name: Brunner
citation:
ama: 'Bruckmaier G, Krauss S, Binder K, Hilbert S, Brunner M. Tversky and Kahneman’s
Cognitive Illusions: Who Can Solve Them, and Why? Frontiers in Psychology.
2021;12. doi:10.3389/fpsyg.2021.584689'
apa: 'Bruckmaier, G., Krauss, S., Binder, K., Hilbert, S., & Brunner, M. (2021).
Tversky and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why? Frontiers
in Psychology, 12. https://doi.org/10.3389/fpsyg.2021.584689'
bibtex: '@article{Bruckmaier_Krauss_Binder_Hilbert_Brunner_2021, title={Tversky
and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why?}, volume={12},
DOI={10.3389/fpsyg.2021.584689},
journal={Frontiers in Psychology}, publisher={Frontiers Media SA}, author={Bruckmaier,
Georg and Krauss, Stefan and Binder, Karin and Hilbert, Sven and Brunner, Martin},
year={2021} }'
chicago: 'Bruckmaier, Georg, Stefan Krauss, Karin Binder, Sven Hilbert, and Martin
Brunner. “Tversky and Kahneman’s Cognitive Illusions: Who Can Solve Them, and
Why?” Frontiers in Psychology 12 (2021). https://doi.org/10.3389/fpsyg.2021.584689.'
ieee: 'G. Bruckmaier, S. Krauss, K. Binder, S. Hilbert, and M. Brunner, “Tversky
and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why?,” Frontiers
in Psychology, vol. 12, 2021, doi: 10.3389/fpsyg.2021.584689.'
mla: 'Bruckmaier, Georg, et al. “Tversky and Kahneman’s Cognitive Illusions: Who
Can Solve Them, and Why?” Frontiers in Psychology, vol. 12, Frontiers Media
SA, 2021, doi:10.3389/fpsyg.2021.584689.'
short: G. Bruckmaier, S. Krauss, K. Binder, S. Hilbert, M. Brunner, Frontiers in
Psychology 12 (2021).
date_created: 2025-04-08T11:29:50Z
date_updated: 2025-04-12T18:11:23Z
doi: 10.3389/fpsyg.2021.584689
intvolume: ' 12'
language:
- iso: eng
publication: Frontiers in Psychology
publication_identifier:
issn:
- 1664-1078
publication_status: published
publisher: Frontiers Media SA
status: public
title: 'Tversky and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why?'
type: journal_article
user_id: '83381'
volume: 12
year: '2021'
...
---
_id: '59439'
abstract:
- lang: eng
text: 'AbstractWhen physicians are asked to determine
the positive predictive value from the a priori probability of a disease and the
sensitivity and false positive rate of a medical test (Bayesian reasoning), it
often comes to misjudgments with serious consequences. In daily clinical practice,
however, it is not only important that doctors receive a tool with which they
cancorrectlyjudge—thespeedof
these judgments is also a crucial factor. In this study, we analyzed accuracy
and efficiency in medical Bayesian inferences. In an empirical study we varied
information format (probabilities vs. natural frequencies) and visualization (text
only vs. tree only) for four contexts. 111 medical students participated in this
study by working on four Bayesian tasks with common medical problems. The correctness
of their answers was coded and the time spent on task was recorded. The median
time for a correct Bayesian inference is fastest in the version with a frequency
tree (2:55 min) compared to the version with a probability tree (5:47 min) or
to the text only versions based on natural frequencies (4:13 min) or probabilities
(9:59 min).The scorediagnostic efficiency(calculated
by: median time divided by percentage of correct inferences) is best in the version
with a frequency tree (4:53 min). Frequency trees allow more accurateandfaster
judgments. Improving correctness and efficiency in Bayesian tasks might help to
decrease overdiagnosis in daily clinical practice, which on the one hand cause
cost and on the other hand might endanger patients’ safety.'
article_type: original
author:
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Ralf
full_name: Schmidmaier, Ralf
last_name: Schmidmaier
- first_name: Leah T.
full_name: Braun, Leah T.
last_name: Braun
citation:
ama: Binder K, Krauss S, Schmidmaier R, Braun LT. Natural frequency trees improve
diagnostic efficiency in Bayesian reasoning. Advances in Health Sciences Education.
2021;26(3):847-863. doi:10.1007/s10459-020-10025-8
apa: Binder, K., Krauss, S., Schmidmaier, R., & Braun, L. T. (2021). Natural
frequency trees improve diagnostic efficiency in Bayesian reasoning. Advances
in Health Sciences Education, 26(3), 847–863. https://doi.org/10.1007/s10459-020-10025-8
bibtex: '@article{Binder_Krauss_Schmidmaier_Braun_2021, title={Natural frequency
trees improve diagnostic efficiency in Bayesian reasoning}, volume={26}, DOI={10.1007/s10459-020-10025-8},
number={3}, journal={Advances in Health Sciences Education}, publisher={Springer
Science and Business Media LLC}, author={Binder, Karin and Krauss, Stefan and
Schmidmaier, Ralf and Braun, Leah T.}, year={2021}, pages={847–863} }'
chicago: 'Binder, Karin, Stefan Krauss, Ralf Schmidmaier, and Leah T. Braun. “Natural
Frequency Trees Improve Diagnostic Efficiency in Bayesian Reasoning.” Advances
in Health Sciences Education 26, no. 3 (2021): 847–63. https://doi.org/10.1007/s10459-020-10025-8.'
ieee: 'K. Binder, S. Krauss, R. Schmidmaier, and L. T. Braun, “Natural frequency
trees improve diagnostic efficiency in Bayesian reasoning,” Advances in Health
Sciences Education, vol. 26, no. 3, pp. 847–863, 2021, doi: 10.1007/s10459-020-10025-8.'
mla: Binder, Karin, et al. “Natural Frequency Trees Improve Diagnostic Efficiency
in Bayesian Reasoning.” Advances in Health Sciences Education, vol. 26,
no. 3, Springer Science and Business Media LLC, 2021, pp. 847–63, doi:10.1007/s10459-020-10025-8.
short: K. Binder, S. Krauss, R. Schmidmaier, L.T. Braun, Advances in Health Sciences
Education 26 (2021) 847–863.
date_created: 2025-04-08T11:36:11Z
date_updated: 2025-05-17T18:23:31Z
ddc:
- '370'
doi: 10.1007/s10459-020-10025-8
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:23:17Z
date_updated: 2025-05-17T18:23:17Z
file_id: '59931'
file_name: Binder Krauss Schmidmaier Braun 2021 Natural Frequency Trees Improve
Diagnostic Efficiency in BR.pdf
file_size: 1265280
relation: main_file
success: 1
file_date_updated: 2025-05-17T18:23:17Z
has_accepted_license: '1'
intvolume: ' 26'
issue: '3'
language:
- iso: eng
page: 847-863
publication: Advances in Health Sciences Education
publication_identifier:
issn:
- 1382-4996
- 1573-1677
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Natural frequency trees improve diagnostic efficiency in Bayesian reasoning
type: journal_article
user_id: '83381'
volume: 26
year: '2021'
...
---
_id: '59433'
abstract:
- lang: eng
text: 'AbstractWhen physicians are asked to determine
the positive predictive value from the a priori probability of a disease and the
sensitivity and false positive rate of a medical test (Bayesian reasoning), it
often comes to misjudgments with serious consequences. In daily clinical practice,
however, it is not only important that doctors receive a tool with which they
cancorrectlyjudge—thespeedof
these judgments is also a crucial factor. In this study, we analyzed accuracy
and efficiency in medical Bayesian inferences. In an empirical study we varied
information format (probabilities vs. natural frequencies) and visualization (text
only vs. tree only) for four contexts. 111 medical students participated in this
study by working on four Bayesian tasks with common medical problems. The correctness
of their answers was coded and the time spent on task was recorded. The median
time for a correct Bayesian inference is fastest in the version with a frequency
tree (2:55 min) compared to the version with a probability tree (5:47 min) or
to the text only versions based on natural frequencies (4:13 min) or probabilities
(9:59 min).The scorediagnostic efficiency(calculated
by: median time divided by percentage of correct inferences) is best in the version
with a frequency tree (4:53 min). Frequency trees allow more accurateandfaster
judgments. Improving correctness and efficiency in Bayesian tasks might help to
decrease overdiagnosis in daily clinical practice, which on the one hand cause
cost and on the other hand might endanger patients’ safety.'
article_type: original
author:
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Ralf
full_name: Schmidmaier, Ralf
last_name: Schmidmaier
- first_name: Leah T.
full_name: Braun, Leah T.
last_name: Braun
citation:
ama: Binder K, Krauss S, Schmidmaier R, Braun LT. Natural frequency trees improve
diagnostic efficiency in Bayesian reasoning. Advances in Health Sciences Education.
2021;26(3):847-863. doi:10.1007/s10459-020-10025-8
apa: Binder, K., Krauss, S., Schmidmaier, R., & Braun, L. T. (2021). Natural
frequency trees improve diagnostic efficiency in Bayesian reasoning. Advances
in Health Sciences Education, 26(3), 847–863. https://doi.org/10.1007/s10459-020-10025-8
bibtex: '@article{Binder_Krauss_Schmidmaier_Braun_2021, title={Natural frequency
trees improve diagnostic efficiency in Bayesian reasoning}, volume={26}, DOI={10.1007/s10459-020-10025-8},
number={3}, journal={Advances in Health Sciences Education}, publisher={Springer
Science and Business Media LLC}, author={Binder, Karin and Krauss, Stefan and
Schmidmaier, Ralf and Braun, Leah T.}, year={2021}, pages={847–863} }'
chicago: 'Binder, Karin, Stefan Krauss, Ralf Schmidmaier, and Leah T. Braun. “Natural
Frequency Trees Improve Diagnostic Efficiency in Bayesian Reasoning.” Advances
in Health Sciences Education 26, no. 3 (2021): 847–63. https://doi.org/10.1007/s10459-020-10025-8.'
ieee: 'K. Binder, S. Krauss, R. Schmidmaier, and L. T. Braun, “Natural frequency
trees improve diagnostic efficiency in Bayesian reasoning,” Advances in Health
Sciences Education, vol. 26, no. 3, pp. 847–863, 2021, doi: 10.1007/s10459-020-10025-8.'
mla: Binder, Karin, et al. “Natural Frequency Trees Improve Diagnostic Efficiency
in Bayesian Reasoning.” Advances in Health Sciences Education, vol. 26,
no. 3, Springer Science and Business Media LLC, 2021, pp. 847–63, doi:10.1007/s10459-020-10025-8.
short: K. Binder, S. Krauss, R. Schmidmaier, L.T. Braun, Advances in Health Sciences
Education 26 (2021) 847–863.
date_created: 2025-04-08T11:32:48Z
date_updated: 2025-05-17T18:36:06Z
ddc:
- '370'
doi: 10.1007/s10459-020-10025-8
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:35:43Z
date_updated: 2025-05-17T18:35:43Z
file_id: '59932'
file_name: Binder et al. 2021 Natural frequency trees improve.pdf
file_size: 1389359
relation: main_file
success: 1
file_date_updated: 2025-05-17T18:35:43Z
intvolume: ' 26'
issue: '3'
language:
- iso: eng
page: 847-863
publication: Advances in Health Sciences Education
publication_identifier:
issn:
- 1382-4996
- 1573-1677
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Natural frequency trees improve diagnostic efficiency in Bayesian reasoning
type: journal_article
user_id: '83381'
volume: 26
year: '2021'
...
---
_id: '59423'
author:
- first_name: S.
full_name: Krauss, S.
last_name: Krauss
- first_name: G.
full_name: Bruckmaier, G.
last_name: Bruckmaier
- first_name: A.
full_name: Lindl, A.
last_name: Lindl
- first_name: S.
full_name: Hilbert, S.
last_name: Hilbert
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: N.
full_name: Steib, N.
last_name: Steib
- first_name: W.
full_name: Blum, W.
last_name: Blum
citation:
ama: 'Krauss S, Bruckmaier G, Lindl A, et al. Competence as a continuum in the COACTIV
study: the “cascade model.” ZDM. 2020;52(2):311-327. doi:10.1007/s11858-020-01151-z'
apa: 'Krauss, S., Bruckmaier, G., Lindl, A., Hilbert, S., Binder, K., Steib, N.,
& Blum, W. (2020). Competence as a continuum in the COACTIV study: the “cascade
model.” ZDM, 52(2), 311–327. https://doi.org/10.1007/s11858-020-01151-z'
bibtex: '@article{Krauss_Bruckmaier_Lindl_Hilbert_Binder_Steib_Blum_2020, title={Competence
as a continuum in the COACTIV study: the “cascade model”}, volume={52}, DOI={10.1007/s11858-020-01151-z},
number={2}, journal={ZDM}, publisher={Springer Science and Business Media LLC},
author={Krauss, S. and Bruckmaier, G. and Lindl, A. and Hilbert, S. and Binder,
Karin and Steib, N. and Blum, W.}, year={2020}, pages={311–327} }'
chicago: 'Krauss, S., G. Bruckmaier, A. Lindl, S. Hilbert, Karin Binder, N. Steib,
and W. Blum. “Competence as a Continuum in the COACTIV Study: The ‘Cascade Model.’”
ZDM 52, no. 2 (2020): 311–27. https://doi.org/10.1007/s11858-020-01151-z.'
ieee: 'S. Krauss et al., “Competence as a continuum in the COACTIV study:
the ‘cascade model,’” ZDM, vol. 52, no. 2, pp. 311–327, 2020, doi: 10.1007/s11858-020-01151-z.'
mla: 'Krauss, S., et al. “Competence as a Continuum in the COACTIV Study: The ‘Cascade
Model.’” ZDM, vol. 52, no. 2, Springer Science and Business Media LLC,
2020, pp. 311–27, doi:10.1007/s11858-020-01151-z.'
short: S. Krauss, G. Bruckmaier, A. Lindl, S. Hilbert, K. Binder, N. Steib, W. Blum,
ZDM 52 (2020) 311–327.
date_created: 2025-04-08T11:27:09Z
date_updated: 2025-04-12T18:10:32Z
doi: 10.1007/s11858-020-01151-z
intvolume: ' 52'
issue: '2'
language:
- iso: eng
page: 311-327
publication: ZDM
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Competence as a continuum in the COACTIV study: the “cascade model”'
type: journal_article
user_id: '83381'
volume: 52
year: '2020'
...
---
_id: '59431'
author:
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Patrick
full_name: Weber, Patrick
last_name: Weber
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Georg
full_name: Bruckmaier, Georg
last_name: Bruckmaier
citation:
ama: Krauss S, Weber P, Binder K, Bruckmaier G. Natürliche Häufigkeiten als numerische
Darstellungsart von Anteilen und Unsicherheit – Forschungsdesiderate und einige
Antworten Natural Frequencies as Numerical Representation of Proportions and Uncertainty—Research
Desiderata and Some Answers. Journal für Mathematik-Didaktik. 2020;41(2):485-521.
doi:10.1007/s13138-019-00156-w
apa: Krauss, S., Weber, P., Binder, K., & Bruckmaier, G. (2020). Natürliche
Häufigkeiten als numerische Darstellungsart von Anteilen und Unsicherheit – Forschungsdesiderate
und einige Antworten Natural Frequencies as Numerical Representation of Proportions
and Uncertainty—Research Desiderata and Some Answers. Journal für Mathematik-Didaktik,
41(2), 485–521. https://doi.org/10.1007/s13138-019-00156-w
bibtex: '@article{Krauss_Weber_Binder_Bruckmaier_2020, title={Natürliche Häufigkeiten
als numerische Darstellungsart von Anteilen und Unsicherheit – Forschungsdesiderate
und einige Antworten Natural Frequencies as Numerical Representation of Proportions
and Uncertainty—Research Desiderata and Some Answers}, volume={41}, DOI={10.1007/s13138-019-00156-w},
number={2}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science
and Business Media LLC}, author={Krauss, Stefan and Weber, Patrick and Binder,
Karin and Bruckmaier, Georg}, year={2020}, pages={485–521} }'
chicago: 'Krauss, Stefan, Patrick Weber, Karin Binder, and Georg Bruckmaier. “Natürliche
Häufigkeiten als numerische Darstellungsart von Anteilen und Unsicherheit – Forschungsdesiderate
und einige Antworten Natural Frequencies as Numerical Representation of Proportions
and Uncertainty—Research Desiderata and Some Answers.” Journal für Mathematik-Didaktik
41, no. 2 (2020): 485–521. https://doi.org/10.1007/s13138-019-00156-w.'
ieee: 'S. Krauss, P. Weber, K. Binder, and G. Bruckmaier, “Natürliche Häufigkeiten
als numerische Darstellungsart von Anteilen und Unsicherheit – Forschungsdesiderate
und einige Antworten Natural Frequencies as Numerical Representation of Proportions
and Uncertainty—Research Desiderata and Some Answers,” Journal für Mathematik-Didaktik,
vol. 41, no. 2, pp. 485–521, 2020, doi: 10.1007/s13138-019-00156-w.'
mla: Krauss, Stefan, et al. “Natürliche Häufigkeiten als numerische Darstellungsart
von Anteilen und Unsicherheit – Forschungsdesiderate und einige Antworten Natural
Frequencies as Numerical Representation of Proportions and Uncertainty—Research
Desiderata and Some Answers.” Journal für Mathematik-Didaktik, vol. 41,
no. 2, Springer Science and Business Media LLC, 2020, pp. 485–521, doi:10.1007/s13138-019-00156-w.
short: S. Krauss, P. Weber, K. Binder, G. Bruckmaier, Journal für Mathematik-Didaktik
41 (2020) 485–521.
date_created: 2025-04-08T11:31:24Z
date_updated: 2025-04-12T18:11:46Z
doi: 10.1007/s13138-019-00156-w
intvolume: ' 41'
issue: '2'
language:
- iso: ger
page: 485-521
publication: Journal für Mathematik-Didaktik
publication_identifier:
issn:
- 0173-5322
- 1869-2699
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Natürliche Häufigkeiten als numerische Darstellungsart von Anteilen und Unsicherheit
– Forschungsdesiderate und einige Antworten Natural Frequencies as Numerical Representation
of Proportions and Uncertainty—Research Desiderata and Some Answers
type: journal_article
user_id: '83381'
volume: 41
year: '2020'
...
---
_id: '59424'
author:
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Patrick
full_name: Wiesner, Patrick
last_name: Wiesner
citation:
ama: 'Binder K, Krauss S, Wiesner P. A New Visualization for Probabilistic Situations
Containing Two Binary Events: The Frequency Net. Frontiers in Psychology.
2020;11. doi:10.3389/fpsyg.2020.00750'
apa: 'Binder, K., Krauss, S., & Wiesner, P. (2020). A New Visualization for
Probabilistic Situations Containing Two Binary Events: The Frequency Net. Frontiers
in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.00750'
bibtex: '@article{Binder_Krauss_Wiesner_2020, title={A New Visualization for Probabilistic
Situations Containing Two Binary Events: The Frequency Net}, volume={11}, DOI={10.3389/fpsyg.2020.00750},
journal={Frontiers in Psychology}, publisher={Frontiers Media SA}, author={Binder,
Karin and Krauss, Stefan and Wiesner, Patrick}, year={2020} }'
chicago: 'Binder, Karin, Stefan Krauss, and Patrick Wiesner. “A New Visualization
for Probabilistic Situations Containing Two Binary Events: The Frequency Net.”
Frontiers in Psychology 11 (2020). https://doi.org/10.3389/fpsyg.2020.00750.'
ieee: 'K. Binder, S. Krauss, and P. Wiesner, “A New Visualization for Probabilistic
Situations Containing Two Binary Events: The Frequency Net,” Frontiers in Psychology,
vol. 11, 2020, doi: 10.3389/fpsyg.2020.00750.'
mla: 'Binder, Karin, et al. “A New Visualization for Probabilistic Situations Containing
Two Binary Events: The Frequency Net.” Frontiers in Psychology, vol. 11,
Frontiers Media SA, 2020, doi:10.3389/fpsyg.2020.00750.'
short: K. Binder, S. Krauss, P. Wiesner, Frontiers in Psychology 11 (2020).
date_created: 2025-04-08T11:28:05Z
date_updated: 2025-04-12T18:11:34Z
doi: 10.3389/fpsyg.2020.00750
intvolume: ' 11'
language:
- iso: eng
publication: Frontiers in Psychology
publication_identifier:
issn:
- 1664-1078
publication_status: published
publisher: Frontiers Media SA
status: public
title: 'A New Visualization for Probabilistic Situations Containing Two Binary Events:
The Frequency Net'
type: journal_article
user_id: '83381'
volume: 11
year: '2020'
...
---
_id: '59989'
author:
- first_name: Raphael
full_name: Müller, Raphael
id: '55246'
last_name: Müller
- first_name: Jürgen
full_name: Klüners, Jürgen
last_name: Klüners
citation:
ama: Müller R, Klüners J. The conductor density of local function fields with abelian
Galois group. Journal of Number Theory. 2020;212.
apa: Müller, R., & Klüners, J. (2020). The conductor density of local function
fields with abelian Galois group. Journal of Number Theory, 212.
bibtex: '@article{Müller_Klüners_2020, title={The conductor density of local function
fields with abelian Galois group}, volume={212}, journal={Journal of Number Theory},
author={Müller, Raphael and Klüners, Jürgen}, year={2020} }'
chicago: Müller, Raphael, and Jürgen Klüners. “The Conductor Density of Local Function
Fields with Abelian Galois Group.” Journal of Number Theory 212 (2020).
ieee: R. Müller and J. Klüners, “The conductor density of local function fields
with abelian Galois group,” Journal of Number Theory, vol. 212, 2020.
mla: Müller, Raphael, and Jürgen Klüners. “The Conductor Density of Local Function
Fields with Abelian Galois Group.” Journal of Number Theory, vol. 212,
2020.
short: R. Müller, J. Klüners, Journal of Number Theory 212 (2020).
date_created: 2025-05-19T08:31:53Z
date_updated: 2025-06-13T08:15:14Z
department:
- _id: '43'
intvolume: ' 212'
language:
- iso: eng
publication: Journal of Number Theory
related_material:
link:
- relation: earlier_version
url: https://arxiv.org/abs/1904.02573
status: public
title: The conductor density of local function fields with abelian Galois group
type: journal_article
user_id: '82981'
volume: 212
year: '2020'
...
---
_id: '59428'
author:
- first_name: Georg
full_name: Bruckmaier, Georg
last_name: Bruckmaier
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Han-Min
full_name: Kufner, Han-Min
last_name: Kufner
citation:
ama: Bruckmaier G, Binder K, Krauss S, Kufner H-M. An Eye-Tracking Study of Statistical
Reasoning With Tree Diagrams and 2 × 2 Tables. Frontiers in Psychology.
2019;10. doi:10.3389/fpsyg.2019.00632
apa: Bruckmaier, G., Binder, K., Krauss, S., & Kufner, H.-M. (2019). An Eye-Tracking
Study of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables. Frontiers
in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.00632
bibtex: '@article{Bruckmaier_Binder_Krauss_Kufner_2019, title={An Eye-Tracking Study
of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables}, volume={10}, DOI={10.3389/fpsyg.2019.00632},
journal={Frontiers in Psychology}, publisher={Frontiers Media SA}, author={Bruckmaier,
Georg and Binder, Karin and Krauss, Stefan and Kufner, Han-Min}, year={2019} }'
chicago: Bruckmaier, Georg, Karin Binder, Stefan Krauss, and Han-Min Kufner. “An
Eye-Tracking Study of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables.”
Frontiers in Psychology 10 (2019). https://doi.org/10.3389/fpsyg.2019.00632.
ieee: 'G. Bruckmaier, K. Binder, S. Krauss, and H.-M. Kufner, “An Eye-Tracking Study
of Statistical Reasoning With Tree Diagrams and 2 × 2 Tables,” Frontiers in
Psychology, vol. 10, 2019, doi: 10.3389/fpsyg.2019.00632.'
mla: Bruckmaier, Georg, et al. “An Eye-Tracking Study of Statistical Reasoning With
Tree Diagrams and 2 × 2 Tables.” Frontiers in Psychology, vol. 10, Frontiers
Media SA, 2019, doi:10.3389/fpsyg.2019.00632.
short: G. Bruckmaier, K. Binder, S. Krauss, H.-M. Kufner, Frontiers in Psychology
10 (2019).
date_created: 2025-04-08T11:29:36Z
date_updated: 2025-04-12T18:11:03Z
doi: 10.3389/fpsyg.2019.00632
intvolume: ' 10'
language:
- iso: eng
publication: Frontiers in Psychology
publication_identifier:
issn:
- 1664-1078
publication_status: published
publisher: Frontiers Media SA
status: public
title: An Eye-Tracking Study of Statistical Reasoning With Tree Diagrams and 2 × 2
Tables
type: journal_article
user_id: '83381'
volume: 10
year: '2019'
...
---
_id: '59425'
author:
- first_name: Patrick
full_name: Weber, Patrick
last_name: Weber
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
citation:
ama: 'Weber P, Binder K, Krauss S. Why Can Only 24% Solve Bayesian Reasoning Problems
in Natural Frequencies: Frequency Phobia in Spite of Probability Blindness. Frontiers
in Psychology. 2018;9. doi:10.3389/fpsyg.2018.01833'
apa: 'Weber, P., Binder, K., & Krauss, S. (2018). Why Can Only 24% Solve Bayesian
Reasoning Problems in Natural Frequencies: Frequency Phobia in Spite of Probability
Blindness. Frontiers in Psychology, 9. https://doi.org/10.3389/fpsyg.2018.01833'
bibtex: '@article{Weber_Binder_Krauss_2018, title={Why Can Only 24% Solve Bayesian
Reasoning Problems in Natural Frequencies: Frequency Phobia in Spite of Probability
Blindness}, volume={9}, DOI={10.3389/fpsyg.2018.01833},
journal={Frontiers in Psychology}, publisher={Frontiers Media SA}, author={Weber,
Patrick and Binder, Karin and Krauss, Stefan}, year={2018} }'
chicago: 'Weber, Patrick, Karin Binder, and Stefan Krauss. “Why Can Only 24% Solve
Bayesian Reasoning Problems in Natural Frequencies: Frequency Phobia in Spite
of Probability Blindness.” Frontiers in Psychology 9 (2018). https://doi.org/10.3389/fpsyg.2018.01833.'
ieee: 'P. Weber, K. Binder, and S. Krauss, “Why Can Only 24% Solve Bayesian Reasoning
Problems in Natural Frequencies: Frequency Phobia in Spite of Probability Blindness,”
Frontiers in Psychology, vol. 9, 2018, doi: 10.3389/fpsyg.2018.01833.'
mla: 'Weber, Patrick, et al. “Why Can Only 24% Solve Bayesian Reasoning Problems
in Natural Frequencies: Frequency Phobia in Spite of Probability Blindness.” Frontiers
in Psychology, vol. 9, Frontiers Media SA, 2018, doi:10.3389/fpsyg.2018.01833.'
short: P. Weber, K. Binder, S. Krauss, Frontiers in Psychology 9 (2018).
date_created: 2025-04-08T11:28:23Z
date_updated: 2025-04-12T18:10:03Z
doi: 10.3389/fpsyg.2018.01833
intvolume: ' 9'
language:
- iso: eng
publication: Frontiers in Psychology
publication_identifier:
issn:
- 1664-1078
publication_status: published
publisher: Frontiers Media SA
status: public
title: 'Why Can Only 24% Solve Bayesian Reasoning Problems in Natural Frequencies:
Frequency Phobia in Spite of Probability Blindness'
type: journal_article
user_id: '83381'
volume: 9
year: '2018'
...
---
_id: '59426'
article_number: e0195029
author:
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Georg
full_name: Bruckmaier, Georg
last_name: Bruckmaier
- first_name: Jörg
full_name: Marienhagen, Jörg
last_name: Marienhagen
citation:
ama: 'Binder K, Krauss S, Bruckmaier G, Marienhagen J. Visualizing the Bayesian
2-test case: The effect of tree diagrams on medical decision making. PLOS ONE.
2018;13(3). doi:10.1371/journal.pone.0195029'
apa: 'Binder, K., Krauss, S., Bruckmaier, G., & Marienhagen, J. (2018). Visualizing
the Bayesian 2-test case: The effect of tree diagrams on medical decision making.
PLOS ONE, 13(3), Article e0195029. https://doi.org/10.1371/journal.pone.0195029'
bibtex: '@article{Binder_Krauss_Bruckmaier_Marienhagen_2018, title={Visualizing
the Bayesian 2-test case: The effect of tree diagrams on medical decision making},
volume={13}, DOI={10.1371/journal.pone.0195029},
number={3e0195029}, journal={PLOS ONE}, publisher={Public Library of Science (PLoS)},
author={Binder, Karin and Krauss, Stefan and Bruckmaier, Georg and Marienhagen,
Jörg}, year={2018} }'
chicago: 'Binder, Karin, Stefan Krauss, Georg Bruckmaier, and Jörg Marienhagen.
“Visualizing the Bayesian 2-Test Case: The Effect of Tree Diagrams on Medical
Decision Making.” PLOS ONE 13, no. 3 (2018). https://doi.org/10.1371/journal.pone.0195029.'
ieee: 'K. Binder, S. Krauss, G. Bruckmaier, and J. Marienhagen, “Visualizing the
Bayesian 2-test case: The effect of tree diagrams on medical decision making,”
PLOS ONE, vol. 13, no. 3, Art. no. e0195029, 2018, doi: 10.1371/journal.pone.0195029.'
mla: 'Binder, Karin, et al. “Visualizing the Bayesian 2-Test Case: The Effect of
Tree Diagrams on Medical Decision Making.” PLOS ONE, vol. 13, no. 3, e0195029,
Public Library of Science (PLoS), 2018, doi:10.1371/journal.pone.0195029.'
short: K. Binder, S. Krauss, G. Bruckmaier, J. Marienhagen, PLOS ONE 13 (2018).
date_created: 2025-04-08T11:28:38Z
date_updated: 2025-04-12T18:10:53Z
doi: 10.1371/journal.pone.0195029
intvolume: ' 13'
issue: '3'
language:
- iso: eng
publication: PLOS ONE
publication_identifier:
issn:
- 1932-6203
publication_status: published
publisher: Public Library of Science (PLoS)
status: public
title: 'Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical
decision making'
type: journal_article
user_id: '83381'
volume: 13
year: '2018'
...
---
_id: '59430'
article_type: original
author:
- first_name: Sven
full_name: Hilbert, Sven
last_name: Hilbert
- first_name: Georg
full_name: Bruckmaier, Georg
last_name: Bruckmaier
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Markus
full_name: Bühner, Markus
last_name: Bühner
citation:
ama: Hilbert S, Bruckmaier G, Binder K, Krauss S, Bühner M. Prediction of elementary
mathematics grades by cognitive abilities. European Journal of Psychology of
Education. 2018;34(3):665-683. doi:10.1007/s10212-018-0394-9
apa: Hilbert, S., Bruckmaier, G., Binder, K., Krauss, S., & Bühner, M. (2018).
Prediction of elementary mathematics grades by cognitive abilities. European
Journal of Psychology of Education, 34(3), 665–683. https://doi.org/10.1007/s10212-018-0394-9
bibtex: '@article{Hilbert_Bruckmaier_Binder_Krauss_Bühner_2018, title={Prediction
of elementary mathematics grades by cognitive abilities}, volume={34}, DOI={10.1007/s10212-018-0394-9},
number={3}, journal={European Journal of Psychology of Education}, publisher={Springer
Science and Business Media LLC}, author={Hilbert, Sven and Bruckmaier, Georg and
Binder, Karin and Krauss, Stefan and Bühner, Markus}, year={2018}, pages={665–683}
}'
chicago: 'Hilbert, Sven, Georg Bruckmaier, Karin Binder, Stefan Krauss, and Markus
Bühner. “Prediction of Elementary Mathematics Grades by Cognitive Abilities.”
European Journal of Psychology of Education 34, no. 3 (2018): 665–83. https://doi.org/10.1007/s10212-018-0394-9.'
ieee: 'S. Hilbert, G. Bruckmaier, K. Binder, S. Krauss, and M. Bühner, “Prediction
of elementary mathematics grades by cognitive abilities,” European Journal
of Psychology of Education, vol. 34, no. 3, pp. 665–683, 2018, doi: 10.1007/s10212-018-0394-9.'
mla: Hilbert, Sven, et al. “Prediction of Elementary Mathematics Grades by Cognitive
Abilities.” European Journal of Psychology of Education, vol. 34, no. 3,
Springer Science and Business Media LLC, 2018, pp. 665–83, doi:10.1007/s10212-018-0394-9.
short: S. Hilbert, G. Bruckmaier, K. Binder, S. Krauss, M. Bühner, European Journal
of Psychology of Education 34 (2018) 665–683.
date_created: 2025-04-08T11:30:19Z
date_updated: 2025-05-17T18:38:46Z
ddc:
- '370'
doi: 10.1007/s10212-018-0394-9
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2025-05-17T18:38:26Z
date_updated: 2025-05-17T18:38:26Z
file_id: '59934'
file_name: Hilbert Bruckmaier Binder Krauss Bühner 2018.pdf
file_size: 707288
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intvolume: ' 34'
issue: '3'
language:
- iso: eng
page: 665-683
publication: European Journal of Psychology of Education
publication_identifier:
issn:
- 0256-2928
- 1878-5174
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Prediction of elementary mathematics grades by cognitive abilities
type: journal_article
user_id: '83381'
volume: 34
year: '2018'
...
---
_id: '59427'
author:
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Stefan
full_name: Krauss, Stefan
last_name: Krauss
- first_name: Sven
full_name: Hilbert, Sven
last_name: Hilbert
- first_name: Martin
full_name: Brunner, Martin
last_name: Brunner
- first_name: Yvonne
full_name: Anders, Yvonne
last_name: Anders
- first_name: Mareike
full_name: Kunter, Mareike
last_name: Kunter
citation:
ama: 'Binder K, Krauss S, Hilbert S, Brunner M, Anders Y, Kunter M. Diagnostic Skills
of Mathematics Teachers in the COACTIV Study. In: Diagnostic Competence of
Mathematics Teachers. Springer International Publishing; 2017. doi:10.1007/978-3-319-66327-2_2'
apa: Binder, K., Krauss, S., Hilbert, S., Brunner, M., Anders, Y., & Kunter,
M. (2017). Diagnostic Skills of Mathematics Teachers in the COACTIV Study. In
Diagnostic Competence of Mathematics Teachers. Springer International Publishing.
https://doi.org/10.1007/978-3-319-66327-2_2
bibtex: '@inbook{Binder_Krauss_Hilbert_Brunner_Anders_Kunter_2017, place={Cham},
title={Diagnostic Skills of Mathematics Teachers in the COACTIV Study}, DOI={10.1007/978-3-319-66327-2_2},
booktitle={Diagnostic Competence of Mathematics Teachers}, publisher={Springer
International Publishing}, author={Binder, Karin and Krauss, Stefan and Hilbert,
Sven and Brunner, Martin and Anders, Yvonne and Kunter, Mareike}, year={2017}
}'
chicago: 'Binder, Karin, Stefan Krauss, Sven Hilbert, Martin Brunner, Yvonne Anders,
and Mareike Kunter. “Diagnostic Skills of Mathematics Teachers in the COACTIV
Study.” In Diagnostic Competence of Mathematics Teachers. Cham: Springer
International Publishing, 2017. https://doi.org/10.1007/978-3-319-66327-2_2.'
ieee: 'K. Binder, S. Krauss, S. Hilbert, M. Brunner, Y. Anders, and M. Kunter, “Diagnostic
Skills of Mathematics Teachers in the COACTIV Study,” in Diagnostic Competence
of Mathematics Teachers, Cham: Springer International Publishing, 2017.'
mla: Binder, Karin, et al. “Diagnostic Skills of Mathematics Teachers in the COACTIV
Study.” Diagnostic Competence of Mathematics Teachers, Springer International
Publishing, 2017, doi:10.1007/978-3-319-66327-2_2.
short: 'K. Binder, S. Krauss, S. Hilbert, M. Brunner, Y. Anders, M. Kunter, in:
Diagnostic Competence of Mathematics Teachers, Springer International Publishing,
Cham, 2017.'
date_created: 2025-04-08T11:29:08Z
date_updated: 2025-04-12T18:09:36Z
doi: 10.1007/978-3-319-66327-2_2
language:
- iso: eng
place: Cham
publication: Diagnostic Competence of Mathematics Teachers
publication_identifier:
isbn:
- '9783319663258'
- '9783319663272'
publication_status: published
publisher: Springer International Publishing
status: public
title: Diagnostic Skills of Mathematics Teachers in the COACTIV Study
type: book_chapter
user_id: '83381'
year: '2017'
...