---
_id: '59438'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>It has been established
    that, in Bayesian tasks, performance and typical errors in <jats:italic>reading</jats:italic>
    information from filled visualizations depend both on the type of the provided
    visualization and information format. However, apart from reading visualizations,
    students should also be able to create visualizations on their own and successfully
    use them as heuristic tools in modeling tasks. In this paper, we first want to
    broaden the view on Bayesian reasoning to probabilistic tasks with two binary
    events in general and embed the whole process of solving these tasks using probabilistic
    visualizations in a modified modeling framework. Thereby, it becomes apparent
    that most of the steps remained untouched by existing research. Second, in the
    present empirical study, we focused on one part of the largely unexplored creation
    process and examined <jats:italic>entering</jats:italic> statistical information
    into empty visualizations as heuristic tools. <jats:italic>N</jats:italic> = 172
    participants had to enter conditional and joint probabilities or the corresponding
    frequencies into empty visualizations in a paper-and-pencil test. We analyze (a)
    students’ performance when entering information in visualizations and (b) typical
    errors, both dependent on the <jats:italic>information format</jats:italic> (probabilities
    vs. natural frequencies), which <jats:italic>empty visualization structure</jats:italic>
    (2⨯2 table, double tree, net diagram) was provided, and <jats:italic>type of information</jats:italic>
    (conditional vs. joint information). The well-known positive effect of natural
    frequencies on participants’ performance was evident when entering conditional
    information into 2⨯2 tables and net diagrams. However, with respect to joint information,
    no superior effect of frequencies was observed. Furthermore, the theoretical implementation
    of our research in a modeling cycle allows us to identify desiderata for future
    research.</jats:p>"
author:
- first_name: Michael
  full_name: Rößner, Michael
  last_name: Rößner
- first_name: Karin
  full_name: Binder, Karin
  id: '83381'
  last_name: Binder
- first_name: Corbinian
  full_name: Geier, Corbinian
  last_name: Geier
- first_name: Stefan
  full_name: Krauss, Stefan
  last_name: Krauss
citation:
  ama: Rößner M, Binder K, Geier C, Krauss S. Students’ performance and typical errors
    in filling empty probabilistic visualizations with probabilities or frequencies.
    <i>Educational Studies in Mathematics</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>
  apa: Rößner, M., Binder, K., Geier, C., &#38; Krauss, S. (2025). Students’ performance
    and typical errors in filling empty probabilistic visualizations with probabilities
    or frequencies. <i>Educational Studies in Mathematics</i>. <a href="https://doi.org/10.1007/s10649-024-10372-y">https://doi.org/10.1007/s10649-024-10372-y</a>
  bibtex: '@article{Rößner_Binder_Geier_Krauss_2025, title={Students’ performance
    and typical errors in filling empty probabilistic visualizations with probabilities
    or frequencies}, DOI={<a href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>},
    journal={Educational Studies in Mathematics}, publisher={Springer Science and
    Business Media LLC}, author={Rößner, Michael and Binder, Karin and Geier, Corbinian
    and Krauss, Stefan}, year={2025} }'
  chicago: Rößner, Michael, Karin Binder, Corbinian Geier, and Stefan Krauss. “Students’
    Performance and Typical Errors in Filling Empty Probabilistic Visualizations with
    Probabilities or Frequencies.” <i>Educational Studies in Mathematics</i>, 2025.
    <a href="https://doi.org/10.1007/s10649-024-10372-y">https://doi.org/10.1007/s10649-024-10372-y</a>.
  ieee: 'M. Rößner, K. Binder, C. Geier, and S. Krauss, “Students’ performance and
    typical errors in filling empty probabilistic visualizations with probabilities
    or frequencies,” <i>Educational Studies in Mathematics</i>, 2025, doi: <a href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>.'
  mla: Rößner, Michael, et al. “Students’ Performance and Typical Errors in Filling
    Empty Probabilistic Visualizations with Probabilities or Frequencies.” <i>Educational
    Studies in Mathematics</i>, Springer Science and Business Media LLC, 2025, doi:<a
    href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>.
  short: M. Rößner, K. Binder, C. Geier, S. Krauss, Educational Studies in Mathematics
    (2025).
date_created: 2025-04-08T11:35:36Z
date_updated: 2025-05-17T18:05:23Z
ddc:
- '370'
doi: 10.1007/s10649-024-10372-y
file:
- access_level: closed
  content_type: application/pdf
  creator: binder
  date_created: 2025-05-17T18:05:03Z
  date_updated: 2025-05-17T18:05:03Z
  file_id: '59926'
  file_name: Rößner et al. 2025 Typical student errors.pdf
  file_size: 2982734
  relation: main_file
  success: 1
file_date_updated: 2025-05-17T18:05:03Z
language:
- iso: eng
publication: Educational Studies in Mathematics
publication_identifier:
  issn:
  - 0013-1954
  - 1573-0816
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Students’ performance and typical errors in filling empty probabilistic visualizations
  with probabilities or frequencies
type: journal_article
user_id: '83381'
year: '2025'
...
---
_id: '60602'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>It has been established
    that, in Bayesian tasks, performance and typical errors in <jats:italic>reading</jats:italic>
    information from filled visualizations depend both on the type of the provided
    visualization and information format. However, apart from reading visualizations,
    students should also be able to create visualizations on their own and successfully
    use them as heuristic tools in modeling tasks. In this paper, we first want to
    broaden the view on Bayesian reasoning to probabilistic tasks with two binary
    events in general and embed the whole process of solving these tasks using probabilistic
    visualizations in a modified modeling framework. Thereby, it becomes apparent
    that most of the steps remained untouched by existing research. Second, in the
    present empirical study, we focused on one part of the largely unexplored creation
    process and examined <jats:italic>entering</jats:italic> statistical information
    into empty visualizations as heuristic tools. <jats:italic>N</jats:italic> = 172
    participants had to enter conditional and joint probabilities or the corresponding
    frequencies into empty visualizations in a paper-and-pencil test. We analyze (a)
    students’ performance when entering information in visualizations and (b) typical
    errors, both dependent on the <jats:italic>information format</jats:italic> (probabilities
    vs. natural frequencies), which <jats:italic>empty visualization structure</jats:italic>
    (2⨯2 table, double tree, net diagram) was provided, and <jats:italic>type of information</jats:italic>
    (conditional vs. joint information). The well-known positive effect of natural
    frequencies on participants’ performance was evident when entering conditional
    information into 2⨯2 tables and net diagrams. However, with respect to joint information,
    no superior effect of frequencies was observed. Furthermore, the theoretical implementation
    of our research in a modeling cycle allows us to identify desiderata for future
    research.</jats:p>"
author:
- first_name: Michael
  full_name: Rößner, Michael
  last_name: Rößner
- first_name: Karin
  full_name: Binder, Karin
  last_name: Binder
- first_name: Corbinian
  full_name: Geier, Corbinian
  last_name: Geier
- first_name: Stefan
  full_name: Krauss, Stefan
  last_name: Krauss
citation:
  ama: Rößner M, Binder K, Geier C, Krauss S. Students’ performance and typical errors
    in filling empty probabilistic visualizations with probabilities or frequencies.
    <i>Educational Studies in Mathematics</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>
  apa: Rößner, M., Binder, K., Geier, C., &#38; Krauss, S. (2025). Students’ performance
    and typical errors in filling empty probabilistic visualizations with probabilities
    or frequencies. <i>Educational Studies in Mathematics</i>. <a href="https://doi.org/10.1007/s10649-024-10372-y">https://doi.org/10.1007/s10649-024-10372-y</a>
  bibtex: '@article{Rößner_Binder_Geier_Krauss_2025, title={Students’ performance
    and typical errors in filling empty probabilistic visualizations with probabilities
    or frequencies}, DOI={<a href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>},
    journal={Educational Studies in Mathematics}, publisher={Springer Science and
    Business Media LLC}, author={Rößner, Michael and Binder, Karin and Geier, Corbinian
    and Krauss, Stefan}, year={2025} }'
  chicago: Rößner, Michael, Karin Binder, Corbinian Geier, and Stefan Krauss. “Students’
    Performance and Typical Errors in Filling Empty Probabilistic Visualizations with
    Probabilities or Frequencies.” <i>Educational Studies in Mathematics</i>, 2025.
    <a href="https://doi.org/10.1007/s10649-024-10372-y">https://doi.org/10.1007/s10649-024-10372-y</a>.
  ieee: 'M. Rößner, K. Binder, C. Geier, and S. Krauss, “Students’ performance and
    typical errors in filling empty probabilistic visualizations with probabilities
    or frequencies,” <i>Educational Studies in Mathematics</i>, 2025, doi: <a href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>.'
  mla: Rößner, Michael, et al. “Students’ Performance and Typical Errors in Filling
    Empty Probabilistic Visualizations with Probabilities or Frequencies.” <i>Educational
    Studies in Mathematics</i>, Springer Science and Business Media LLC, 2025, doi:<a
    href="https://doi.org/10.1007/s10649-024-10372-y">10.1007/s10649-024-10372-y</a>.
  short: M. Rößner, K. Binder, C. Geier, S. Krauss, Educational Studies in Mathematics
    (2025).
date_created: 2025-07-14T12:26:14Z
date_updated: 2025-07-14T12:30:58Z
doi: 10.1007/s10649-024-10372-y
language:
- iso: eng
publication: Educational Studies in Mathematics
publication_identifier:
  issn:
  - 0013-1954
  - 1573-0816
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Students’ performance and typical errors in filling empty probabilistic visualizations
  with probabilities or frequencies
type: journal_article
user_id: '87801'
year: '2025'
...
---
_id: '59435'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Previous studies on Bayesian situations,
    in which probabilistic information is used to update the probability of a hypothesis,
    have often focused on the calculation of a posterior probability. We argue that
    for an in-depth understanding of Bayesian situations, it is (apart from mere calculation)
    also necessary to be able to evaluate the effect of <jats:italic>changes of parameters</jats:italic>
    in the Bayesian situation and the consequences, e.g., for the posterior probability.
    Thus, by understanding Bayes’ formula as a function, the concept of covariation
    is introduced as an extension of conventional Bayesian reasoning, and <jats:italic>covariational
    reasoning</jats:italic> in Bayesian situations is studied. Prospective teachers
    (<jats:italic>N</jats:italic>=173) for primary (<jats:italic>N</jats:italic>=112)
    and secondary (<jats:italic>N</jats:italic>=61) school from two German universities
    participated in the study and reasoned about covariation in Bayesian situations.
    In a mixed-methods approach, firstly, the elaborateness of prospective teachers’
    covariational reasoning is assessed by analysing the arguments qualitatively,
    using an adaption of the Structure of Observed Learning Outcome (SOLO) taxonomy.
    Secondly, the influence of possibly supportive variables on covariational reasoning
    is analysed quantitatively by checking whether (i) the changed parameter in the
    Bayesian situation (false-positive rate, true-positive rate or base rate), (ii)
    the visualisation depicting the Bayesian situation (double-tree vs. unit square)
    or (iii) the calculation (correct or incorrect) influences the SOLO level. The
    results show that among these three variables, only the changed parameter seems
    to influence the covariational reasoning. Implications are discussed.</jats:p>
article_type: original
author:
- first_name: Theresa
  full_name: Büchter, Theresa
  last_name: Büchter
- first_name: Andreas
  full_name: Eichler, Andreas
  last_name: Eichler
- first_name: Katharina
  full_name: Böcherer-Linder, Katharina
  last_name: Böcherer-Linder
- first_name: Markus
  full_name: Vogel, Markus
  last_name: Vogel
- first_name: Karin
  full_name: Binder, Karin
  id: '83381'
  last_name: Binder
- first_name: Stefan
  full_name: Krauss, Stefan
  last_name: Krauss
- first_name: Nicole
  full_name: Steib, Nicole
  last_name: Steib
citation:
  ama: Büchter T, Eichler A, Böcherer-Linder K, et al. Covariational reasoning in
    Bayesian situations. <i>Educational Studies in Mathematics</i>. 2024;115(3):481-505.
    doi:<a href="https://doi.org/10.1007/s10649-023-10274-5">10.1007/s10649-023-10274-5</a>
  apa: Büchter, T., Eichler, A., Böcherer-Linder, K., Vogel, M., Binder, K., Krauss,
    S., &#38; Steib, N. (2024). Covariational reasoning in Bayesian situations. <i>Educational
    Studies in Mathematics</i>, <i>115</i>(3), 481–505. <a href="https://doi.org/10.1007/s10649-023-10274-5">https://doi.org/10.1007/s10649-023-10274-5</a>
  bibtex: '@article{Büchter_Eichler_Böcherer-Linder_Vogel_Binder_Krauss_Steib_2024,
    title={Covariational reasoning in Bayesian situations}, volume={115}, DOI={<a
    href="https://doi.org/10.1007/s10649-023-10274-5">10.1007/s10649-023-10274-5</a>},
    number={3}, journal={Educational Studies in Mathematics}, publisher={Springer
    Science and Business Media LLC}, author={Büchter, Theresa and Eichler, Andreas
    and Böcherer-Linder, Katharina and Vogel, Markus and Binder, Karin and Krauss,
    Stefan and Steib, Nicole}, year={2024}, pages={481–505} }'
  chicago: 'Büchter, Theresa, Andreas Eichler, Katharina Böcherer-Linder, Markus Vogel,
    Karin Binder, Stefan Krauss, and Nicole Steib. “Covariational Reasoning in Bayesian
    Situations.” <i>Educational Studies in Mathematics</i> 115, no. 3 (2024): 481–505.
    <a href="https://doi.org/10.1007/s10649-023-10274-5">https://doi.org/10.1007/s10649-023-10274-5</a>.'
  ieee: 'T. Büchter <i>et al.</i>, “Covariational reasoning in Bayesian situations,”
    <i>Educational Studies in Mathematics</i>, vol. 115, no. 3, pp. 481–505, 2024,
    doi: <a href="https://doi.org/10.1007/s10649-023-10274-5">10.1007/s10649-023-10274-5</a>.'
  mla: Büchter, Theresa, et al. “Covariational Reasoning in Bayesian Situations.”
    <i>Educational Studies in Mathematics</i>, vol. 115, no. 3, Springer Science and
    Business Media LLC, 2024, pp. 481–505, doi:<a href="https://doi.org/10.1007/s10649-023-10274-5">10.1007/s10649-023-10274-5</a>.
  short: T. Büchter, A. Eichler, K. Böcherer-Linder, M. Vogel, K. Binder, S. Krauss,
    N. Steib, Educational Studies in Mathematics 115 (2024) 481–505.
date_created: 2025-04-08T11:34:19Z
date_updated: 2025-05-17T18:20:59Z
ddc:
- '370'
doi: 10.1007/s10649-023-10274-5
file:
- access_level: closed
  content_type: application/pdf
  creator: binder
  date_created: 2025-05-17T18:20:24Z
  date_updated: 2025-05-17T18:20:24Z
  file_id: '59929'
  file_name: Büchter et al. 2024 Covariational reasoning.pdf
  file_size: 2193461
  relation: main_file
  success: 1
file_date_updated: 2025-05-17T18:20:24Z
intvolume: '       115'
issue: '3'
language:
- iso: eng
page: 481-505
publication: Educational Studies in Mathematics
publication_identifier:
  issn:
  - 0013-1954
  - 1573-0816
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Covariational reasoning in Bayesian situations
type: journal_article
user_id: '83381'
volume: 115
year: '2024'
...
---
_id: '57558'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>Mathematical modelling emphasizes
    the connection between mathematics and reality — still, tasks are often exclusively
    introduced inside the classroom. The paper examines the potential of different
    task settings for mathematical modelling with real objects: outdoors at the real
    object itself, with photographs and with a 3D model representation. It is the
    aim of the study to analyze how far the mathematical modelling steps of students
    solving the tasks differ in comparison to the settings and representations. In
    a qualitative study, 19 lower secondary school students worked on tasks of all
    three settings in a Latin square design. Their working processes in the settings
    are compared with a special focus on the modelling steps Simplifying and Structuring,
    as well as Mathematizing. The analysis by means of activity diagrams and a qualitative
    content analysis shows that both steps are particularly relevant when students
    work with real objects — independent from the three settings. Still, differences
    in the actual activities could be observed in the students’ discussion on the
    appropriateness of a model and in dealing with inaccuracies at the real object.
    In addition, the process of data collection shows different procedures depending
    on the setting which presents each of them as an enrichment for the acquisition
    of modelling skills.</jats:p>'
author:
- first_name: Simone
  full_name: Jablonski, Simone
  last_name: Jablonski
citation:
  ama: Jablonski S. Is it all about the setting? — A comparison of mathematical modelling
    with real objects and their representation. <i>Educational Studies in Mathematics</i>.
    2023;113(2):307-330. doi:<a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>
  apa: Jablonski, S. (2023). Is it all about the setting? — A comparison of mathematical
    modelling with real objects and their representation. <i>Educational Studies in
    Mathematics</i>, <i>113</i>(2), 307–330. <a href="https://doi.org/10.1007/s10649-023-10215-2">https://doi.org/10.1007/s10649-023-10215-2</a>
  bibtex: '@article{Jablonski_2023, title={Is it all about the setting? — A comparison
    of mathematical modelling with real objects and their representation}, volume={113},
    DOI={<a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>},
    number={2}, journal={Educational Studies in Mathematics}, publisher={Springer
    Science and Business Media LLC}, author={Jablonski, Simone}, year={2023}, pages={307–330}
    }'
  chicago: 'Jablonski, Simone. “Is It All about the Setting? — A Comparison of Mathematical
    Modelling with Real Objects and Their Representation.” <i>Educational Studies
    in Mathematics</i> 113, no. 2 (2023): 307–30. <a href="https://doi.org/10.1007/s10649-023-10215-2">https://doi.org/10.1007/s10649-023-10215-2</a>.'
  ieee: 'S. Jablonski, “Is it all about the setting? — A comparison of mathematical
    modelling with real objects and their representation,” <i>Educational Studies
    in Mathematics</i>, vol. 113, no. 2, pp. 307–330, 2023, doi: <a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>.'
  mla: Jablonski, Simone. “Is It All about the Setting? — A Comparison of Mathematical
    Modelling with Real Objects and Their Representation.” <i>Educational Studies
    in Mathematics</i>, vol. 113, no. 2, Springer Science and Business Media LLC,
    2023, pp. 307–30, doi:<a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>.
  short: S. Jablonski, Educational Studies in Mathematics 113 (2023) 307–330.
date_created: 2024-12-04T10:46:36Z
date_updated: 2024-12-04T10:47:00Z
doi: 10.1007/s10649-023-10215-2
intvolume: '       113'
issue: '2'
language:
- iso: eng
page: 307-330
publication: Educational Studies in Mathematics
publication_identifier:
  issn:
  - 0013-1954
  - 1573-0816
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Is it all about the setting? — A comparison of mathematical modelling with
  real objects and their representation
type: journal_article
user_id: '111489'
volume: 113
year: '2023'
...
---
_id: '57556'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>Mathematical modelling emphasizes
    the connection between mathematics and reality — still, tasks are often exclusively
    introduced inside the classroom. The paper examines the potential of different
    task settings for mathematical modelling with real objects: outdoors at the real
    object itself, with photographs and with a 3D model representation. It is the
    aim of the study to analyze how far the mathematical modelling steps of students
    solving the tasks differ in comparison to the settings and representations. In
    a qualitative study, 19 lower secondary school students worked on tasks of all
    three settings in a Latin square design. Their working processes in the settings
    are compared with a special focus on the modelling steps Simplifying and Structuring,
    as well as Mathematizing. The analysis by means of activity diagrams and a qualitative
    content analysis shows that both steps are particularly relevant when students
    work with real objects — independent from the three settings. Still, differences
    in the actual activities could be observed in the students’ discussion on the
    appropriateness of a model and in dealing with inaccuracies at the real object.
    In addition, the process of data collection shows different procedures depending
    on the setting which presents each of them as an enrichment for the acquisition
    of modelling skills.</jats:p>'
author:
- first_name: Simone
  full_name: Jablonski, Simone
  last_name: Jablonski
citation:
  ama: Jablonski S. Is it all about the setting? — A comparison of mathematical modelling
    with real objects and their representation. <i>Educational Studies in Mathematics</i>.
    2023;113(2):307-330. doi:<a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>
  apa: Jablonski, S. (2023). Is it all about the setting? — A comparison of mathematical
    modelling with real objects and their representation. <i>Educational Studies in
    Mathematics</i>, <i>113</i>(2), 307–330. <a href="https://doi.org/10.1007/s10649-023-10215-2">https://doi.org/10.1007/s10649-023-10215-2</a>
  bibtex: '@article{Jablonski_2023, title={Is it all about the setting? — A comparison
    of mathematical modelling with real objects and their representation}, volume={113},
    DOI={<a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>},
    number={2}, journal={Educational Studies in Mathematics}, publisher={Springer
    Science and Business Media LLC}, author={Jablonski, Simone}, year={2023}, pages={307–330}
    }'
  chicago: 'Jablonski, Simone. “Is It All about the Setting? — A Comparison of Mathematical
    Modelling with Real Objects and Their Representation.” <i>Educational Studies
    in Mathematics</i> 113, no. 2 (2023): 307–30. <a href="https://doi.org/10.1007/s10649-023-10215-2">https://doi.org/10.1007/s10649-023-10215-2</a>.'
  ieee: 'S. Jablonski, “Is it all about the setting? — A comparison of mathematical
    modelling with real objects and their representation,” <i>Educational Studies
    in Mathematics</i>, vol. 113, no. 2, pp. 307–330, 2023, doi: <a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>.'
  mla: Jablonski, Simone. “Is It All about the Setting? — A Comparison of Mathematical
    Modelling with Real Objects and Their Representation.” <i>Educational Studies
    in Mathematics</i>, vol. 113, no. 2, Springer Science and Business Media LLC,
    2023, pp. 307–30, doi:<a href="https://doi.org/10.1007/s10649-023-10215-2">10.1007/s10649-023-10215-2</a>.
  short: S. Jablonski, Educational Studies in Mathematics 113 (2023) 307–330.
date_created: 2024-12-04T10:46:14Z
date_updated: 2025-12-17T08:56:50Z
doi: 10.1007/s10649-023-10215-2
intvolume: '       113'
issue: '2'
language:
- iso: eng
page: 307-330
publication: Educational Studies in Mathematics
publication_identifier:
  issn:
  - 0013-1954
  - 1573-0816
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Is it all about the setting? — A comparison of mathematical modelling with
  real objects and their representation
type: journal_article
user_id: '111489'
volume: 113
year: '2023'
...