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Tree Diagrams and Unit Squares 4.0: Digitizing Stochastic Classes with the Didactic Modeling Tool ProVis

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Domain-Specific Conceptual Modeling

Abstract

ProVisProbability Visualized—is a tool for constructing tree diagrams and unit squares. Tree diagrams are often used in mathematics education to structure multi-stage random experiments. Unit squares illustrate dependencies between two-dimensional characteristics and their values. The intention of this project is to foster the use of digital tree diagrams and unit squares in the classroom. ProVis exempts the students from operating and gives them opportunity to model, interpret, and analyse complex statistical situations. For the development of ProVis, seven requirements based on didactic considerations are proposed, which a statistical education software should fulfil. The metamodel of the method underlying ProVis is presented. Also the related functionalities are outlined. The realization of the metamodel and the implementation of the involved concepts appear to be complex in construction as well as in interdependence. Nevertheless, it was the intention of the developers to realize a software, which is quite easy to handle. For this reason, a convenient interface is offered. The features of ProVis are demonstrated by discussing a case study in a recent context. ProVis is implemented on the metamodeling platform ADOxx. It is available for free on the OMiLAB-Austria homepage.

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References

  1. Aue, V., Bleier, G., Lechner, J., Malle, G.: Handreichung zum Lehrplan Mathematik 2016 Oberstufe AHS (Secondary level two). Bundesministerium für Bildung Lehrplangruppe Mathematik AHS Oberstufe, Vienna (2016)

    Google Scholar 

  2. Bennett, K.: Teaching the monty hall dilemma to explore decision-making, probability, and regret in behavioralscience classrooms. Int. J. Scholarship Teach. Learn. 12(2), Article 13 (2018). https://doi.org/10.20429/ijsotl.2018.120213

  3. Binder, K., Krauss, S., Bruckmaier, G.: Effects of visualizing statistical information—an empirical study on tree diagrams and 2—2 tables. Front. Psychol. 6, Article 1186 (2015). https://doi.org/10.3389/fpsyg.2015.01186

    Article  Google Scholar 

  4. Böcherer-Linder, K., Eichler, A., Vogel, M.: Visualising conditional probabilities—Three perspectives on unit squares and tree diagrams. In: Batanero, C., Chernoff, E. (eds.) Teaching and Learning Stochastics, pp. 73-88. ICME-13 Monographs. Springer, Cham. (2018). https://doi.org/10.1007/978-3-319-72871-1_5

    Google Scholar 

  5. Brase, C.H., Brase, C.P.: Understanding Basic Statistics, 8th edn. Cengage, Boston (2019)

    Google Scholar 

  6. Döller, V.: ProVis—Probability Visualized: Technologische Unterstützung für den Einsatz von Einheitsquadraten und Baumdiagrammen im Stochastikunterricht. University of Vienna: Diploma Thesis (2020). http://othes.univie.ac.at/61461/

    Google Scholar 

  7. Döller, V.: ProVis—probability visualized: a modeling tool for teaching stochastics. In: Companion Proceedings of Modellierung 2020 Short, Workshop and Tools & Demo Papers. CEUR Workshop Proceedings, vol. 2542, pp. 222–226. CEUR-WS.org (2020)

    Google Scholar 

  8. Döller, V., Götz, S.: Baumdiagramme und Einheitsquadrate 4.0. Stochastik in der Schule 41(3), 9–19 (2021)

    Google Scholar 

  9. Eichler, A., Vogel, M.: Leitidee Daten und Zufall: Von konkreten Beispielen zur Didaktik der Stochastik, 2nd edn. Springer Fachmedien, Wiesbaden (2013)

    Google Scholar 

  10. Gesamte Rechtsvorschrift für Lehrpläne—allgemeinbildende höhere Schulen, Fassung vom 16.02.2021, pp. 79-85 (Secondary level one). Bundesministerium Bildung, Wissenschaft und Forschung, Vienna (2021)

    Google Scholar 

  11. Johnston, H.: The Spiral Curriculum. Research into Practice. Education Partnerships, (2012) https://eric.ed.gov/?id=ED538282

  12. Karagiannis, D., Burzynski, P., Utz, W., Buchmann, R.A.: A metamodeling approach to support the engineering of modeling method requirements. In: 27th IEEE International Requirements Engineering Conference, pp. 199–210 (2019)

    Google Scholar 

  13. Olofsson, P., Andersson, M.: Probability, Statistics, and Stochastic Processes, 2nd edn. Wiley, New York (2012)

    Book  Google Scholar 

  14. Russel, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 4th edn. Pearson Education, Harlow (2021)

    Google Scholar 

  15. Winter, H.: Entdeckendes Lernen im Mathematikunterricht. Einblicke in die Ideengeschichte und ihre Bedeutung für die Pädagogik, 3rd edn. Springer Spektrum, Wiesbaden (2016)

    Google Scholar 

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Döller, V., Götz, S. (2022). Tree Diagrams and Unit Squares 4.0: Digitizing Stochastic Classes with the Didactic Modeling Tool ProVis . In: Karagiannis, D., Lee, M., Hinkelmann, K., Utz, W. (eds) Domain-Specific Conceptual Modeling. Springer, Cham. https://doi.org/10.1007/978-3-030-93547-4_21

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  • DOI: https://doi.org/10.1007/978-3-030-93547-4_21

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