Datum
2024-01-27Autor
Büchter, TheresaEichler, AndreasBöcherer-Linder, KatharinaVogel, MarkusBinder, KarinKrauss, StefanSteib, NicoleMetadata
Zur Langanzeige
Aufsatz
Covariational reasoning in Bayesian situations
Zusammenfassung
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 changes of parameters 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 covariational reasoning in Bayesian situations is studied. Prospective teachers (N=173) for primary (N=112) and secondary (N=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.
Zitierform
In: Educational Studies in Mathematics Volume 115 / Issue 3 (2024-01-27) , S. 481 - 505 ; eissn:1573-0816Förderhinweis
Gefördert im Rahmen des Projekts DEALZitieren
@article{doi:10.17170/kobra-202404109950,
author={Büchter, Theresa and Eichler, Andreas and Böcherer-Linder, Katharina and Vogel, Markus and Binder, Karin and Krauss, Stefan and Steib, Nicole},
title={Covariational reasoning in Bayesian situations},
journal={Educational Studies in Mathematics},
year={2024}
}
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2024-04-11T12:35:18Z 2024-04-11T12:35:18Z 2024-01-27 doi:10.17170/kobra-202404109950 http://hdl.handle.net/123456789/15650 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Covariational reasoning Bayesian reasoning Double-tree Unit square Natural frequencies SOLO taxonomy 510 Covariational reasoning in Bayesian situations Aufsatz 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 changes of parameters 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 covariational reasoning in Bayesian situations is studied. Prospective teachers (N=173) for primary (N=112) and secondary (N=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. open access Büchter, Theresa Eichler, Andreas Böcherer-Linder, Katharina Vogel, Markus Binder, Karin Krauss, Stefan Steib, Nicole doi:10.1007/s10649-023-10274-5 Mathematik Denken Bayes-Verfahren publishedVersion eissn:1573-0816 Issue 3 Educational Studies in Mathematics 481 - 505 Volume 115 false
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