Covariational reasoning in Bayesian situations

dc.date.accessioned2024-04-11T12:35:18Z
dc.date.available2024-04-11T12:35:18Z
dc.date.issued2024-01-27
dc.description.sponsorshipGefördert im Rahmen des Projekts DEAL
dc.identifierdoi:10.17170/kobra-202404109950
dc.identifier.urihttp://hdl.handle.net/123456789/15650
dc.language.isoeng
dc.relation.doidoi:10.1007/s10649-023-10274-5
dc.rightsNamensnennung 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectCovariational reasoningeng
dc.subjectBayesian reasoningeng
dc.subjectDouble-treeeng
dc.subjectUnit squareeng
dc.subjectNatural frequencieseng
dc.subjectSOLO taxonomyeng
dc.subject.ddc510
dc.subject.swdMathematikger
dc.subject.swdDenkenger
dc.subject.swdBayes-Verfahrenger
dc.titleCovariational reasoning in Bayesian situationseng
dc.typeAufsatz
dc.type.versionpublishedVersion
dcterms.abstractPrevious 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.eng
dcterms.accessRightsopen access
dcterms.creatorBüchter, Theresa
dcterms.creatorEichler, Andreas
dcterms.creatorBöcherer-Linder, Katharina
dcterms.creatorVogel, Markus
dcterms.creatorBinder, Karin
dcterms.creatorKrauss, Stefan
dcterms.creatorSteib, Nicole
dcterms.source.identifiereissn:1573-0816
dcterms.source.issueIssue 3
dcterms.source.journalEducational Studies in Mathematicseng
dcterms.source.pageinfo481 - 505
dcterms.source.volumeVolume 115
kup.iskupfalse

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