Designing Visualisations for Bayesian Problems According to Multimedia Principles

Büchter, Theresa; Steib, Nicole; Böcherer-Linder, Katharina; Eichler, A.; Krauß, Stefan; Binder, Karin; Vogel, Markus

doi:10.3390/educsci12110739

Cited by 3 publications

(1 citation statement)

References 81 publications

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“…Of course, in these domains a training in covariational reasoning could be constructed and implemented. In such a training on covariational reasoning, one could, for instance, work with dynamic geometry software to make changes in b , t , and f even more intuitive, for example by using a dynamic double-tree or a dynamic unit square (for a proposal of such dynamic visualizations see Büchter et al, 2022b ; for information on a respective training course, see http://www.bayesian-reasoning.de/en/br_trainbayes_en.html or Büchter et al, 2022a ).…”

Section: Discussionmentioning

confidence: 99%

Measuring people’s covariational reasoning in Bayesian situations

Steib,

Krauss,

Binder

et al. 2023

Front. Psychol.

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Previous research on Bayesian reasoning has typically investigated people’s ability to assess a posterior probability (i.e., a positive predictive value) based on prior knowledge (i.e., base rate, true-positive rate, and false-positive rate). In this article, we systematically examine the extent to which people understand the effects of changes in the three input probabilities on the positive predictive value, that is, covariational reasoning. In this regard, two different operationalizations for measuring covariational reasoning (i.e., by single-choice vs. slider format) are investigated in an empirical study with N = 229 university students. In addition, we aim to answer the question wheter a skill in “conventional” Bayesian reasoning is a prerequisite for covariational reasoning.

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Section: Discussionmentioning

confidence: 99%

Measuring people’s covariational reasoning in Bayesian situations

Steib,

Krauss,

Binder

et al. 2023

Front. Psychol.

Self Cite

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Covariational reasoning in Bayesian situations

Büchter,

Eichler,

Böcherer-Linder

et al. 2024

Educ Stud Math

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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.

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Working with digital textbooks or printed materials: A study with boys and girls on conditional probability

Brnic,

Greefrath,

Reinhold

2024

ZDM Mathematics Education

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The integration of dynamic visualisations, feedback formats and digital tools is characteristic of state-of-the-art digital mathematics textbooks. Although there already is evidence that students can benefit from these technology-based features in their learning, the direct comparison between the use of a comparable digital and printed resource has not yet been sufficiently investigated. We address this research gap by contrasting the use of an enriched digital textbook that includes these features and comparable printed materials without them. To do so, we investigate the achievement of 314 students in a pretest-posttest control group design in a five-hour series of lessons on conditional probability. Using the Rasch model and mixed ANOVA, the results indicate that students can benefit from digital textbook features, especially compared to the use of comparable printed materials. In line with other studies on mathematical achievement and the use of digital resources, our study also shows differences between boys and girls. It seems that particularly girls benefit from the use of the digital textbook, whereas, for the boys, it does not seem to make a difference what kind of resources they use. The group and gender differences are discussed against the background of other studies considering that, especially in Bayesian situations, the way statistical situations are visualised can be decisive for a student’s performance.

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Designing Visualisations for Bayesian Problems According to Multimedia Principles

Cited by 3 publications

References 81 publications

Measuring people’s covariational reasoning in Bayesian situations

Measuring people’s covariational reasoning in Bayesian situations

Covariational reasoning in Bayesian situations

Working with digital textbooks or printed materials: A study with boys and girls on conditional probability

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