Bruckmaier, Georg
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- PublikationEye-Tracking visual and textual information. What matters in Bayesian situations?(University of Haifa, 2023) Julia Sirock; Bruckmaier, Georg; Markus Vogel; Stefan Krauss; Ayalon, Michal; Koichu, Boris; Leikin, Roza; Rubel, Laurie; Tabach, Michal [in: Proceeding of the 46th Conference of the International Group for the Psychology of Mathematics Education]04B - Beitrag Konferenzschrift
- PublikationTversky and Kahneman’s cognitive illusions. Who can solve them, and why?(Frontiers Research Foundation, 12.04.2021) Bruckmaier, Georg; Krauss, Stefan; Binder, Karin; Hilbert, Sven; Brunner, Martin [in: Frontiers in Psychology]In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically explaining people’s faulty thinking, or proposing and experimentally implementing measures to foster insight and to make these problems accessible to the human mind. Yet these problems have thus far usually been empirically analyzed on an individual-item level only (e.g., by experimentally comparing participants’ performance on various versions of one of these problems). In this paper, by contrast, we examine these illusions as a group and look at the ability to solve them as a psychological construct. Based on an sample of = 2,643 Luxembourgian school students of age 16–18 we investigate the internal psychometric structure of these illusions (i.e., Are they substantially correlated? Do they form a reflexive or a formative construct?), their connection to related constructs (e.g., Are they distinguishable from intelligence or mathematical competence in a confirmatory factor analysis?), and the question of which of a person’s abilities can predict the correct solution of these brain teasers (by means of a regression analysis).01A - Beitrag in wissenschaftlicher Zeitschrift
- PublikationTransfer effects of mathematical literacy: an integrative longitudinal study(Springer, 07.08.2020) Holenstein, Mathias; Bruckmaier, Georg; Grob, Alexander [in: European Journal of Psychology of Education]Mathematical literacy (ML) is considered central to the application of mathematical knowledge in everyday life and thus is found in many comparative international educational standards. However, there exists barely any evidence about predictors and outcomes of ML having a lasting effect on achievement in non-mathematical domains. We drew on a large longitudinal sample of N= 4001 secondary school students in Grades 5 to 9 and tested for effects of ML on later academic achievement. We took prior achievement in different domains (information and communication technology literacy, scientific literacy, reading comprehension, and listening comprehension), socioeconomic status, and gender into account and investigated predictive effects of math grade, mathematical self-concept, reasoning, and prior achievement on ML. Using structural equation models, we found support for the importance of integrating multiple predictors and revealed a transfer effect of ML on achievement in different school domains. The findings highlight the importance of ML for school curricula and lasting educational decisions.01A - Beitrag in wissenschaftlicher Zeitschrift
- PublikationStrategien beim Lösen statistischer Aufgaben – Eine Eyetracking-Studie zur visuellen Durchmusterung von Baumdiagrammen und Vierfeldertafeln(WTM, 2019) Bruckmaier, Georg; Binder, Karin; Krauss, Stefan [in: Beiträge zum Mathematikunterricht 2019]04B - Beitrag Konferenzschrift
- PublikationAn eye-tracking study of statistical reasoning with tree diagrams and 2 x 2 tables(Frontiers, 2019) Bruckmaier, Georg; Binder, Karin; Krauss, Stefan; Kufner, Han-Min [in: Frontiers in Psychology]Changing the information format from probabilities into frequencies as well as employing appropriate visualizations such as tree diagrams or 2 × 2 tables are important tools that can facilitate people’s statistical reasoning. Previous studies have shown that despite their widespread use in statistical textbooks, both of those visualization types are only of restricted help when they are provided with probabilities, but that they can foster insight when presented with frequencies instead. In the present study, we attempt to replicate this effect and also examine, by the method of eye tracking, why probabilistic 2 × 2 tables and tree diagrams do not facilitate reasoning with regard to Bayesian inferences (i.e., determining what errors occur and whether they can be explained by scan paths), and why the same visualizations are of great help to an individual when they are combined with frequencies. All ten inferences of N = 24 participants were based solely on tree diagrams or 2 × 2 tables that presented either the famous “mammography context” or an “economics context” (without additional textual wording). We first asked participants for marginal, conjoint, and (non-inverted) conditional probabilities (or frequencies), followed by related Bayesian tasks. While solution rates were higher for natural frequency questions as compared to probability versions, eye-tracking analyses indeed yielded noticeable differences regarding eye movements between correct and incorrect solutions. For instance, heat maps (aggregated scan paths) of distinct results differed remarkably, thereby making correct and faulty strategies visible in the line of theoretical classifications. Moreover, the inherent structure of 2 × 2 tables seems to help participants avoid certain Bayesian mistakes (e.g., “Fisherian” error) while tree diagrams seem to help steer them away from others (e.g., “joint occurrence”). We will discuss resulting educational consequences at the end of the paper.01A - Beitrag in wissenschaftlicher Zeitschrift