Bruckmaier, Georg

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Bruckmaier
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Georg
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Bruckmaier, Georg

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2015 - 201992020 - 20224
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Autor:in: Binder, Karin × Anfangsdatum: 2006 ×

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    Publikation
    Eine Frage der Taktik. Fairness beim Spiel „Schere – Stein – Papier“
    (Friedrich, 08.02.2022) Binder, Karin; Bruckmaier, Georg [in: Mathematik lehren]
    Anhand des Spiels Schere – Stein – Papier lässt sich das Thema Fairness im Unterricht spielerisch behandeln, die zugehörigen mathematischen Zusammenhänge geeignet visualisieren und psychologische Aspekte des Spiels Spielstrategien) thematisieren. Wir werden hier, ausgehend von der Grundform des Spiels, drei Varianten betrachten: unterschiedlich viele Symbole für einzelne Spieler (Variante 1), zusätzliche Symbole (Variante 2) und unterschiedlich hoher Gewinn je Spielausgang (Variante 3).
    01A - Beitrag in wissenschaftlicher Zeitschrift
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    Publikation
    Tversky 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
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    Publikation
    Competence as a continuum in the COACTIV study: the “cascade model”
    (Springer, 11.04.2020) Krauss, Stefan; Bruckmaier, Georg; Lindl, Alfred; Hilbert, Sven; Binder, Karin; Steib, Nicole; Blum, Werner [in: ZDM]
    Two different tools for assessing pedagogical content knowledge (PCK) of mathematics teachers used in the framework of the COACTIV study are systematically compared in this paper, namely the paper-and-pencil test consisting of items on the three facets knowledge of explaining and representation, knowledge of student thinking and typical mistakes, and knowledge of the potential of mathematical tasks, and the video vignettes instrument that examines teachers’ proposed continuations for presented lesson video clips specific to their subject-related and methodological competence aspects. Initially, both COACTIV PCK assessment tools are systematically contrasted for the first time with respect to their predictive validity for instructional quality (N = 163 German secondary mathematics teachers) as well as student learning gains (N = 3806 PISA students from 169 different classes) by means of path models showing that PCK, when assessed by the paper-and-pencil method, can better predict instructional quality than the video vignettes instrument can. Next, we theoretically propose the cascade model as capable of integrating pertinent theories on teacher competence and instructional quality. This model implies five ‘columns’ that are ordered according to a sequential causal chain (teacher disposition → situation-specific skills → observable teaching behavior → student mediation → learning gains). Finally, we specify four out of the five ‘columns’ of this cascade model, based empirically on the COACTIV data.
    01A - Beitrag in wissenschaftlicher Zeitschrift
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    Publikation
    Natürliche Häufigkeiten als numerische Darstellungsart von Anteilen und Unsicherheit – Forschungsdesiderate und einige Antworten
    (Springer, 28.01.2020) Krauss, Stefan; Weber, Patrick; Binder, Karin; Bruckmaier, Georg [in: Journal für Mathematik-Didaktik]
    Das aus der Kognitionspsychologie stammende Konzept der sogenannten natürlichen Häufigkeiten wird seit etwa 20 Jahren auch in der Mathematikdidaktik diskutiert. Im vorliegenden Beitrag soll illustriert werden, dass trotz der mittlerweile enormen Fülle an empirischen Studien noch zahlreiche fachdidaktische Fragestellungen unbeantwortet sind. So ist die Ersetzung von Wahrscheinlichkeiten (wie z. B. „80 %“) durch zwei absolute Häufigkeiten in der Form von natürlichen Häufigkeiten (z. B. „4 von 5“) zwar als verständnisfördernd anerkannt, es ist aber noch unklar, wie genau sich natürliche Häufigkeiten definieren lassen, welche Eigenschaften entsprechende Verknüpfungen haben, aber auch, welche Grundvorstellungen für den verständnisfördernden Effekt verantwortlich sein könnten. Ein drängendes Desiderat ist darüber hinaus, dass natürliche Häufigkeiten bislang zwar im Zusammenhang mit Bayesianischen Aufgabenstellungen diskutiert werden (d. h. beim Thema Wahrscheinlichkeit), aber noch nicht im Hinblick auf ihr tatsächliches Vorkommen in der Welt (d. h., beim Thema Daten). Obschon aktuelle Strömungen in der Didaktik der Stochastik nahelegen, dass gerade eine Analyse der Darstellungsformate statistischer Informationen, denen wir in der Welt begegnen, überhaupt erst die Voraussetzung ist, um Schülerinnen und Schüler im Sinne einer statistical literacy adäquat auf eine reflektierte Teilnahme an unserer Informationsgesellschaft vorzubereiten, geschieht dies im Zusammenhang mit Daten bislang meist mit einem Fokus auf graphische Darstellungen. Im vorliegenden Artikel (a) analysieren wir numerische Darstellungen von Anteilen und Wahrscheinlichkeiten in Alltagskommunikation und Medien, (b) vergleichen diese mit entsprechenden Darstellungen im schulischen Stochastikunterricht und (c) machen konstruktive Vorschläge, wie die hierbei zu Tage tretende Diskrepanz zwischen (a) und (b) im Stochastikunterricht adressiert werden könnte. Der Schwerpunkt liegt dabei auf dem Konzept der natürlichen Häufigkeiten.
    01A - Beitrag in wissenschaftlicher Zeitschrift
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    Publikation
    Strategien 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
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    Publikation
    An 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
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    Publikation
    Prediction of elementary mathematics grades by cognitive abilities
    (Springer, 2018) Hilbert, Sven; Bruckmaier, Georg; Binder, Karin; Krauss, Stefan; Bühner, Markus [in: European Journal of Psychology of Education]
    In the present study, the relationship between the mathematics grade and the three basic cognitive abilities (inhibition, working memory, and reasoning) was analyzed regarding possible alterations during elementary school. In a sample of N = 244 children, the mathematics grade was best predicted by working memory performance in the second grade and by reasoning in the third and fourth grades. Differentiation of these abilities during elementary school was considered as a cause for this pattern but discarded after the analysis of structural equation models. Thus, with respect to output-orientated curricula, scholastic standards, and a large inter-individual heterogeneity of students, it is implied for teachers to account for different cognitive strengths and weaknesses of their students, using adequate tasks and teaching strategies like self-differentiating tasks and adaptive explorative learning.
    01A - Beitrag in wissenschaftlicher Zeitschrift
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    Publikation
    Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making
    (Public Library of Science, 2018) Binder, Karin; Krauss, Stefan; Bruckmaier, Georg; Marienhagen, Jörg [in: PLOS ONE]
    In medicine, diagnoses based on medical test results are probabilistic by nature. Unfortunately, cognitive illusions regarding the statistical meaning of test results are well documented among patients, medical students, and even physicians. There are two effective strategies that can foster insight into what is known as Bayesian reasoning situations: (1) translating the statistical information on the prevalence of a disease and the sensitivity and the false-alarm rate of a specific test for that disease from probabilities into natural frequencies, and (2) illustrating the statistical information with tree diagrams, for instance, or with other pictorial representation. So far, such strategies have only been empirically tested in combination for “1-test cases”, where one binary hypothesis (“disease” vs. “no disease”) has to be diagnosed based on one binary test result (“positive” vs. “negative”). However, in reality, often more than one medical test is conducted to derive a diagnosis. In two studies, we examined a total of 388 medical students from the University of Regensburg (Germany) with medical “2-test scenarios”. Each student had to work on two problems: diagnosing breast cancer with mammography and sonography test results, and diagnosing HIV infection with the ELISA and Western Blot tests. In Study 1 (N = 190 participants), we systematically varied the presentation of statistical information (“only textual information” vs. “only tree diagram” vs. “text and tree diagram in combination”), whereas in Study 2 (N = 198 participants), we varied the kinds of tree diagrams (“complete tree” vs. “highlighted tree” vs. “pruned tree”). All versions were implemented in probability format (including probability trees) and in natural frequency format (including frequency trees). We found that natural frequency trees, especially when the question-related branches were highlighted, improved performance, but that none of the corresponding probabilistic visualizations did.
    01A - Beitrag in wissenschaftlicher Zeitschrift
  • Vorschaubild nicht verfügbar
    Publikation
    Visualisierung des Bayesianischen 2-Test-Falls
    (WTM, 2017) Binder, Karin; Krauss, Stefan; Marienhagen, Jörg; Bruckmaier, Georg [in: Beiträge zum Mathematikunterricht 2017]
    04B - Beitrag Konferenzschrift
  • Vorschaubild nicht verfügbar
    Publikation
    Visualisierung komplexer Bayesianischer Aufgaben
    (WTM, 2016) Binder, Karin; Krauss, Stefan; Bruckmaier, Georg [in: Beiträge zum Mathematikunterricht 2016]
    04B - Beitrag Konferenzschrift