Abstract
The purpose of this article is to address the lack of research on teachers’ knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and informal reasoning, we have utilized logical fallacies for our analysis of the results. From this new perspective, we determined that certain individuals’—those who provided normatively incorrect responses—utilized the fallacy of composition when making comparisons of relative likelihood. In addition, we discuss how our findings impact models established in the research literature (e.g., the representativeness heuristic) and, further, we suggest that logical fallacies should supplement heuristic and informal reasoning as potential perspectives for research investigating comparisons of relative likelihood.
Résumé
Le but de cet article est de combler en partie le manque de recherches sur les connaissances des enseignants dans le domaine des probabilités. Comme cela avait été fait dans des études précédentes, nous avons demandé à des futurs enseignants des mathématiques quelle était la moins probable parmi les séquences présentées de tirs à pile ou face. Toutefois, au lieu d’adopter les perspectives traditionnelles du raisonnement heuristique et informel, nous nous sommes servis de sophismes logiques pour analyser les résultats. Dans cette nouvelle perspective, nous avons constaté que certaines personnes—celles qui ont fourni des réponses incorrectes sur le plan normatif—se sont servies de sophismes de composition lorsqu’elles ont comparé les différents niveaux de probabilité. Par ailleurs, nous examinons les façons dont nos résultats peuvent avoir un impact sur les modèles établis dans la recherche actuelle (par exemple l’heuristique de représentativité), et nous proposons que les sophismes logiques soient utilisés pour complémenter le raisonnement heuristique et informel dans la recherche visant à analyser les comparaisons de probabilités relatives.
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Chernoff, E.J., Russell, G.L. The Fallacy of Composition: Prospective Mathematics Teachers’ Use of Logical Fallacies. Can J Sci Math Techn 12, 259–271 (2012). https://doi.org/10.1080/14926156.2012.704128
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DOI: https://doi.org/10.1080/14926156.2012.704128