Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen– kognitive Überlastung oder didaktische Unterstützung?

Binder, Karin; Steib, Nicole und Krauss, Stefan (2022): Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen– kognitive Überlastung oder didaktische Unterstützung? In: Journal für Mathematik-Didaktik

Abstract

In stochastic situations with two dichotomous events, neither typical tree diagrams nor 2 x 2 tables allow the simultaneous representation of all possible probabilities in the situation. The net diagram presented in this paper has the capacity to represent all four possible marginal probabilities, all four joint probabilities, and all eight conditional probabilities simultaneously. Furthermore, due to the node-branch structure of the frequency net, the simultaneous representation of probabilities and absolute frequencies is also possible with this visualization. With the successive extension of the typical tree diagram to the double tree and finally to the net diagram, the inference degree, e.g., for questions about conditional probabilities, decreases (i.e., less mental steps are required), however, at the same time the complexity of the representation increases and thus the extrinsic cognitive load. In the present article, a theoretical comparison of these node-branch-structures is made. Furthermore, we demonstrate with an empirical study that the successive extension of these node-branch structures, which were already completely worked out, positively affects the performance of N = 269 students. Although frequency double trees and frequency nets were entirely unfamiliar to the students, these visualizations provided the best support to the students in completing the tasks.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0173-5322
• Sprache: Deutsch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892