Abstract
The article reports an empirical study on the introduction of elementary probabilistic concepts in school, focusing on tasks related to the psychological tradition of heuristics and biases. The concepts involved were studied using an extensional natural frequencies approach. We describe the school intervention conducted in an interaction across different school levels (5th and 9th grades) with the aim of promoting motivation and cooperation thereby strengthening learning. The different tests were assessed both qualitatively (based on argumentation analyses) and quantitatively. The results provide further evidence on the diversity of obstacles tied to probabilistic notions. More importantly, they exhibit an overall improvement in performance of students at both levels. This work confirms the efficacy of natural frequencies in eliciting the intended interpretation of probabilistic tasks and suggests that an appropriate interaction between different scholastic levels can be implemented as a fruitful learning arrangement.
Highlights
According to the editors of the compendium Probabilistic Thinking: Presenting Plural Perspectives (Chernoff & Sriraman, 2014), research in mathematics education concerning probabilistic thought during the “Contemporary Period” has been described as “investigating the teaching and learning of probability in classrooms and schools, which is due, in large part, to probability becoming a mainstream strand of worldwide curricula.” Stochastic literacy is of paramount importance both for informed citizenship and a required tool in a variety of disciplines.Even so, educational research is still engaged with some open issues such as, for example, the discus-sion on the different interpretations of probability, the sources of obstacles and biases, and the possible strategies to be adopted in the teaching-learning process
A further question is: do participants provide the same amount of D-type answers with or without the explicit mention of the false positives rate? The present results show a similar high-D/low-A trend for both conditions, but that in the “without False Positives Rate” condition we have even a increase in the A answers
Externalized argumentation may not faithfully reflect these processes, yet it may provide some empirical indication about interpretation and reasoning mechanisms. This is relevant, as the same answer may be obtained by different students through entirely different processes, as we shall see
Summary
Educational research is still engaged with some open issues such as, for example, the discus-sion on the different interpretations of probability, the sources of obstacles and biases, and the possible strategies to be adopted in the teaching-learning process. These are main topics of interest in the “Assimilation Period” (Chernoff & Sriraman, 2014) which corresponds to the current phase. We base our work on the results of cognitive psychology on probabilistic thought These are inherent to modern frameworks of rationality
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