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<p>Risk is seen as a&#xa0;relevant topic in school across all disciplines. However, there is a&#xa0;need for research in mathematics education, especially regarding the design of curriculum-embedded instruction units. The Risk-Design project addresses this gap. It is a&#xa0;design-based research project aiming to develop a&#xa0;teaching unit to promote the handling of risk in stochastics lessons. In this article we present the analysis of the first of eight lessons. This lesson introduces expected value in the context of multiple coin tosses. It investigates decision-making processes under uncertainty and learners’ reasoning processes that accompany these decision-making processes. It combines two theoretical approaches. A&#xa0;literacy concept of risk and the inferential view of conceptualization embedded in the social practice of <i>giving and asking for reasons</i>. These approaches are used for the lesson design and its empirical investigation by using videography. The data analyses follow a&#xa0;reconstructive approach aiming to characterize learners’ decision-making and reasoning practices. The main results are the identification of teaching phenomena regarding decision-making processes, a&#xa0;reasoning model with four modes of informal stochastic reasoning, and the finding that risk competency can already be activated in the initial lesson on the topic of risk. In the practice, these results can make teachers aware of the design of lessons on the topic of risk. In particular, the model has diagnostic potential and may reveal developmental nuances of reasoning in other decision-making situations. Theoretically, the model points to different reasoning qualities extending previous research on informal stochastical reasoning.</p>

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Risiko im Stochastikunterricht: Wie Lernende Entscheidungen unter Unsicherheit treffen und begründen

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月22日

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  • Marie-Theres Brehm,
  • Angelika Bikner-Ahsbahs

摘要

Risk is seen as a relevant topic in school across all disciplines. However, there is a need for research in mathematics education, especially regarding the design of curriculum-embedded instruction units. The Risk-Design project addresses this gap. It is a design-based research project aiming to develop a teaching unit to promote the handling of risk in stochastics lessons. In this article we present the analysis of the first of eight lessons. This lesson introduces expected value in the context of multiple coin tosses. It investigates decision-making processes under uncertainty and learners’ reasoning processes that accompany these decision-making processes. It combines two theoretical approaches. A literacy concept of risk and the inferential view of conceptualization embedded in the social practice of giving and asking for reasons. These approaches are used for the lesson design and its empirical investigation by using videography. The data analyses follow a reconstructive approach aiming to characterize learners’ decision-making and reasoning practices. The main results are the identification of teaching phenomena regarding decision-making processes, a reasoning model with four modes of informal stochastic reasoning, and the finding that risk competency can already be activated in the initial lesson on the topic of risk. In the practice, these results can make teachers aware of the design of lessons on the topic of risk. In particular, the model has diagnostic potential and may reveal developmental nuances of reasoning in other decision-making situations. Theoretically, the model points to different reasoning qualities extending previous research on informal stochastical reasoning.