Sibel Kazak

Conceptual Challenges in Coordinating Theoretical and Data-Centered Estimates of Probability.

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both “theoretical” and “experimental” probability, typically with the hope that students will come to see the latter as converging on the former as the number of observations grows. On the surface of it, this approach would seem to fit well with objectives in teaching informal inference. However, our in-depth analysis of one eighth-graders reasoning about experimental and theoretical probabilities points to various pitfalls in this approach. We offer tentative recommendations about how some of these issues might be addressed.

Research on Uncertainty

We discuss research on the teaching and learning of uncertainty, with a particular emphasis on quantifiable aspects as might be represented by probability. We acknowledge earlier reviews of the field by integrating research, especially from the last 10 years, with previous studies. In particular, we focus on three issues, which have become increasingly significant: (1) the realignment of previous work on heuristics and biases, (2) conceptual and experiential engagement with uncertainty and (3) adopting a modelling perspective on probability. The role of the teacher in shaping the learning environment in various critical ways emerges as a key finding. In the concluding section, we indicate promising directions for research, including the need for more exploratory research in new areas such as the role of modelling and carefully designed experiments to test hypotheses that are apparent from more established studies.

Emergent Reasoning About Uncertainty in Primary School Children with a Focus on Subjective Probability

The classical, frequentist and subjective interpretations of probability are the three main perspectives on the quantification of uncertainty. While the first two are emphasised in most school curriculum materials, the subjective notion of probability either is neglected or has minimal mention. Yet, it is closely related to what people commonly use for everyday reasoning. In this chapter, we combine a critical literature review of children’s reasoning about uncertainty from both qualitative and quantitative perspectives with an analysis of empirical data. We explore the types of language 7–8-year-old children use to predict and describe outcomes and how they reason about the likelihood of outcomes of chance events using subjective probability evaluations before and after experiment and simulation. Data show that children used chance language relatively accurately to describe the likelihood of chance events and most of them had a quantitative understanding of equal likelihoods. Modifying predictions based on experiment and simulation results seemed to be intuitive for young children.