Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and provide examples and tentative explanations of a number of statistical…

This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this…

Previous research has suggested that infants are able to distinguish between possible and impossible events and make basic probabilistic inferences. However, much of this research has focused on children's intuitions about past events for which the outcome is already determined but unknown. Here, we investigated children's ability to use…

The purpose of this study was twofold. First, to explore middle and high school students' intuitively-based (mis)conceptions in probability, particularly availability and representativeness heuristics. Second, to investigate teachers' awareness of these intuitively-based (mis)conceptions and the effectiveness of their instructional practices to…

Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

Students expose various intuitions in probability comparison and calculation tasks. Large volumes of research looked into these intuitions by categorizing learners' strategies, but fewer studies considered how these intuitions may be associated with learners' judgments. Even fewer examined the mixed effects of multiple intuitions held by the same…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

Young children encounter uncertainty and challenges on a daily basis; through their intuitions, experiences and experimentation they construct knowledge, skills and dispositions towards probabilistic concepts. The aim of this exploratory ethnographic study is to identify how young children engage with probabilistic thinking and reasoning while…

The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

Using the famous Birthday problem, we present here a practical activity that allows students to perceive the basic reasoning behind simulation and explore its potential. Through a playful approach with probabilities, students are led along a path that illustrates difficulties with intuition and introduces them to theoretical results for sample…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

Recent research shows that preverbal infants can reason about single-case probabilities without relying on observed frequencies, adapting their predictions to relevant dynamic parameters of the situation (Téglás, Vul, Girotto, Gonzalez, Tenenbaum & Bonatti, [Téglás, E., 2011]; Téglás, Girotto, Gonzalez & Bonatti, [Téglás, E., 2007]). Here…

This article reports on a pilot study that used concrete materials and TinkerPlots to support a Year 4 student's understanding of the big ideas of variation and expectation when investigating a random chance experiment using spinners.