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…

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…

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…

Preschoolers develop a wide range of mathematical informal knowledge and intuitive thinking before they enter formal, goal-oriented education. In their everyday activities young children get engaged with situations that enhance them to develop skills, concepts, strategies, representations, attitudes, constructs and operations concerning a wide…

This paper is based on research that investigated the development of probabilistic language and thinking by students 10-12 years old. The focus was on the adequate use of probabilistic terms in social practice. A series of tasks was developed for the investigation and completed by the students working in groups. The discussions were video recorded…

Recent evidence suggests that people are highly efficient at detecting conflicting outputs produced by competing intuitive and analytic reasoning processes. Specifically, De Neys and Glumicic (2008) demonstrated that participants reason longer about problems that are characterized by conflict (as opposed to agreement) between stereotypical…

Dual Process Theories (DPT) of reasoning posit that judgments are mediated by both fast, automatic processes and more deliberate, analytic ones. A critical, but unanswered question concerns the issue of monitoring and control: When do reasoners rely on the first, intuitive output and when do they engage more effortful thinking? We hypothesised…

This research shows that the motivation to posses a desired characteristic (or to avoid an undesired one) results in self-perceptions that guide people's use of base rate in the Lawyer-Engineer problem (Kahneman & Tversky, 1973). In four studies, participants induced to believe (or recall, Exp. 2) that a rational cognitive style is…

This article reports on a case study from a design-based research project that investigated how students make sense of the disciplinary tools they are taught to use, and specifically, what personal, interpersonal, and material resources support this process. The probability topic of binomial distribution was selected due to robust documentation of…

I report on what teachers in an Advanced Certificate in Education (ACE) inservice programme learned about probabilistic reasoning in relation to teaching it. I worked "on the inside" using my practice as a site for studying teaching and learning. The teachers were from three different towns in the Northern Cape province and had limited…

Outlines a theory of naive probability in which individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an "extensional" way. The theory accommodates reasoning based on numerical premises, and explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem.…

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…

Discusses the performance of Malaysian secondary school students on a probability concepts test covering various intuitive and taught probability concepts. Describes the establishment of a probability concepts hierarchy and considers probability understanding in relation to independent variables. Boys, Form Six students, and students with a higher…

One theoretical framework which addresses students' conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students' reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common…