In this report, we analyze students' learning of compound probability by describing connections they generated while engaged with tasks involving two independent events. Several of their connections were compatible with the development of expertise, such as recognizing the need to determine sample spaces across a variety of situations and noting…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students' abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis…

In the Australian mathematics curriculum, Year 12 students (aged 16-17) are asked to solve conditional probability problems that involve the representation of the problem situation with two-way tables or three-dimensional diagrams and consider sampling procedures that result in different correct answers. In a small exploratory study, we…

Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization…

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…