Technology Innovations in Statistics Education

In manufacturing industry, many employees need to interpret and communicate statistical information to monitor and improve production processes. Often the information is reduced to the form of numerical measures, on the logic that numbers are a convenient and understandable type of information to pass among the diverse groups of employees that make up a manufacturing operation. We investigated by means of interviews and observation how several numerical measures, ‘process capability indices’, were used in an automotive factory and how employees were trained to use them. We found that the typical introduction to the measures deployed statistical and algebraic symbolism as well as laborious manual calculations that did not appear to support employees’ understanding of the underlying mathematical relationships. These measures therefore failed to be ‘boundary objects’ – artifacts that inhabit different social worlds and satisfy the informational requirements of each. The goal of our subsequent design-based research was to design a representation of the process capability indices that would be easier to engage with than the existing formal symbolism used in shop floor calculations and in training. We did this by re-presenting relevant mathematical relationships in computer tools – technology-enhanced boundary objects (TEBOs) – developed in collaboration with company trainers. To evaluate our interaction with three trainers and 37 trainees in three courses in two factories, and the impact of the computer tools on practice, we followed the computer tools’ trajectory from the stage of co-design with the original car factory through to the stage at which the computer tools were used by factories beyond this research project. The evaluation points to the importance of aligning statistical and workplace norms and meanings, and gives illustrations of how the tools facilitated communication between employees.

In this paper we provide a glimpse of the iterations of design, research and theorizing of a probability simulation tool, Probability Explorer, that have occurred over the past decade. We provide a brief description of the key features of the technology designed to allow young students opportunities to explore probabilistic situations. This is followed by details about several research observations made in multiple investigations of student explorations with this probability micro-world software package. We then explicate how research results suggest that a focus on a bidirectional interplay between theoretical distribution and empirical data can promote reasoning about probabilistic phenomena, and offer implications for instruction. The paper concludes with a discussion of a next generation innovation in the software for representing a theoretical distribution that we believe may promote better students reasoning about the bidirectional connection between theoretical distributions and empirical data.

An attractive way of introducing Bayesian thinking is through a discrete model approach where the parameter is assigned a discrete prior. Two generic R functions are introduced for implementing posterior and predictive calculations for arbitrary choices of prior and sampling densities. Several examples illustrate the usefulness of these functions in summarizing the posterior distributions for one and two parameter problems and for comparing models by the use of Bayes factors.

This paper discusses the development of graphical user interfaces (GUIs) to illustrate sampling from a trinomial distribution by the natural extension of Galton's Quincunx to three dimensions.

This paper addresses the problem of generating a large number of data sets for classes of students that exhibit certain characteristics but which are sufficiently different to minimise the possiblity of plagiarism. A number of R functions are provided to perform the production of the data and the answers to the relevant data.