The "Borel" board game consists of a series of experiments involving dice rolls, coin flips, or drawing colored balls from bags. Before each experiment is conducted, each player bets for or bets against a statement regarding the random outcome. We suggest that the collection of "Borel" experiments be used as a resource to…

A formula is derived for a 'two-dice horse race', in which two ordinary dice are thrown repeatedly and each time the sum of the scores determines which horse (numbered 2 to 12) moves forward one space. This paper answers a question posed in a former "Teaching Statistics" article, and demonstrates the value of simulation.

The frequentist and classical models of probability provide students with different lenses through which they can view probability. Prior research showed that students may bridge these two lenses through instructional designs that begin with a clear connection between the two, such as coin tossing. Considering that this connection is not always…

The Monte Carlo method is one of the basic simulation statistical methods which can be used both to demonstrate basic probability and statistical concepts as well as to analyse the behaviour stochastic models. The introduction part of the article provides a brief description of the Monte Carlo method. The main part of the article is concentrated…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation…

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 report summarises the research activities and findings from the TLRI-funded project entitled "Visualising Chance: Learning Probability Through Modelling." This exploratory study was a 2-year collaboration among two researchers, two conceptual software developers/interactive graphics experts, three university lecturers/practitioners,…

Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of…

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the…

Real-world phenomena simulation models, which can be used to engage middle-school students with probability, are described. Links to R instructional material and easy-to-use code are provided to facilitate implementation in the classroom.

In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

No risk, no fun--betting on sports events costs the gamblers a lot of money and brings excellent profits to those who offer the bets. Among the people who bet on a regular basis, the proportion of young adults is frighteningly high. We now suggest a concept (as part of a basic mathematics course) for acquiring the necessary mathematical knowledge…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

Although simulation training improves post-training performance, it is unclear how well performance soon after simulation training predicts longer term outcomes (i.e., learning). Here our objective was to assess the predictive value of performance 1 h post-training of performance 6 weeks later. We trained 84 first year medical students a simulated…