To ensure the learning of mathematics, teachers must be able to analyse their students' mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students' difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual…

This article presents ways to explore mathematical concepts using Catan, a popular board game. After a brief overview of game play, we explore considerations with many potential entry points for mathematical modeling, such as which resource is the best, which resources will be rare or plentiful, where to build, and risk assessment.

The aim of this paper is to approach the teaching of the Poisson distribution in a friendly and amusing way. It constitutes a common practice to adopt the main probability distributions in order to predict results of sport events and to estimate the win return of betting activities (Chalikias 2009). In particular, by using the Poisson…

The two most popular decision-making processes are tossing a coin and playing rock, paper, scissors. In the activity described in this article, students find the theoretical probabilities of winning a coin toss and a round of the rock, paper, scissors game. They next devise strategies to win and test them out. Students then compare the theoretical…

The adaptive learning problem concerns how to create an individualized learning plan (also referred to as a learning policy) that chooses the most appropriate learning materials based on a learner's latent traits. In this article, we study an important yet less-addressed adaptive learning problem--one that assumes continuous latent traits.…

The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what…

In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons…

The Monty Hall Dilemma (MHD), made famous by the television game show Let's Make a Deal, can be an effective teaching tool with wide ranging behavioral science applications. The format and history of the problem are presented as well as experimental data and variations on the original design. Strategic game playing choices are discussed from…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

This study focuses on pre-service teachers' experimentation with a game-modding process in a constructionist setting whilst they experimented with randomness embedded in wider socio-scientific issues that call for decision making under uncertainty. In this process, participants created 39 different game mods. Our observations of the participants…

A more motivating way of introducing students to probability theory is through real-world problems. Since heuristics play an important role in our probabilistic judgement, knowing how to avoid incorrect probabilistic reasoning, which leads to several biases, could help students to develop more critical thinking skills. In this paper, we present a…

The aim of this study is to explore the judgments and reasoning in probabilistic tasks that require comparing two probabilities either with or without introducing an additional degree of uncertainty. The reasoning associated with the task having an additional condition of uncertainty has not been discussed in previous studies. The 66 undergraduate…

In this paper, we make a qualitative analysis of didactic experiments performed with five 6 to 10-year-old children and five primary school teachers, starting from a structured game with probabilistic elements. The fundamental idea is to stimulate probabilistic thinking not only by playing a card game with decision making in uncertain situations,…

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…

Although Bayesian methodology has become a powerful approach for describing uncertainty, it has largely been avoided in undergraduate statistics education. Here we demonstrate that one can present Bayes' Rule in the classroom through a hypothetical, yet realistic, legal scenario designed to spur the interests of students in introductory- and…