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.

Learning the fundamentals of probability and random variables can be a struggle for many students. Games by their nature require active participation and reward mastery, lending naturally to the framework of active learning. In this study, we designed and evaluated the efficacy of a lab activity using a game where strategy hinges on sums of dice…

We investigate the level of understanding of probability as related to games and gambling, and the concept of independence of events using a convenience sample of college undergraduates taking an introductory course in applied business statistics. We examined the students' perception of the role of skill in winning at four different games through…

This research is aimed to describe a learning trajectory for probability through game-based learning. The research employed design research consisting of three stages: preparing for the experiment, design experiment, and retrospective analysis. A hypothetical learning trajectory (HLT) using Sudoku and Snake-and-ladder games was developed by…

Playing board games is known to improve pre-school student numeracy and many board games are used to motivate and explore concepts in probability. This study investigates whether college students in liberal arts mathematics courses assigned to play the board game "Settlers of Catan" develop a stronger grasp of basic probability concepts…

In this paper, the dice game "Unders and Overs" is described and presented as an active learning exercise to introduce basic probability concepts. The implementation of the exercise is outlined and the resulting presentation of various probability concepts are described.

Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.

This article shows a generalization of Galileo's "passe-dix" game. The game was born following one of Galileo's [G. Galileo, "Sopra le Scoperte dei Dadi" (Galileo, Opere, Firenze, Barbera, Vol. 8). Translated by E.H. Thorne, 1898, pp. 591-594] explanations on a paradox that occurred in the experiment of tossing three fair "six-sided" dice.…

This article describes activities in which students deepen their relational understanding of the equals sign through exploring inequalities in a competitive dice game, built around the familiar fairy-tale "The Three Little Pigs" and "The Big Bad Wolf." The activity can be adapted to different abilities by choosing more or less…

The "Monty Hall" problem or "Three Door" problem--where a person chooses one of three doors in hope of winning a valuable prize but is subsequently offered the choice of changing his or her selection--is a well known and often discussed probability problem. In this paper, the structure, history, and ultimate solution of the…

The sampling (probability) distribution for the sum of dice is presented graphically as a compelling demonstration of the Central Limit Theorem.

The "Price Is Right" ("TPIR") provides a wealth of material for studying statistics at various levels of mathematical sophistication. The authors have used elements of this show to motivate students from undergraduate probability and statistics courses to graduate level executive management courses. The material consistently generates a high…

This study investigates students' conceptual variation and coordination among theoretical and experimental interpretations of probability. In the analysis we follow how Swedish students (12-13 years old) interact with a dice game, specifically designed to offer the students opportunities to elaborate on the logic of sample space,…

In this article, the author describes the format of the Con Test, an Australian television game show which followed the same general rules and game play as the UK show PokerFace. At the end of each round a contestant needs to decide whether or not he or she should fold. A contestant needs to know how likely it is that he or she is in last place.…

This article explores the question, "When should you mail in your entries to a sweepstakes in order to have the best chance of winning?"