A number of memorable tasks have been revealed through collegial exchanges with underlying philosophical, theoretical, and potentially nefarious motivations. Such was the origin of the probability problem, and the various differences of opinion, presented herein. This article recounts how, together, we explored and disputed the probabilities…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

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,…

Simulation or game-based assessments produce outcome data and process data. In this article, some statistical models that can potentially be used to analyze data from simulation or game-based assessments are introduced. Specifically, cognitive diagnostic models that can be used to estimate latent skills from outcome data so as to scale these…

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…

This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…

Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

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

If one rolls a coin across a chessboard and it comes to rest on the board, what is the probability that it covers some corner of one of the grid squares? The online magazine "Plus" (2004) posed this problem for students to solve. It is a useful problem for several reasons: it introduces the idea of probability in a continuous sample space, it has…

Methods of determining probabilities of various outcomes of the game Yahtzee are described. (SD)

This report considers the reasoning of sixth grade students as they explore problem tasks concerning the fairness of dice games. The particular focus is the students' interactions, verbal and non-verbal, as they build and justify representations that extend their basic understanding of number combinations in order to model the outcome set of a…

The famous birthday problem is discussed and activities which can be used with it as an introduction to probability are examined. (SD)

In order to investigate the use of strategies in a game-playing computer program, "Gammon," a computer program that plays Backgammon, was developed. It focuses on the play of a given strategy, as well as the process of strategy selection, and examines the concept of strategy as an integrating and driving force in the play of a game. A…

The game of roulette is analyzed. (SD)