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The striking results of this coin-tossing simulation help students understand the law of large numbers.

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## The Back Page: My Favorite Lesson: Playing the River Crossing Game

A favorite lesson is discussed. This one involves an MT article by Dan Canada and Dave Goering from May 2008 using probability in a game setting.

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## The Back Page: My Favorite Lesson – The Birthday Problem, Empirically

The author uses real-world data to bring life to the birthday problem.

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## Gaming the Law of Large Numbers

A dice game makes understanding the connection between relative frequency and probability easier for students.

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## What Does It Mean to Do Something Randomly?

Similar assumptions seem to give rise to conflicting answers when students approach probability questions differently.

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## Investigating the Law of Large Numbers with Visual Basic

By using technology, students can conduct an experiment that quickly simulates a large number of random events. Much research has been done on students' conceptions and reasoning about probability (Jones et al. 2007). Recommendations for teaching probability have included just such use of concrete and digital manipulatives to simulate events as well as students' reflection on their initial predictions and analysis of their experiments and their results (NCTM 2000; Van de Walle et al. 2010). In fact, by using Excel® and Visual Basic to simulate coin flipping, students have been able to capitalize on these technological benefits to investigate, conceptualize, and refine their understanding of the law of large numbers.

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## Delving Deeper: Rolling the Dice

The outcome distribution for rolling a single die is horizontal; for rolling a pair of dice it is a triangle. What happens when more than two dice are rolled? What happens when the die has other than six sides? These and other questions are answered in an accessible and useful treatise.

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## Reader Reflections – August 2013

Readers comment on published articles or offer their own ideas.

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## Statistical Simulation with Web-Based Apps

While looking for an inexpensive Web application to illustrate the Central Limit theorem, I found the Rossman/Chance Applet Collection, a group of free Web-based statistics apps. In addition to illustrating the Central Limit theorem, the apps could be used to cover many classic statistics concepts, including confidence intervals, regression, and a virtual version of the popular Reese's® Pieces problem. The apps allow users to investigate concepts using either preprogrammed or original data.