Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

In this work we are going to present how an interactive platform can be used as a powerful tool to allow students to better explore a foundational problem in quantum chemistry: the application of the variational method to the dihydrogen molecule using simple Gaussian trial functions. The theoretical approach for the hydrogen atom is quite…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…

Quantum mechanics (QMs) is a foundational subject in many science and engineering fields. It is difficult to teach, however, as it requires a fundamental revision of the assumptions and laws of classical physics and probability. Furthermore, introductory QM courses and texts predominantly focus on the mathematical formulations of the subject and…

The unexpectedness of the birthday problem has long been used by teachers of statistics in discussing basic probability calculation. An activity is described that engages students in understanding probability and sampling using the popular Facebook social networking site. (Contains 2 figures and 1 table.)

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships,…

This undergraduate physical chemistry laboratory exercise introduces students to the study of probability distributions both experimentally and using computer simulations. Students perform the classic coin toss experiment individually and then pool all of their data together to study the effect of experimental sample size on the binomial…

The use of data is critical to the teaching of probability and statistics. At the very least, data should be provided within a meaningful context rather than presented as a generic, meaningless collection of numbers. Students often respond better, however, when working with data that they have gathered themselves. Having students collect data is a…

Effectively teaching the concepts of osmosis to college-level students is a major obstacle in biological education. Therefore, a novel computer model is presented that allows students to observe the random nature of particle motion simultaneously with the seemingly directed net flow of water across a semipermeable membrane during osmotic…

This article will expand upon the techniques of Criminologist, D. Kim Rossmo, and Social Psychologist, David Canter for determining a serial criminal's base of operations. The basic framework for our investigation is that of Rossmo, but uses a different criterion for analysing the relationship of points within the hunting area defined by the crime…

The television show Deal or No Deal and an Excel spreadsheet help students see how understanding probability and mean--and the concept of expected value (EV)--can lead to game show wins.

A well-designed experiment is the best method for establishing efficacy of any intervention, be it medical, behavioral, or educational in nature. This paper reviews the steps necessary in conducting a comparative experiment in an educational setting, and illustrates how these steps might be fulfilled within the context of a large-scale randomized…

This paper describes an interactive activity that revolves around the dice-based golf game GOLO. The GOLO game can be purchased at various retail locations or online at igolo.com. In addition, the game may be played online free of charge at igolo.com. The activity is completed in four parts. The four parts can be used in a sequence or they can be…

Data analysis plays a prominent role in various facets of modern life: Schools evaluate and revise programs on the basis of test scores; policymakers make decisions on the basis of information gleaned from polling data; supermarkets stock shelves on the basis of data collected at checkout lanes. Data analysis provides teachers with new tools and…