Chaotic phenomena are not part of standard curricula, although this subject offers several interesting aspects which can help students better understand basic features of science. A central observation is that even simple physical systems, if chaotic, are unpredictable, just like the weather. We present the principles applied when developing a…

Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle's trajectory. Quantum physics is an inherently probabilistic theory in that only…

A number of probabilistic experiments are described to estimate e, p and v2, with results from computer simulations being used to investigate convergence. A number of possible classroom exercises and extensions are presented.

The authors describe how the Monty Hall Dilemma, a well-known choice anomaly, can be demonstrated with a simple and versatile classroom experiment. In addition to demonstrating the anomaly, the experiment can be used to introduce students to some institutional modifications that have been shown to ameliorate it. This experiment, which can be…

There is growing pressure to make efficacy experiments more useful. This requires attending to the twin goals of generalizing experimental results to those schools that will use the results and testing the intervention's theory of action. We show how electronic records, created naturally during the daily operation of technology-based…

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…

Research shows that playing games in the classroom improves students' attitudes toward mathematics, increases motivation to practice skills inside and outside the classroom, and increases learning by encouraging students of all levels to participate. Rutherford asserts that playing games encourages strategic mathematical thinking and supports…

The "radioactive dice" experiment is a commonly used classroom analogue to model the decay of radioactive nuclei. However, the value of the half-life obtained from this experiment differs significantly from that calculated for real nuclei decaying exponentially with the same decay constant. This article attempts to explain the discrepancy and…

Computational thinking is a component of the Science and Engineering Practices in the Next Generation Science Standards, which were adopted by some states. We describe the activities in a high school chemistry course that may develop students' computational thinking skills by primarily using Excel, a widely available spreadsheet software. These…

The quantal hypothesis is central to the modern understanding of how a neurotransmitter is released from synapses. This hypothesis expresses that a neurotransmitter is packaged together in quanta that are released probabilistically. The experiments that led to the quantal hypothesis are often related in introductory neuroscience textbooks, but…

Tossing a fair coin 1000 times can have an unexpected result. In the activities presented here, players keep track of the accumulated total for heads and tails after each toss, noting which player is in the lead or whether the players are tied. The winner is the player who was in the lead for the higher number of turns over the course of the game.…

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…

It is known that visual working memory capacity is limited, but the nature of this limit remains a subject of controversy. Increasingly, two factors are thought to limit visual memory: an object-based limit associated with so-called "slots" models, and an information-based limit associated with resource models. Recently, Barton, Ester, and Awh…

This paper is an elementary introduction to particle diffusion in a medium where the coefficient of diffusion varies with position. The introduction is aimed at third-year university courses. We start from a simple model of particles hopping on a discrete lattice, in one or more dimensions, and then take the continuous-space limit so as to obtain…

Statisticians use words deliberately and specifically, but not necessarily in the way they are used colloquially. For example, in general parlance "statistics" can mean numerical information, usually data. In contrast, one large statistics textbook defines the term "statistic" to denote "a characteristic of a…