Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

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 use of computer simulations in the teaching of introductory statistics can help undergraduate students understand difficult or abstract statistics concepts. The free software environment R is a good candidate for computer simulations since it allows users to add additional functionality by defining new functions. In this paper, we illustrate…

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…

As literature has reported, it is usual that university students in statistics courses, and even statistics teachers, interpret the confidence level associated with a confidence interval as the probability that the parameter value will be between the lower and upper interval limits. To confront this misconception, class activities have been…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software "R for Statistical Computing." The author illustrates the computer simulation approach by focusing on several problems of…

In demand paging virtual memory systems, the page fault rate of a process varies with the number of memory frames allocated to the process. When an increase in the number of allocated frames leads to an increase in the number of page faults, Belady's anomaly is said to occur. In this paper, we present a probability model for Belady's anomaly. We…

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive…

The Wednesday before Thanksgiving presents a challenge to teachers in many U.S. schools. Some students are absent because they are traveling to be with their extended families for the holiday. Other students, assuming that nothing important will happen at school when so many of their peers are absent, may also be absent. One school's solution to…

Probability is an essential tool for understanding heredity and modern genetics, yet many students have difficulty with this topic due to the abstract and quantitative nature of the subject. To facilitate student learning of probability in genetics, we have developed a set of hands-on, cooperative activities that allow students to determine…

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

This snapshot introduces a computer-based representation and activity that enables students to simultaneously "see" the combinatorial space of a stochastic device (e.g., dice, spinner, coins) and its outcome distribution. The author argues that the "ambiguous" representation fosters student insight into probability. [Snapshots are subject to peer…

Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual's true number-correct score; presents two general interval estimation procedures for an individual's true scale score (i.e., normal approximation and endpoints conversion methods); compares various…