The Monte Carlo method and related multiple imputation methods are traditionally used in math, physics and science to estimate and analyze data and are now becoming standard tools in analyzing business and financial problems. However, few sources explain the application of the Monte Carlo method for individuals and business professionals who are…

Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of…

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…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

The purpose of this article is to sketch a hypothetical descriptive framework of statistical knowledge for teaching. Because statistics is a discipline in its own right rather than a branch of mathematics, the knowledge needed to teach statistics is likely to differ from the knowledge needed to teach mathematics. Doing statistics involves many…

This article describes several methods from discrete mathematics used to simulate and solve an interesting problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? (Contains 5 figures.)

The evolution of a computer program that plays a game involving dice is described. The overall strategy was improved by introducing skill levels. (MP)

The benefits of using computer simulations in teaching elementary probability topics are discussed. Sample probability problems suitable for simulation are suggested. (DT)

Student written computer programs simulated the play of the 1969 World Series. The probabilities for National League wins were determined under varying circumstances. (RS)

The computer is used to simulate repetitions of games used in teaching expected value. Details of the games and the computer programs are given. (MP)

The purpose of this paper is to present problems (and solutions) from the areas of marketing, population planning, system reliability, and mathematics to show how a computer simulation can be used as a problem-solving strategy in probability. Examples using BASIC and two methods of generating random numbers are given. (Author/MP)

Various classroom uses of simulation of random phenomena with a table of random digits are described. Examples are given to illustrate the mathematics of simulation. (MP)

Discusses ways to simulate a probability problem of interest to middle school students in which students calculate the average number of packets of trading cards purchased to obtain a complete set of cards. Simulations utilize a spinner, a table of random numbers, and a computer. Includes the BASIC program utilized in the simulation. (MDH)

Mathematical modelling activities related to everyday situations (e.g., traffic lights) can be used to develop probability concepts. (SD)