# ENCOURAGING COLLABORATION IN ONLINE CLASSES: MONTE CARLO SIMULATION PROJECTS TO SUPPLEMENT THE TEACHING OF INTRODUCTORY STATISTICS

While the online experience has much to commend it, students are not exposed to their peers in asynchronous learning. This paper describes the use of a variety of collaborative Monte Carlo simulation project to both assist in the teaching of introductory statistical concepts and to provide peer-to-peer interactions. These simulations are carried out as part of a group project that students do in stages (in parallel with the course material) and hand in periodically during the course of the term. The project consists of a series of exercises that together graphically demonstrate descriptive and inferential statistical concepts in a way that makes for better understanding of these abstract ideas. The primary formula in statistics is the mean. Since all means are calculated based on a sample and all samples are obtained from a population, we begin by defining a population whose parameter values are known and easily accessible: the discrete uniform distribution from 0 to 9. This distribution is readily obtained by picking numbers from a random number table, using a randomly generated number within Excel, by manually picking numbers from a hat or by spinning a miniature roulette wheel. Through repeated sampling from this population the student learns in concrete terms the meaning of such subtle notions as: the Central Limit Theorem; probability; interval estimation; hypothesis testing and alpha and beta. In addition, the student is given an opportunity to hone their computer skills.

Many students find the concepts discussed in introductory statistics to be abstract and difficult. In particular that section of the course called inferential statistics gives much trouble to the student who is not mathematically sophisticated. In the course of this project the student is able to verify that the predictions of the standard statistical formulas correspond to the results obtained from repeated sampling. This educational tool is specifically designed to explain the basic logic of inferential statistics and has been successfully tested over time. Most students have favorable thing to say about their learning experience. A description of the fifty and the studentsâ€™ sample projects will be provided.

In the presentation we will explain why Monte Carlo simulation is a useful tool for teaching and learning statistics. The basics of descriptive statistics (e.g., mean, standard deviation, distributions, histograms) and introductory inferential statistics (e.g., confidence intervals, hypothesis testing) are all taught using a unified framework and an incremental and cumulative technique.

The collaborative aspects of these assignments enriches the studentsâ€™ online learning experience.