The study presented in this article examined the impact of two simulation-based inference activities on students' understanding of p-values in a second undergraduate statistics course. In the study, students familiar with traditional inference methods used physical and computer simulations to estimate p-values. To examine students' conceptions…

Probability is generally considered one of the most challenging areas to teach in mathematics education due to its intricate nature. However, the simulation-based teaching method can increase students' accessibility significantly to the probability problems because it enables students to resolve the problems with minimal mathematical skills. By…

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…

The development of Augmented Reality technologies has enabled students to learn in an environment that combines learning resources from the real and digital world. This paper integrates three mobile Augmented Reality-based applications into a series of mathematics lessons on probabilities in a junior high school. This paper aims to examine how…

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…

English language learners (ELLs) are a rapidly growing part of the student population in many countries. Studies on resources for language learners--especially Spanish-speaking ELLs--have focused on areas such as reading, writing, and mathematics, but not introductory probability and statistics. Semi-structured qualitative interviews investigated…

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

The game of Plinko offers students an exciting real-world example of the applications of probability and data analysis. The Common Core State Standards for Mathematics (CCSSI 2010) and the Guidelines for Assessment in Statistics Education (GAISE) (Franklin et al. 2007) suggest that students in grades 6-8 be given ample opportunities to engage in…

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…

This article seeks to address a pedagogical theory of introducing the classicist and the frequentist approach to probability, by investigating important elements in 9th grade students' learning process while working with a "TinkerPlots2" combinatorial problem. Results from this research study indicate that, after the students had seen…

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, "TinkerPlots." Initial responses indicated that the students were aware of…

Mathematics teachers, researchers and specialists in educational technology from Quebec, Canada developed virtual tools that make interactive simulations of games of chance. These tools were presented to a group of teachers from New Brunswick through workshops and they then got to test and validate them with their students. Semi-structured…

Statistics is taught at every level of education, yet teachers often have to assume their students have no knowledge of statistics and start from scratch each time they set out to teach statistics. The motivation for this experimental study comes from interest in exploring educational applications of augmented reality (AR) delivered via mobile…