One of the first simulation-based introductory statistics curricula to be developed was the NSF-funded Change Agents for Teaching and Learning Statistics curriculum. True to its name, this curriculum is constantly undergoing change. This article describes the story of the curriculum as it has evolved at the University of Minnesota and offers…

We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

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 Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

At universities, we observe a great range of variation in previous knowledge and decreasing mathematical competences of students -- partly due to less limited qualification rules at universities in Germany. To address the challenges which arise by teaching very heterogeneous student groups we use e-tutorials as an addition to traditional classroom…

Teaching undergraduates the basic properties of an estimator can be difficult. Most definitions are easy enough to comprehend, but difficulties often lie in gaining a "good feel" for these properties and why one property might be more desired as compared to another property. Simulations which involve visualization of these properties can…

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

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…

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 offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…