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…

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…

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…

Interactive computer-based simulations have been applied in several contexts to teach statistical concepts in university level courses. In this report, the use of interactive simulations as part of summative assessment in a statistics course is described. Students accessed the simulations via the web and completed questions relating to the…

To create an environment in which all students have opportunities to notice, describe, and wonder about variability, this article takes a context familiar to many teacher--sampling colored chips from a jar--and shows how this context was used to explicitly focus on variation in the classroom. The sampling activity includes physical as well as…

A standard mattress can be positioned on a bed frame in any of four orientations. Suppose that four times a year the mattress is rotated into one of the three possible new orientations, chosen at random. According to an article in The American Scientist, a computer simulation suggests the rather surprising result that over a period of 10 years,…

The projects Xmath (Bringslid and Canessa, 2002) and dMath (Bringslid, de la Villa and Rodriguez, 2007) were supported by the European Commission in the so called Minerva Action (Xmath) and The Leonardo da Vinci programme (dMath). The Xmath eBook (Bringslid, 2006) includes algorithms into a wide range of undergraduate mathematical issues embedded…

This paper explores the use of simulations in virtual reality to teach students the fundamental processes behind retailing and product development. The project described involved one class of students who developed their own clothing lines of "virtual merchandise." A second class of students then "purchased" the wholesale…

The d'Arbeloff Interactive Mathematics Project or d'AIMP is an initiative that seeks to enhance and ultimately transform the teaching and learning of introductory mathematics at the Massachusetts Institute of Technology. A result of this project is a suite of "mathlets," a carefully developed set of dynamic computer applets for use in the…

If larger and larger samples are successively drawn from a population and a running average calculated after each sample has been drawn, the sequence of averages will converge to the mean, [mu], of the population. This remarkable fact, known as the law of large numbers, holds true if samples are drawn from a population of discrete or continuous…

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

Developed are simple recursion formulas for generating the exact distribution of the longest run of heads, both for a fair coin and for a biased coin. Discusses the applications of runs-related phenomena such as molecular biology, Markov chains, geometric variables, and random variables. (YP)