Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

The frequentist and classical models of probability provide students with different lenses through which they can view probability. Prior research showed that students may bridge these two lenses through instructional designs that begin with a clear connection between the two, such as coin tossing. Considering that this connection is not always…

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Real-world phenomena simulation models, which can be used to engage middle-school students with probability, are described. Links to R instructional material and easy-to-use code are provided to facilitate implementation in the classroom.

We investigate factors influencing student sign-ups for Washington State's College Bound Scholarship (CBS) program. We find a substantial share of eligible middle school students fail to sign the CBS, forgoing college financial aid. Student characteristics associated with signing the scholarship parallel characteristics of low-income students who…

This article engages students in a simulation of the Coat Check problem, in which four women check their coats only to have them returned at random. Students examine the experimental and theoretical probability of at least one woman getting her own coat back.

This article addresses misconceptions related to what makes an unfair game fair and describes from a personal perspective the process of discovering for oneself when a particular mathematical method works. (Contains 3 figures and 2 tables.)