All students want to talk about ideas that interest them, but often, multilingual learners are not offered high-challenge, high-support opportunities to connect everyday experiences to mathematical ideas. We describe a single class period that connects students' everyday opinions with two-way tables and notions of independence.

The aim of this article is to buid a Guide to the Analysis of Probability Textbook Lessons for secondary education (students aged 12-14), using the framework of Didactic Suitability. The facets, components and indicators of the didactic suitability construct are applied to categorize and organize didactic-mathematical knowledge on teaching and…

The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact,…

Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

Some situations are presented with perplexing properties, which become clearer by looking at contingency tables. This in turn leads to problems that can be solved using conditional frequencies and thus leading to the Bayes formula with natural frequencies or probabilities.

This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers…

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…

This article asks the question: is the "Last Banana" game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by…

This article presents ways to explore mathematical concepts using Catan, a popular board game. After a brief overview of game play, we explore considerations with many potential entry points for mathematical modeling, such as which resource is the best, which resources will be rare or plentiful, where to build, and risk assessment.

The authors present a new classroom-tested lesson that was designed to engage students in the joy of mathematical inquiry through a card game, Frustration, while building number sense, understanding of uncertainty, statistical reasoning, and discourse skills. The purpose in developing and sharing these lessons is to highlight how games of chance…

This article is motivated by the importance of developing statistically literate students. The authors present a selection of problems that could be used to motivate student interest in probability as well as providing additional depth to the curriculum when used alongside traditional resources. The solutions presented utilise natural frequencies…

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.

Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

Sickle cell disease is a very common disease throughout the world. We used it to contextualize probability for upper elementary school students. Using Punnett squares, activities guide students' evaluation of inheritance using theoretical probability. Then, students perform trials using tools to compare theoretical and experimental probabilities.

The Birthday Paradox problem can be investigated either with a carefully constructed spreadsheet (for greatest precision) or a calculator process (for reasonable precision). A number of ways of approaching this problem as a class activity are provided.