Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. To aid the development of trust in these decisions, we develop a taxonomy delineating where trust in an analysis can break down: (1) in the translation of real-world goals to goals on a particular set of training data, (2) in the…

The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. This article explores an activity in which grade 10 students learned how a famous AI algorithm (the Apriori algorithm) uses conditional probability to automate the process of…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

Whether students are beginning their study of probability or are well into it, distinctions between complementary sets and mutually exclusive sets can be confusing. Cathy Schloemer writes in this article that for years she used typical classroom examples but was not happy with the student engagement or the level of understanding they produced.…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

Fine-grained data on religious communities are often considered sensitive in South Asia and consequently remain inaccessible. Yet without such data, statistical research on communal relations and group-based inequality remains superficial, hampering the development of appropriate policy measures to prevent further social exclusion on the basis of…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

A classic TV commercial once asked, "How many licks does it take to get to the center of a Tootsie Roll Tootsie Pop?" The narrator claims, "The world may never know" (Tootsie Roll 2012), but an Internet search returns a multitude of answers, some of which include rigorous systematic approaches by academics to address the…

This article provides tools and rationale for instructors in math and science to make their assessment and curriculum materials (more) readable for students. The tools discussed (MSWord, LexTutor, Coh-Metrix TEA) are readily available linguistic analysis applications that are grounded in current linguistic theory, but present output that can…

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…

Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

When Martin Gardner first presented the Two-Children problem, he made a mistake in its solution. Later he corrected the error, but unfortunately the incorrect solution is more widely known than his correction. In fact, a Tuesday-Child variation of this problem went viral in 2010, and the same flaw keeps reappearing in proposed solutions of that…

A critical numeracy examination of Benford's Law suggests that our understanding of the integers is faulty. We think of them as equally likely to turn up as the first digit of a random real world number. For many real world data sets this is not true. In many cases, ranging from eBay auction prices to six digit numbers in Google to the…