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…

Statistics students' conceptions of the work of statisticians and the discipline of statistics may play an important role in the topics to which they attend and their interest in pursuing further study. To learn about students' conceptions, we collected open-ended survey responses from 44 undergraduate students who had completed introductory…

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…

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…

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…

In this paper different type of mathematical explanations are presented in relation to the mathematical problem of probabilities Monty Hall (card version) and the computational tool Latent Semantic Analyses (LSA) is used. At the moment the results in the literature about this computational tool to study texts show that this technique is…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

This article explores integrating place-based education with critical mathematics toward teaching mathematics for spatial justice. "Local Lotto," a curricular module with associated digital tools, was designed to investigate the lottery as a critical spatial phenomenon and piloted in urban high schools. This article describes findings…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

A challenging problem in some developing countries such as Nigeria is inadequate training of students in effective problem solving using the core concepts of their disciplines. Related to this is a disconnection between their learning and socio-economic development agenda of a country. These problems are more vivid in statistical education which…

Uniformity, that is, equiprobability of all available options is central as a theoretical presupposition and as a computational tool in probability theory. It is justified only when applied to an appropriate sample space. In five studies, we posed diversified problems that called for "unequal" probabilities or weights to be assigned to the given…

This article, which describes integrating virtual manipulatives with the teaching of probability at the elementary level, puts a "virtual spin" on the teaching of probability to provide more opportunities for students to experience successful learning. The traditional use of concrete manipulatives is enhanced with virtual coins and spinners from…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…