Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and…

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.…

A mysterious conflict of solutions emerged when a group of tenth- and eleventh-grade students were studying a seemingly ordinary problem on combination and probability. By investigating the mysterious "conflicts" caused by multiple randomization procedures, students will gain a deeper understanding of what it means to perform a task…

The dice game Farkle provides an excellent basis for four activities that reinforce probability and expected value concepts for students in an introductory statistics class. These concepts appear in the increasingly popular AP statistics course (Peck 2011) and are used in analyzing ethical issues from insurance and gambling (COMAP 2009; Woodward…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

Many view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas. Fibber's Dice, an adaptation of the game Liar's Dice, is a fast-paced game that rewards gutsy moves and favors the underdog. It also brings to life concepts arising in the study of probability. In particular, Fibber's Dice…

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

Mathematical ideas exist and develop in many different cultures. From this multicultural perspective, teachers can use a variety of approaches to acknowledge the role of culture in the teaching and learning of mathematics. Curricular materials that "emphasize both the mathematical and sociocultural aspects" not only help teachers achieve…

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original…

Today's students demand that their lessons be real, interesting, relevant, and manageable. Mathematics is one subject that eludes many students partly because its traditional presentation lacks those elements that encourage students to learn. Easy accessibility through electronic media has exposed people all over the world to a variety of sports…

The use of data is critical to the teaching of probability and statistics. At the very least, data should be provided within a meaningful context rather than presented as a generic, meaningless collection of numbers. Students often respond better, however, when working with data that they have gathered themselves. Having students collect data is a…

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…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…