Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three…

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…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

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…

Data analysis plays a prominent role in various facets of modern life: Schools evaluate and revise programs on the basis of test scores; policymakers make decisions on the basis of information gleaned from polling data; supermarkets stock shelves on the basis of data collected at checkout lanes. Data analysis provides teachers with new tools and…

This article describes several methods from discrete mathematics used to simulate and solve an interesting problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? (Contains 5 figures.)

Implications of the no-news no-change approach and student perceptions extends beyond the Monty Hall problem to two other situations in which the underlying concepts are similar.

Using the computer to calculate the probability that a quadratic equation will factor over the integers is discussed. (DT)

Two specific cases involving Pascal's Problem of the Points are discussed, followed by a solution in the general case. (MNS)

An analysis is made of overall probabilities of juries making the correct decisions when the juries vary in size from two to beyond five. (DT)

Annual records of the one-mile sun can be used to introduce a variety of statistical ideas including the scatter diagram, theoretical vs. observed values, and normal equations. (SD)

Activities in which the claims of psychics are evaluated can be used in probability classes. (SD)

Included in this section are brief articles on making up a story to explain a graph, the inverse of a function of a single variable, and exotic horse-race wagering and combinatorics. (MNS)

The uses of random number generators are illustrated in three ways: (1) the solution of a probability problem using a coin; (2) the solution of a system of simultaneous linear equations using a die; and (3) the approximation of pi using darts. (MP)