This article presents engaging interactive hypothesis tests which can be conducted with students very efficiently.

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

In this article, we discuss a collection of active learning activities derived from classic psychology studies that illustrate the appropriate use of descriptive and inferential statistics. (Contains 2 tables.)

Practical project work based on eBay selling prices is described. It is suitable for secondary school students of a wide range of statistical expertise and it may be used to introduce a statistical package. (Contains 4 figures and 5 tables.)

The mathematical topic of inverse functions is an important element of algebra courses at the high school and college levels. The inverse function concept is best understood by students when it is presented in a familiar, real-world context. In this article, the authors discuss some misconceptions about inverse functions and suggest some…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

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…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…

The purpose of this article is to provide suggestions for using public speaking tasks in English language teaching (ELT) and to highlight some of their many advantages. For the purpose of this article, the author will focus on two types of these tasks: student presentations and debates. Student presentations may consist of either individual or…

This article investigates the critical thinking difficulties of finance majors when asked to address ill-structured finance problems. The authors build on previous research in which they asked students to analyze an ill-structured investment problem and recommend a course of action. The results revealed numerous critical thinking weaknesses,…

This paper summarizes difficulties that chemistry students at all levels commonly exhibit when translating, manipulating, and interpreting mathematical expressions that contain logarithms, and offers approaches that the authors have found useful to help students overcome such difficulties. The online supplement provides problem sets created by the…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

This monograph provides teachers with a wide range of articles on the teaching of problem solving in the mathematics classroom. The first section, on Understanding the Problem, includes articles which provide a sense of the "problem" of teaching problem solving. The second section, on Devising a Plan, provides suggested plans for…