Last semester, the author had a particularly vocal class that made it clear that they disliked small group exercises. In an attempt to understand their discomfort, she had this class generate a list of the top 10 reasons they disliked small group exercises. Some of the reasons listed by the students are exactly why the author uses small group work…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

Educational problem sets have been developed on structured organic particulate systems (SOPS) used in pharmaceutical technology. The sets present topics such as particle properties and powder flow and can be integrated into K-12 and college-level curricula. The materials educate students in specific areas of pharmaceutical particulate processing,…

This article presents a problem set which includes a selection of probability problems. Probability theory started essentially as an empirical science and developed on the mathematical side later. The problems featured in this article demonstrate diversity of ideas and different concepts of probability, in particular, they refer to Laplace and…

Of the eight scientific practices highlighted in "A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas," the first is for students to develop abilities to ask questions and define problems (NRC 2012). Constructing a range of questions about an object or phenomenon validates not only what students have…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

The necessity of using inquiry-based learning (IBL) was recently recommended by studies and reports made for the European Commission. Several European projects are devoted to the widespread use of IBL methods. The effects of using IBL are studied worldwide. In the framework of the Seventh Framework Program (FP7) project PRIMAS, a series of…

Too often the discourse of the mathematics classroom is defined as the teacher asking the questions and the students answering them--or trying to. Certainly teachers should not be prohibited from asking questions, but if students are always placed in the position of responding rather than initiating, then one can hardly be surprised if at times…

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…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

The author describes a classroom activity in which students generate and then analyze insulting words to gain insights into how gender is socially constructed. After discussing how and why undergraduate students struggle with the concept of gender, the author highlights the usefulness of an active learning pedagogy in clearing these…

In this paper, we describe our experience with the creation and utilization of online assignments for several calculus classes at Simon Fraser University (SFU). We present our findings regarding available software by considering the needs and perspectives of the instructors, students, and administrators. We provide a list of questions that guide…

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…

This article describes the development and implementation of an open-access organic chemistry question bank for online tutorials and assessments at University College Cork and Dublin Institute of Technology. SOCOT (structure-based organic chemistry online tutorials) may be used to supplement traditional small-group tutorials, thereby allowing…