This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from…

For quite some time, research on the use of the History of Mathematics in the classroom has confirmed a lot of academic benefits for students. However, the History of Mathematics can also be used as an inclusion tool in classrooms where there are foreign students because it allows working with the specific contexts of other cultures. This article…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

Learning communities can strengthen early undergraduates' learning, but planning them can be daunting for instructors. Learning communities usually rely on integrative assignments that encourage interdisciplinary analysis. This article reports on our experiences using microloans as an interdisciplinary assignment in a learning community that…

In the 1970s, the movement to the metric system (which has still not completely occurred in the United States) and the advent of hand-held calculators led some to speculate that decimal representation of numbers would render fractions obsolete. This provocative proposition stimulated Zalman Usiskin to write "The Future of Fractions" in 1979. He…

This document presents ideas and activities for teaching algebra. The section on "Week by Week Essentials" provides seven resources in a weekly format. It includes writing ideas that provide an algebra prompt and requires students to organize their thoughts and present them in a coherent fashion, and connections to the real world that…

Two statements concerning magic squares, considered as 3x3 matrices, are discussed and their proofs given using only high school level techniques. (MP)

Some properties of perfect numbers are illustrated. (SD)

Several examples through which the Klein 4-group can be introduced are offered. (SD)

Algebraic and transcendental curves are discussed, with attention focused on computing the area of some special regions bounded by the curves. (MNS)

A mathematics project promoting an exploratory approach to mathematical problems as well as an organization and application of mathematical knowledge is described. (JT)

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

Classroom related topics discussed are: cryptics and statistics; understanding absolute value; recognizing quadratic equations with no real roots; and two derivations of a formula for finding the distance from a point to a line. (MP)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)