This article discusses the role of the commutative, associative, distributive, and identity properties of addition and multiplication in preparing children for future success in algebra. (Contains 3 figures.)

The use of laptops and other technology in teaching and learning of algebra 1 was found to add new dimensions to the way students studied the subject. But all its positives and negatives are still to emerge and students also need to be comfortable using the computer technology.

Spreadsheets to explore regression with an algebra 2 class in a medium-sized rural high school are presented. The use of spreadsheets can help students develop sophisticated understanding of mathematical models and use them to describe real-world phenomena.

Mathematics truly is magical, especially for students with strong number sense and algebra skills. This paper describes a variety of mathematical surprises that will capture students' interest and motivate exploration of mathematical ideas. While the tricks themselves are fascinating, push students to think about the reasons why these stunning…

Computer algebra systems are frequently used for research. In addition, some instructors have based entire advanced courses around these systems. One benefit is that they allow students to become familiar with the methods of calculus by individual experimentation. However, instructors have generally seen computer algebra systems as unsuitable for…

In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct…

This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the…

This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

Domain scores have been proposed as a user-friendly way of providing instructional feedback about examinees' skills. Domain performance typically cannot be measured directly; instead, scores must be estimated using available information. Simulation studies suggest that IRT-based methods yield accurate group domain score estimates. Because…

We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how…

Using the modular ring Zeta[subscript 4], simple algebra is used to study diophantine equations of the form (x[cubed]-a=y[squared]). Fermat challenged his contemporaries to solve this equation when a = 2. They were unable to do so, although Fermat had devised a rather complicated proof himself. (Contains 2 tables.)

Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…

This article shows how Microsoft Excel's ability to vary parameters with sliders allows students to "stand on the shoulders of giants" and discover characteristics of polynomial functions.

This article describes explorations using The Geometer's Sketchpad for algebra and calculus content.

This article describes the rich thinking that can go into solving a difficult equation. The authors also give some sources for challenging mathematical problems.