Equivalence relations with a non-transparent transitive property are scarce in textbook examples. The equivalence relation given here is not only one with an interesting transitive property to prove, but also one that is instructive for students who are encountering proofs and relations for the first time.

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.

This article describes Comer's Method, a student's discovery of an alternative approach to solving the determinant of a 3x3 matrix.

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…

Two visual proofs illustrating a cubic Fibonacci number identity are given. These provide a basis for further activities and consideration of the use of visual approaches to other identities.

Real numbers are often a missing link in mathematical education. The standard working assumption in calculus courses is that there exists a system of "numbers", extending the rational number system, adequate for measuring continuous quantities. Moreover, that such "numbers" are in one-to-one correspondence with points on a "number line". But…

An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.

A model for car following on a closed loop is defined. The stability of the solutions of the model is investigated by considering the evolution of the roots of the corresponding characteristic equation in the complex plane. The solution provides a motivation for investigating the behaviour of the roots of a simple class of algebraic equation.…

The authors hope to show how a geometric insight can add to the richness of our students' experiences when they first encounter the solutions to two equations in two unknowns.

Saxon Algebra is a full-year mathematics curriculum designed for 8th- and 9th-grade students. This WWC Study Report reviews a study of the effects of the Saxon Algebra curriculum on 8th-grade student achievements. Students using this curriculum were compared with students using a curriculum from the University of Chicago Mathematics Project…

In this paper, a contextual approach to teaching Mathematics at the pre-university level is recommended, and an example is illustrated. A "context" in the form of a real common mathematical problem is presented to the students. Different approaches to tackle the problem (from topics within and outside the syllabus) can be elicited from students.…

This article introduces prediction as a useful tool to promote mathematical reasoning. First, the article addresses prediction expectations in state standards and gives examples. It also provides a classroom example and activities to illustrate what prediction can look like and how it can serve as a building block for the development of students'…

Algebra has been identified as the foundational course for all other mathematics courses. Yet, research has shown that African-American students are low achievers in all strands of mathematics (NCES, 2001). Computers, on the other hand, have been marketed as an instructional tool to teach and reinforce classroom instructions. This study…

The purpose of this study was to explore teachers' growth in understanding of algebra using concept maps. The study was set in the context of a five-year National Science Foundation funded teacher retention and renewal professional development project. In this project both beginning and experienced teachers are supported as they increase their…

Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…