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…

The National Council of Teachers of Mathematics (NCTM) asserts that a goal of mathematics education, in Prekindergarten through grade 12, is to develop mathematical power for "all" students, and that educational equity is the nucleus of this goal. Nevertheless, researchers have found that equity for all students in mathematics education has not…

"Perspective" is a monthly e-newsletter presenting news and views from Achieve. This issue contains a report on the highlights of the fifth annual American Diploma Project (ADP) Network Leadership Team Meeting in Washington, D.C. Achieve's most well attended annual meeting, but also its most successful to date. While a variety of topics…

Teaching mathematics in real-word contexts is a strategy to make math relevant for undergraduate students. However, very little research exists on students' methods of integrating contextual and mathematical knowledge through writing. This study uses an interdisciplinary writing assignment to investigate the relationship between students' written…

There is growing concern in Europe that some students are not well-equipped to start a Bachelor's or Master's programme, especially when the programme has a strong mathematical focus. In particular, attention is drawn to problems with mathematics in the transition from secondary to higher education. Higher education expects a certain level of…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the…

There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)

This article presents a Vygotsky-inspired analysis of how a teacher mediated a "thinking aloud" whole-group discussion in a 6th grade mathematics classroom. This discussion centered on finding patterns in a triangular array of consecutive numbers as a phase towards building recursive and direct algebraic formulas. By a "thinking aloud" discussion…