There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number…

While researchers have documented the promise of detracking reform, many teachers still find it difficult to teach students with a wide range of academic skills in one classroom. Through engaging classroom footage and powerful interviews with teachers, students, and administrators, this 80-minute DVD showcases best practices from successful…

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

The transformations found in secondary mathematics curriculum are typically limited to stretches and translations (e.g., ACARA, 2010). Advanced students may find the transformation, twist, to be of further interest. As most available resources are written for professional-level readers, this article is intended to be an introduction accessible to…

Several activities that are based on the ancient method of false position, also called false assumption, are presented in this article as a way to motivate students to find the solution of literal equations in beginning algebra.

This article describes a vision of student use of dynamically connected representations as they investigate mathematical ideas. Although this article is intended to generate discussion about the potential of dynamically connected representations, we situate the discussion within actual descriptions of its use with students in a newly designed…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

This textbook is based on the idea that there should be an intermediate high school course that will sum up the arithmetic of the grades, and give some insight into the coming mathematical problems of algebra and geometry, especially if this course is linked up with work in mechanical drawing, manual training and elementary surveying. Such a…

This textbook, designed for at least one and one-half year's work in algebra, is intended for the use of those schools which find a one-book course best adapted to their needs. Experience thoroughly justifies a careful review at the beginning of the third half year's work. As the first twenty-three chapters contain the greater portion of the usual…

This textbook combines the material of the "New First Course in Algebra" and the "New Second Course in Algebra" in a form convenient for use in courses of more than a year in length. A large amount of review material is to be found at the point where the second year of work commences, since it was felt that there should be an…

Familiarity with modern methods of measurement and skill in doing quantitative thinking are essential. This text offers a "general" course intended for those who continue studies in the senior high school as well as for those who do not continue. It aims to contribute to the pupil's liberal education by preparing him to understand the…

Familiarity with modern methods of measurement and skill in doing quantitative thinking are essential. This text offers a "general" course intended for those who continue studies in the senior high school as well as for those who do not continue. It aims to contribute to the pupil's liberal education by preparing him to understand the…