In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

The mathematical topic of inverse functions is an important element of algebra courses at the high school and college levels. The inverse function concept is best understood by students when it is presented in a familiar, real-world context. In this article, the authors discuss some misconceptions about inverse functions and suggest some…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

Involving students in generating and solving their own problems is proposed. A method for generating problems by using a number puzzle is presented. Ideas for using the "what if not" technique are also given. (MNS)

Presented are eight student worksheets of block problems. Included are diagrams of the squares and hollow squares involved and a separate answer sheet for the problems. (CW)

This study was designed to compare the relative effectiveness of word problem instruction based on Polya's approach to problem solving with Dahmus' word by word translation approach. When ninth-grade students were randomly assigned to one of these approaches, no differences in mean number of problems solved were observed. (SD)

Presented are example activities which are typical of the topic focus and methods of approach evident in the Algebraic Thinking in Children (ATIC) project. This project is aimed at assisting children to ultimately make sense of formal algebra when it is presented. (CW)

Presented is a set of mathematics problems associated with the characteristics, production, and consumption of chicken eggs. Student assignment sheets are included. (CW)

The problem-of-the-week (POW) and problem-solving class openers are exemplified as methods for the integration of course-relevant problem solving into a first-year algebra classroom without sacrificing time spent on developing skills and learning concepts. Illustrated examples, as well as problem sources, are included. (JJK)

This guide was prepared as an instructional aid for teachers of a second-year course in algebra. It was designed to be applicable to a wide range of Algebra II programs offered in senior high schools. The content of the Algebra II program has been divided into 13 major units and a preliminary unit designed to review selected Algebra I skills. Each…

This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…