Illustrations are provided which show how some algebraic manipulations done prior to doing calculations can eliminate unnecessary storage of data, reduce the total number of needed steps, and avoid overflow. (MN)

A theorem concerning the solutions of systems of linear equations is presented. (SD)

A different form of the quadratic formula is developed. (DT)

This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)

Three different methods for factoring a quadratic expression are given, then a case is made for the claim that the inspection method is the one which should be stressed. (DT)

Functions defined on a unit square are considered, so that a basis may be established to carry over important features to the circular functions. (DT)

A common approach used for introducing algebra to young adolescents is an exploration of visual patterns and expressing these patterns as functions and algebraic expressions. Past research has indicated that many adolescents experience difficulties with this approach. This paper explores teaching actions and thinking that begins to bridge many of…

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…

This paper presents an initial attempt to define structure sense for high school algebra and to test part of this definition. A questionnaire was distributed to 92 eleventh grade students in order to identify those who use structure sense. Presence and absence of brackets was examined to see how they affect use of structure sense. The overall use…

Computer algebra system (CAS) calculators are becoming increasingly common in schools and universities. While they offer quite sophisticated mathematical capability to teachers and students, it is not clear at present how they may best be employed. In particular their integration into students' learning and problem-solving remains an issue. In…

We describe highly generative and affectively powerful classroom activity structures that are made possible by applying new levels of connectivity across diverse hardware platforms. Based on teaching experiments involving core topics in basic algebra (slope-as-rate, linear functions, simultaneous conditions), we examine 3 kinds of activity…

A study was undertaken to develop a better understanding of the students enrolled in intermediate algebra (Mathematics 108) at Boise State University, Idaho, and to uncover variables that predicted success in that course. Predictor variables were divided into preenrollment variables and course variables. Examining data for students enrolled in…

The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…