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…

This book begins with a historical and social foundation for belief in the arbitrary nature of the traditional mathematics curriculum. Chapters reflect the way the author learned while working with children. Each chapter is a complete idea and it is not necessary to read them sequentially. Each chapter is illustrated by stories of different work…

If equivalent operations are performed on the left term and right term of an equation, a new equation results. This principle allows one to produce equations with a variable isolated on one side and its value(s) on the other. It also underlies problem-solving in situations where equations are not explicitly used, but the problem calls for…

Achievement on the final exam was the dependent variable in an experiment involving two college algebra classes. The experimental class was allowed retesting on unit tests while a control class took the unit test once. No significant differences were obtained. (JP)

The author provides an example of obtaining the correct answer to a problem through a so-called nonsense solution. The conditions under which this incorrect method will yield a correct solution are examined. (JP)

Using the computer to calculate the probability that a quadratic equation will factor over the integers is discussed. (DT)