The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

Explains the importance of students learning algebra, and provides examples of how it can benefit them in typical life encounters. The article reveals how algebra quantifies relationships between quantities, basic algebraic structures, and its importance in the deductive process. Several algebra problems that illustrate these points are presented.…

Mathematics truly is magical, especially for students with strong number sense and algebra skills. This paper describes a variety of mathematical surprises that will capture students' interest and motivate exploration of mathematical ideas. While the tricks themselves are fascinating, push students to think about the reasons why these stunning…

Our teaching conception acknowledges the teacher's central role as a decision maker, influenced by knowledge, beliefs, and emotions. We believe that teachers' education must be focused on teachers' awareness of the complexity of the teaching process, of the incidence of these factors in it, and of the importance of looking at theory as a strong…

Discusses the emergence of electronic performance support systems and describes some of the ways in which electronic performance support is now influencing learning strategies in elementary and secondary schools. Examples are given that involve writing, music, graphic arts, and algebra, and future directions are suggested. (LRW)

The main aim of this paper is to demonstrate that new and highly effective computer-based learning tools can be designed by adhering to a simple principle: Good learning tools conform to and support the processes and structures that comprise learning. The paper first discusses the processes involved in learning cognitive skills, then describes…

A description of De Morgan's life and work is followed with quotations of his thoughts and insights on the teaching and learning of mathematics. The purpose is to illustrate the sharpness of his ideas, his creative insights, and his wit for the enjoyment of the reader. (DC)

The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…

This paper speaks to the challenges, risks, and rewards of teaching about linear functions in a technology-rich environment from a constructivist perspective by describing a Foundations of Algebra class, which was designed and taught to junior high school students in such an environment in the summer of 1991. The design and implementation of the…

Hurricane Katrina made landfall near New Orleans, Louisiana, on August 29, 2005. The author discusses the efforts she and other Association for Childhood Education International (ACEI) colleagues made for the welfare of children who suffered from the storm. After her initial search for family, friends, and professional colleagues, she began trying…

Argues that first-year algebra should be taught in eighth grade. Outlines an algebra course that could provide average students with a working kowledge of algebra. Proposes that this would require students to have experiences with variables, equations, formulas, and graphs during previous years of study. (TW)

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

Discusses the need to consider the cognitive models of students and their learning processes when designing computer tutorials, and describes a tutorial designed to teach students how to generate algebraic equations for story problems. Testing and revisions of the tutorial, with both college and high school students are described. (14 references)…

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)

Describes a partnership that was formed to develop a fiber optic interactive network and its interface with the development of algebra curriculum and social services in the PATH (Partnership for Access to Higher) Mathematics project in Texas. Equipment connections, costs, and classroom layout are described; and social work components are…