We comment on the paper "The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra" by Carolyn Kieran and Paul Drijvers. We look at aspects of Kieran and Drijvers' analysis with regard to "task-technique-theory" in the light of a model of abstraction in context…

Not so long ago, the common response of teachers to high school use of computer algebra systems (CAS) was invariably along the lines of, "What will be left to teach if our students have access to devices which solve, factorise, do calculus and more?" and "If students use such tools, then they will never learn how to do their mathematics, and their…

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…

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…

Discusses computer methods for finding roots of polynomials. The program provided finds rational roots and prints the roots as rational numbers. (PK)

Describes several ways to implement the NCTM Standards in technically enhanced classrooms. Presents examples from "Computer-Intensive Algebra." Provides suggestions for implementation. (YP)

This document promotes computer symbolic mathematics and computer algebra as ideal instructional materials for mathematics, science, and engineering students. Further, computer algebra is viewed as appropriate for all students throughout the mathematics curriculum, by serving a vast area of mutual reinforcement and cross-motivation between…

Reports 17 recommendations that focus primarily on curriculum in grades 11-13 for students who take a four-year college-preparatory program. Appropriate curricular patterns for students who are intending to pursue careers that depend on mathematics are indicated. (PK)

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)…

Reviews of the courseware "Discovery! Experiences with Scientific Reasoning" and "Guess My Rule" are given. Discusses the accompanying manuals, the relative ease of use, and content of the programs. (PK)

Presented are two reasons discouraging computer symbol manipulation systems use in school mathematics at present: cost for computer laboratories or expensive pocket computers; and impracticality of exact solution representations. Although development with this technology in mathematics education advances, graphing calculators are recommended to…

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)

Discusses criteria that can be used to determine whether it would be effective to integrate computers into classroom instruction. Highlights include improving the quality of instruction; the use of appropriate courseware for difficult subjects, such as algebra and chemistry; drills and practice; improving motivation; and the role and effectiveness…