The first in a series of three articles, successful instructional materials from a 15-year software development effort are analyzed and characterized with special attention given to educational experiences intended to shape students' perceptions of the fundamental nature, interconnectedness, and usefulness of mathematics. The software programs…

Investigated effects of computer assisted instruction (CAI) on learning efficiency, defined as either higher passing percentage or less time on task. Subjects (N=24) were college mathematics students who either were lectured or had a CAI tutorial on the lowest common denominator. The CAI group took less time, but solved more problems incorrectly.…

Describes the design principles of computer-assisted learning (CAL) environments in which the software is interactive yet adaptable to different styles of learning and teaching, illustrated with a mathematics application. Following implementation, initial evaluation data taken from students showed marked performance improvements, and indicated how…

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

Introduces the idea of using computer microworlds--interactive software for exploration of specific concepts--for mathematics education, the theme of this issue's articles. Discusses their development and the advantages of their use. Suggests that they can be successfully used for interactive teaching or for interpreting mathematics textbooks,…

This volume presents a partial description of the lessons in the preliminary version of the PLATO fractions curriculum. Each lesson has three parts: review, new material, and a student-selected option. Students receive immediate feedback from the computer as they progress through each lesson. Five groups of lessons are described: meaning of…

Presents the computer microworlds developed by the Children's Construction of Rational Numbers of Arithmetic (Fractions) Project. Provides an overview of three microworlds: Toys; Sticks; and Candybars. Discusses how children are expected to use the microworlds to construct an understanding of rational numbers. (MDH)

This combination methods and resource book is written for preservice and inservice teachers of mathematics in the elementary school. It presents a program based on the research of the learning theories of Piaget, Brownell, Deines, Skemp, and Gagne and on successful classroom practices. The 14 chapters deal with: (1) "Mathematics in the Elementary…

This paper describes a 4-month-long experiment in computer-based learning called Instructional Software Design and presents aspects of the software evaluation. Results included greater mastery of LOGO and fractions by the experimental class than for either control class and greater acquisition of metacognitive skills. (Author/CW)

Presents eight points to emphasize when teaching the concept of place value. Contends that converting numbers from one base to another helps students understand the concept of place value and the importance of context in establishing meaning. Provides a BASIC computer program to make conversions. (MDH)

Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…

Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…