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…

Described are ways in which some teachers have used a software package called "The Geometric Supposer." The development of inquiry skills is stressed. Recommendations for students using the Supposer are provided. (CW)

This report summarizes results from research aimed at improving the quality of information collected about school curriculum. The research sought to design and pilot a model for collecting benchmark data on school coursework. These more indepth data, such as course textbooks, assignments, exams, and teacher logs, can serve as anchors against which…

A software tool called 3D-LAB has been developed for learning and teaching three-dimensional geometry. With this microworld, educators and students can display three dimensional solid objects, rotate them, modify them, open them up, draw points and segments, and measure lengths, areas, volumes, and angles. The major characteristics of this tool…

Geometer's Sketchpad is an interactive geometry software package used to help students learn geometry principles. Use of Sketchpad in a secondary education math course at the State University of New York (SUNY) at Oswego has allowed geometry to be taught in a dynamic manner. The paper provides three examples of how Sketchpad is used. Traditional…

This document offers instructional materials for a 60-hour course on math operations involving decimals, fractions, proportions, statistics, probability, measurement, geometry, and linear algebra as applied in the workplace. The course was part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its…

A program description and sample program materials of a self-paced, individualized mathematics program designed to improve the achievement of junior high school students are presented. The usual daily activities of the students include a quiz, work in drillbooks, and work in the Basic Skill Levels curriculum--the heart of the program. Each of the…

Four sequential Basic Skill Levels (levels G, H, HA, and I) of a self-paced, individualized mathematics program designed to improve the achievement of junior high school students are presented in this student workbook. Each level includes a pretest, four to seven lessons, quizzes (checkpoints) after each fourth lesson, a posttest, and a level…

One of a series of documents produced by a nationwide network of early childhood education specialists, teachers, parents, and Head Start staff, the unit provides 75 mathematics lessons for kindergarteners. Built around an October theme, the lessons include activities on one-to-one correspondence, money, time, counting, ordering, classifying,…

Mathematics and the use of mathematical thinking should be much more than what has been traditional school arithmetic. Much of the mathematical reasoning can be developed and experienced out of school, particularly in the home. This material is a teacher's guide designed to help parents support what is done with their children in class. Background…

Mathematics and the use of mathematical thinking should be much more than what has been traditional school arithmetic. Much of the mathematical reasoning can be developed and experienced out of school, particularly in the home. This material is a teacher's guide designed to help parents support what is done with their children in class. Background…