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…

The role of computers (especially microcomputers) in the mathematics curriculum and suggestions for using them in mathematics instruction are discussed in this yearbook. The 27 articles are presented under five headings. Part 1, Issues, includes articles on comprehensive instructional computing, possible new curricula, and a syllabus for a…

This is a textbook of games for children of ages two through seven. In each section, games are listed from the basic to the more sophisticated and advanced. The book contains sections addressing: (1) counting and counting games; (2) travel games; (3) card games; (4) board games; and (5) games and activities with other things. (PK)

This is one of a series of monographs developed by teachers in elementary schools near Leeds, England. This document focuses on early instruction of number concepts. It is considered essential that these ideas be presented first in concrete form. The working group attempted to provide a detailed progression in the developmental stages leading to…

This learning module provides students with practice in applying mathematical operations to vocational agriculture. The module consists of unit objectives, definitions, information, problems to solve, worksheets suitable for various levels of vocational agriculture instruction, and answer keys for the problems and worksheets. This module, which…

This material is the result of 1 year of experimental work during the 1976-77 school year with pupils at the fifth-grade level. Once a week students participated in half-hour, small-group sessions in addition to their regular classroom mathematics period. It is felt that the activities described might be appropriate for additional grade levels. It…

These documents are three separate sets of student problems and teaching guides geared towards calculators. Series A is designed for pupils from ages 10 to 13; "B" is structured for 13 through 16, and "C" for 16 through 19. The materials are designed to provide activities for investigation and exploration of number properties and patterns that are…

A student-suggested project at an elementary-level mathematics laboratory using an adding machine to print a million twos is presented and described. Questions, problems, and activities that took place as the project was carried out are described. The process of producing twos presented all children with the necessity of gauging time intervals and…

This book is the teacher's manual to a text designed to meet the particular needs of those children who have "accumulated discouragements" in learning mathematics. It is a manual of suggested teaching strategies and additional materials aimed at compensating for past student failures to understand mathematical concepts. This book, L, is…

Hypothesizes that exploring the mathematical ideas behind mathematical terms enables children to gain insight into the structure of a number system and provides a basis for powerful playing with this structure. Describes visualizing mathematical ideas for exploring aspects of mathematics. Offers rectangular numbers to link and explore structures…

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)