This paper presents a framework for understanding conditions of discovery learning in computer-based microworlds. It begins with a short discussion of problems related to a traditional type of microworld--i.e., learning tools for mathematics--using the Dienes Multibase Arithmetic blocks as an example. In this discussion, hypotheses are developed…

"Primary Mathematics" is a magazine for primary grades teachers. It contains activities which can be used, or adapted for use, with children over a wide ability range. It also contains articles on the teaching and learning of mathematics. The material in this book was selected from 18 issues of "Primary Mathematics" published…

Discussion material and exercises related to pre-algebra groups are provided in this five chapter manual. Chapter 1 (mappings) focuses on restricted domains, order of operations (parentheses and exponents), rules of assignment, and computer extensions. Chapter 2 considers finite number systems, including binary operations, clock arithmetic,…

This paper looks at the issue of mathematics learning from a developmental perspective. It begins by focusing on the importance for teachers of understanding how mathematical thinking develops. The New Zealand Number Framework is used as an example of a developmental progression that is of particular relevance to the teaching of mathematics. The…

The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through…

The goal of this practicum was to involve parents in their children's mathematics learning. To accomplish this aim, efforts were made to improve children's performance and attitudes toward mathematics; to enable teachers to recognize the value of activities and games as an alternate to learning by rote; and to offer opportunities for parents to…

This module is the first in a series of 12 learning modules designed to teach occupational mathematics. Designed for improving machine shop technology skills, this module begins with an introduction to the topic. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are…

This module is the seventh in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include fractions, fraction to decimal conversion,…

This module is the ninth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include measurement conversions, the English system of…

This module is the 11th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include multiplication, powers, calculator use, and roots.…

This book contains revised versions of the major papers presented at the Research Agenda Project Conference on Number Concepts in the Middle Grades. It is organized into three major sections, along with an introductory chapter and two brief summaries. Part I includes chapters that deal primarily with analyses of subject matter. The four chapters…

The psychometric integrity of selected items from the Mathematics Association of America (MAA) placement tests for college students was investigated. Two alternative and parallel versions of the test were developed (Form A and Form B) for this study. Data for 539 students seeking admission into an undergraduate mathematics curriculum at a private…

Over a 14-month period, infants who were initially 10 months old were intermittently allowed to play with three sets of graduated objects presented in disarray. All of the infants acquired the ability to completely organize the materials. The infants exhibited patterned behavior in their organizing practices when they individualized objects by…

A comprehensive system of literacy instruction is outlined in this monograph. The system involves two stages--learning to read and reading to learn (reading to get information from printed materials)--which are integrated through two overlapping teaching spirals organized around a chosen subject matter theme. The nine chapters of the monograph…

Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and…