The chapters in this book reflect the work of science and mathematics educators who have worked for many years at the international level. As members of the International Consortium for Research in Science and Mathematics Education, their work provides readers with issues, models, practices, and research results that have applicability and…

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

Described are children's strategies in thinking about fraction order and equivalence. The data are based on two teaching experiments with fourth and fifth-grade children. Some sample activities for teaching order and equivalence are included. (RH)

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

Reports the third grade and seventh grade results of the fourth mathematics assessment of the National Assessment of Educational Progress. Summarizes the major results of the performance on number, operations, and word problem items. Some examples of data are given. (PK)

Presented is a brief overview of Japanese education followed by specific ideas about important considerations in the teaching of mathematics in elementary grades. Examples are given for teaching flexibility in mathematical thinking. (RH)

The principles of cognitive psychology as they relate to rational number learning and instruction are discussed. Issues of knowledge acquisition, organization, retrieval and transfer are reviewed as they affect this area of the elementary school curriculum. Specific problems in learning about rational numbers and systematic student errors are…

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

This study addressed the problem of promoting generalization of knowledge in people with mental handicaps, by presenting an approach based on the idea that certain cognitive representations of strategies and related concepts are common to solving a wide variety of problems. The surface context of these problems may vary considerably, but all will…

Argues that, though considerable difference of view is evident between Montessori and Piaget about the importance of certain concepts and level of cognitive development necessary for genuine understanding, the ideas and methods first presented by Montessori 80 years ago stand up well when evaluated through the lens of current research. (PK)

Mathematics learning objectives and specifications for third graders, which are congruent with the Texas "State Board of Education Rules for Curriculum," are presented. They are designed for use by teachers and test development specialists involved with the preparation of the Texas Educational Assessment of Minimum Skills (TEAMS) tests.…

Reports on a seminar conducted by the Massachusetts Institute of Technology which was designed to help teachers develop their understanding of learning and teaching arithmetic. Describes some of the sessions and the activities and includes some of the dialogue exchanged within the group during the sessions. (TW)

The National Assessment of Educational Progress (NAEP) reports on the status and progress of educational achievement in the United States. Based on its surveys, "The Nation's Report Card" provides comprehensive information about what students in the United States can do in various subject areas. The framework for the 1990 mathematics…