Students have the opportunity to verbalize relationships that demonstrate the acquisition of good number sense. They are to develop clues about the answer to a problem without computing or telling the answer, and to state or write several things they know about the answer to each problem. (MNS)

Young children benefit from activities that involve various partitions of numbers, especially the number 10. Presented are two activities that require students partition and recombine numbers to solve problems in a gamelike situations. Examples and worksheets are provided. (MDH)

Presents the general postage-stamp problem on Diophantine equations. Discusses ways to uncover all solutions to the problem. (ASK)

Presents responses to a division problem appearing in the September, 1998 "problem solvers" section of this journal. (ASK)

Examines ways in which teachers can develop children's abilities to mathematize their world by articulating mathematical problems in situations, then solving and discussing their solutions. Contains 11 references. (ASK)

This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…

This document, the first of three volumes, reports on the 15th annual conference of the International Group for the Psychology of Mathematics Education (PME) held in Italy 1991. Plenary addresses and speakers are: "Social Interaction and Mathematical Knowledge" (B. M. Bartolini); "Meaning: Image Schemata and Protocols" (W.…

This book is designed to provide middle-grade mathematics teachers with ideas for enlivening instruction to help students acquire a sense about numbers. Guided classroom discussions for writing opportunities centered on the theme of problem solving are provided. Following an introduction, chapters include the following: Counterintuitive Problems;…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

A series of problems involving number theory, the law of cosines, and geometric interpretations of solutions to equations is discussed. (SD)

Investigations which employ a search for a number pattern as an approach to solving a geometry problem are discussed. Four problems are presented, with suggestions for testing simple cases, discussion questions, organizing information, and conclusions to be drawn. (MNS)

A case is given against teaching division of fractional numbers. Types of problems usually solved by division are solved by methods involving only multiplication. (JP)

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

ACCORDING TO PIAGET, THE CONCEPT OF CONSERVATION IS A PREREQUISITE TO MATHEMATICAL UNDERSTANDING. THIS STUDY SOUGHT TO DETERMINE WHETHER THE ABILITY OF FIRST GRADE CHILDREN TO SOLVE ADDITION PROBLEMS WAS DEPENDENT ON THEIR MASTERY OF CONSERVATION OF NUMEROUSNESS. SECONDARY PURPOSES WERE TO INVESTIGATE THE EFFECT IN PROBLEM STATEMENTS OF (1)…