This mathematics textbook, written in Portuguese, is the third book of a Mathematics Program in Portuguese. It is designed for third graders. It closely follows the objectives and methodology of the major curricula used throughout the schools in the United States. The 11 chapters deal with: numeration (0-999,999); addition with and without…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

In order to describe developments in children's conceptions of numbers and numerical relations, judgments of similarities between numbers were solicited from adults and from children in kindergarten and grades 3 and 6. A nonmetric multidimensional scaling analysis suggested that children gradually become sensitive to an expanding set of numerical…

How does one teach number? Is there any way to apply Piaget's theory to the classroom? What activities are better than worksheets for helping children develop number concepts? Arguing that Piaget's research and theory are indeed useful to the classroom teacher and can make a major difference in how one teaches elementary number concepts, the…

Details of an investigation into polygonal numbers are given. From a study of the tabled series, patterns are discovered both within and between the various polygonal series. From a study of these results and the corresponding figures, formulas are developed. (LS)

This textbook is based on the SMSG kindergarten and first grade materials as a framework. This special edition is designed to meet the needs of disadvantaged children. Chapters in the book include: (1) Sets and Numbers; (2) Numerals and the Number Line; (3) Sets of Ten; and (4) Introduction to Addition and Subtraction. The student text contains a…

Basic computational problems admit several different solution algorithms. A student's choice of method may be related to personal characteristics which also bear on his ability to learn other mathematical techniques and theories. (SD)

Presented are a series of conjectures and proofs resulting from an examination of patterns and relationships among natural numbers. (JP)

This document lists references on the teaching of fractions, with many of the entries annotated. They are alphabetized by the author by categories: Activity and Game; Addition and Subtraction; Teaching Aids; Application; Assessment; Curriculum; Decimal; Common Fraction; Division; Equivalence of Fractions; Errors; Fraction Concept; Multiplication;…

This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

This guide is for the use of teachers in the primary grades and is organized around six concepts: sets, numbers and numeration; operations, their properties and number theory; relations and functions; geometry; measurement; and probability and statistics. Objectives and sample activities are presented for each concept. Separate sections deal with…

This is part one of a two-part SMSG text for grade seven students whose mathematical talents are underdeveloped. The reading level of this text has been adjusted downward, chapters shortened, and additional concrete examples included. Nevertheless, the authors warn that the text may not be appropriate for the very slow non-college-bound student.…

This is volume one of a two-volume manual for teachers using SMSG text materials for students in grades 7 and 8 whose mathematical talents are underdeveloped. The overall purpose for each of the chapters is described and the mathematical development detailed. Background information for key concepts, answers for all exercises in each chapter, and…

This is part one of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include number line and coordinates, equations, scientific notation,…