EARLY FORMS OF NUMERICAL REASONING WERE INVESTIGATED BY EXAMINING THE ROLE OF A SET OF VARIABLES IN THE DEVELOPMENT OF CONSERVATION OF NUMBER. CONSERVATION OF NUMBER WAS DEFINED AS THE RECOGNITION THAT THE NUMBER OF OBJECTS CONSTITUTES AN AGGREGATE WHICH IS NOT CHANGED MERELY BY REARRANGING THEM. EXPERIMENT ONE WAS CONDUCTED WITH CHILDREN FROM…

This is part two of a two-part SMSG algebra text for ninth-grade students. The text was written for those students whose mathematical talent is underdeveloped. Chapter topics include the real numbers, addition of real numbers, multiplication of real numbers, properties of order, and subtraction and division for real numbers. (MP)

This is part three of a three-part manual for teachers using SMSG high school text materials. Each chapter contains a commentary on the text, answers to the exercises, and a set of illustrative test questions. Chapter topics include: (1) the system of vectors; (2) polar form of complex numbers; (3) sequences and series; (4) permutations; (5)…

This mathematics data bank of generic objectives was developed as the major element of an implementation of Comprehensive Achievement Monitoring in the Individualized and Personalized Adult Basic Education Program of the Canadore College (North Bay, Ontario) Continuing Education Division. The bank contains approximately 900 objectives organized…

Chapters 4-5 of the special materials written for low achieving students in grades 7-8 by SMSG deal with number theory and the properties of the integers. Included for each chapter are pretest exercises, a self-test, instructional lessons and exercises, and a chapter test. (CT)

This booklet has been written for elementary school teachers as an introductory survey of the real number system. The topics which are developed include the number line, infinite decimals, density, rational numbers, repeating decimals, irrational numbers, approximation, and operations on the real numbers. (RS)

The purpose of this study was to explore among first grade children the relationship between achievement in mathematics and the understanding of the principles of conservation, seriation, and categorization as these are defined by Jean Piaget. Research instruments included those designed by Piaget and the Greater Cleveland Mathematics Tests.…

A method of systematic behavior analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors…

The development of number concepts from prehistoric time to the present day are presented. Section 1 presents the historical development, logical development, and the infinitude of numbers. Section 2 focuses on non-positional and positional numeration systems. Section 3 compares historical and modern techniques and devices for computation. Section…

The child's ability to identify numerousness as a property of a set, distinct from all the other properties of that set, may be a prerequisite to conservation of numerousness of sets. To test this theory, 11 lessons designed to develop the ability to identify properties of objects and of sets of objects and to represent length and numerousness…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

The third student text in this SMSG series of 14 covers the following topics from number theory: the division algorithm, divisibility, prime numbers, prime factorization, common divisors and common multiples, and properties of the whole number system. A second chapter discusses properties and operations with integers. For a special edition of this…

The teacher's guide for Unit 13 of this SMSG series covers the chapter on systems of sentences in two variables and the chapter on exponents and logarithms. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral…

This guidebook specifies minimum course content covering number systems and bases, rational numbers and operations with rationals, and solving simple open sentences. Course goals are stated, then performance objectives, a course outline, references, and suggested teaching strategies are listed for each topic covered. Posttest items and a list of…

This study sought to determine whether a number of specific counting and numeration behaviors emerge within children in a fixed developmental sequence; at what point in the development of mathematical behavior the use of numerical representations normally appears; and what relationship holds between development of counting skills and development…