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 is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a…

This teacher's guide is written to be used in conjunction with the new materials for low achieving students in grades 7 and 8 by SMSG. It includes helpful hints about working with low achievers and suggestions regarding the implementation of this particular program. Most chapter discussions include behavioral objectives for the chapter, background…

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 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 first chapter in this fourth unit in this SMSG series of student texts covers properties and operations with rational numbers (both negative and non-negative rationals), equations involving rational numbers, and the structure of the rational number system. The second chapter on congruence discusses congruent segments, angles, and triangles;…

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…

The first of a series of three workbook texts on beginning algebra. Designed primarily for use by lower ability mathematics students, the texts have been used by average ability students as supplementary materials. Volume 1 contains material on multiplying, prime factors, signed numbers, problem solving involving addition, subtraction, and…

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…

The discovery method, according to the author, promotes logical thinking, is motivational in nature, makes learning more permanent, produces more usable knowledge, and gets students actively involved. A discovery lesson is characterized by the following: (1) the concept to be learned is not announced, (2) experiences and activities are developed…

The role of negative instances in the acquisition of the mathematical concepts of commutativity and associativity of a binary operation was examined. Two levels of instruction (positive instances, and positive and negative instances) for commutativity and for associativity were crossed to form a 2 x 2 factorial design with 16 ninth grade subjects…

This booklet includes short descriptions of the history of the calendar, Napier's Bones, and the beginnings of algebra. The remaining two stories discuss the number nine raised to the ninth power of nine, and repeating decimals. (DT)