LEVEL I-A UNIT AREAS COVER THE MEANING OF "NUMBER," ADDITION, MULTIPLICATION, SUBTRACTION, AND DIVISION. LEVEL I-B COVERS INTRODUCTION TO COMMON FRACTIONS, COMBINING FRACTION, FRACTIONAL PARTS, SEPARATING FRACTIONS, AND APPLICATIONS. EACH UNIT UNDER I-B HAS SUBDIVISIONS, WITH A PARAGRAPH OF TEACHING HINTS AND EXAMPLES. STRESS IS UPON…

One of a series of guides to the teaching of writing at the elementary and secondary levels, this publication focuses on teaching writing through models that introduce ideas, patterns, and styles through specific examples. The major portion of the publication describes learning activities, grouped into seven categories according to purpose:…

This paper is divided into three parts. Part I connects the reality of the classroom with the idealism which arises from some of the problem solving literature. It is argued that a broader concept of problem solving is needed to provide a perspective for bridging the gap between the conceptions of problem solving in the literature and typical…

This guide provides enrichment for students to develop tools and concepts used in various areas of mathematics. The first part presents arithmetic progressions, geometric progressions, and harmonic progression. In the second section, the concept of mathematic induction is developed from intuitive induction, using concrete activities, to the…

The described inservice teacher education learning module is designed for middle school teachers who are interested in better understanding the relationships of algebraic expressions. The contents of the module are outlined and the activities and resources involved in its use are described. Ordering information for materials is included as well as…

This publication is the first part of a series "Mathematics - Pre-Kindergarten, Kindergarten, and Grade One." This bulletin is a part of the developing curriculum program that incorporates the pre-kindergarten into the educational system and reorganizes mathematics materials in the early childhood years. Part One of the program presented…

Research literature concerning children's comprehension of pictures was compiled in order to clarify the role of textbook-type pictures in primary school children's learning of mathematics. The review is presented in eight sections: (1) psychological studies which investigated the role of imagery, comparing pictures with words, including (a)…

This teaching experiment investigated variables which affect how well children learn from manipulative aids and how to use such aids in teaching mathematics. Five small groups from one second-grade classroom were stratified by achievement and taught using (1) counting sticks; (2) Dienes blocks; (3) abacus; (4) all three materials; or (5) counting…

This study examines the extent to which modeling facilitates transformational problem solving in mathematics for children in kindergarten and first grade. Subjects were 20 children selected from each level. They responded to two problems for each of four problem types (counting on, story problems, quantitative comparisons, and ordination) under…

The impetus for this study developed from a search for intervention procedures applicable to children with learning difficulties in the regular grades. It was noted that, when certain aspects of the curriculum which involved extensive repetition were being taught to pupils, approximately 90 percent of the interactions between teachers and pupils…

This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…

This study was designed to compare the effects of the traditional teacher-centered mathematics classroom with that of a laboratory-based program, on achievement and attitudes of low-achieving seventh graders. Five teachers and 87 pupils participated in the study for 101 days. Mental ability was measured by the SRA Primary Mental Abilities Test,…

The purpose of this study was to measure the effects of tutoring low achievers on the concepts of carrying and borrowing before they were introduced in the classroom. Twelve low-achieving second-grade students were tutored on these concepts. The tutored children, along with members of two control groups, participated in a pretest covering these…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…