Investigated were concepts of conservation (number and length), cardination, one-to-one correspondence, and counting ability, and the role of these concepts in learning first-grade mathematics. A Piagetian-type number concept test was developed and administered at the end of the school year to a sample of 38 entering first-grade students selected…

This publication is designed to extend and strengthen the computational skills and mathematical understandings of children in Grades 2 and 3. It presents an overall scope and detailed sequence for implementation by teachers and supervisors, based on the modern program introduced in pre-kindergarten, kindergarten and first grade classes. The scope…

This curriculum bulletin is one of a planned series of bulletins designed to meet the needs of teachers and supervisors. The materials in this bulletin consist of a series of daily lesson plans for use by teachers in presenting a modern program of seventh year mathematics. In these lesson plans are developed the concepts, skills, and applications…

This is the Teacher's Commentary for Mathematics for the Elementary School, Book K, Special Edition. The writers have relied on the existing SMSG kindergarten and first grade materials as a framework. This special edition is designed to meet the needs of disadvantaged children. Included in the Commentary are background information for the teacher,…

The varied forms and semantic factors of Japanese ordinal expressions are related to one another in a coherent system. In Japanese, the cardinal number form is a numeral compound in construction with a referent. The numeral compound consists of a number and a numeral adjunct. Numeral adjuncts are derived from bound forms, or numeral suffixes, and…

This study examines the effects of using different classes of ratios on adolescent performance on proportionality problems. Problems of the form a/b = c/x varied on four dimensions: size of a/b, equality or inequality of b and c, complex or simple fractions, and form of the test. Tests consisted of six proportionality problems involving sizes of…

This book is a partially annotated bibliography of books, articles, and periodicals concerned with mathematical games, puzzles, and amusements. It is a reprinting of Volume 1 of a three-volume series. This volume, originally published in 1955, treats problems and recreations which have been important in the history of mathematics as well as some…

This pamphlet recommends that elementary-school teachers be provided with inservice courses which deal with probability concepts. The recommendations are based on the experiences of 120 teachers who taught probability in elementary school as part of a project of the National Science Foundation. The authors observe that probability is important…

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…

After a brief description of three Piagetian stages (pre-operational, transition to concrete operations, and concrete operations), the author identifies 12 key statements from Piaget's writings. These statements, together with related implications for teaching elementary school mathematics, methods of diagnosing stage acquisition, and examples are…

This report is a continuation of a study conducted at the University of Wisconsin during the spring of 1967. The previous study, Technical Report #38, succeeded in teaching conservation of numerousness to small groups of kindergarten children, in a middle-class community. The purpose of the present study was to determine if the typical classroom…

Chapters 7-8 of the special materials for low achieving students in grades 7-8 by SMSG deal with properties of the rational numbers and elementary probability. Included for each chapter are pretest exercises, a self-test, instructional lessons and exercises, and a chapter test. (CT)

These materials were designed to provide a logical development of the number systems from the natural numbers through the real number system. The course attempts to develop pedagogical strategies which will enable naive mathematics students to cope with its content. Revised versions of these materials will be used with prospective elementary…

This bulletin provides an overview of research studies which relate to the teaching of certain mathematical topics in the elementary school. The studies cited pertain directly to the following questions: (1) What measurement and geometry is included in textbooks and programs? (2) What do children know about geometry and measurement? (3) What can…

This paper appraises recent developments in the curriculum and teaching of mathematics in the secondary schools and analyzes mathematics education in the United States with particular emphasis on Nebraska. The first section focuses upon characteristics that distinguish the modern secondary school mathematics curriculum from the traditional. The…