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 manual was designed for use with the first of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

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…

This work, a revised version of the author's original "outline of Bielorussian Morphology" (1967), is intended as a contribution to a structurally oriented grammar of Bielorussian in English. It is based on published grammars and handbooks. Opening sections of this outline deal with phonology and morphophonemic alternations, followed by sections…

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…

The sixth in a series of six guidebooks on minimum course content for second-year algebra, this booklet presents an introduction to sequences, series, permutation, combinations, and probability. Included are arithmetic and geometric progressions and problems solved by counting and factorials. Overall course goals are specified, a course outline is…

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

The role of negative instances in the acquisition of the mathematical concepts of distributivity and homomorphism was examined. Two treatment levels for distributivity (positive instances and positive and negative instances) and the same treatment levels for homomorphism were crossed to form a 2 x 2 factorial design with 23 subjects per cell.…

A group of 161 kindergarten and first grade children were instructed in mathematics using exercises in linear measurement to increase understanding of unit-quantity relations. A comparison group made up from two adjacent and comparable middle-class schools was taught mathematics without intervention into the mathematics content. Treatment and…

The purpose of the study was to examine the informal and more formal mathematical notions of children of ages four to six, and to evaluate the interaction between these two sets of notions. Two groups of problems were given to 60 children. The first included 14 Quantity Tasks in the form of stories which were illustrated by manipulable items. The…

Designed for the student who has acquired basic computational skills with non-negative rational numbers, this guidebook delineates minimum course content to further develop students' computational skills with whole numbers. Place value and estimation are also covered. General goals, performance objectives, a course outline, suggested teaching…

This is the ninth in a series of ten self-contained units designed for use by students in ninth grade general mathematics classes. This unit is divided into six sections dealing with different concepts involving positive and negative numbers. Some concepts presented include positive and negative integers, addition and subtraction, multiplication,…

This teaching guide outlines a semester course for those students who need review work in concepts from algebra and geometry. Successful completion of this material would serve as a prerequisite to the study of trigonometry. Sequence, textbook references, and time allotments are suggested. Units studied are: the real numbers; operations on the…