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…

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…

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and…

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…

Topics covered in the first chapter of Unit 8 of this SMSG series include square roots, operations with radicals, operations with real numbers, and the structure of the real number system. The second chapter deals with measurement of area (for rectangular regions, other polygons, and circles), volume and surface area, computation involving…

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…

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…

This workbook along with a set of transparent 2" x 3" cards was developed for use with underachieving seventh and eighth grade boys. It is designed for a 14 week term or less. The format uses the cards extensively to learn about fractions and operations with fractions. The cards have circles etched on them and the circles are divided into varying…

The study concerns the performances of first grade children in solving problems involving subtraction situations and the relationship of these performances to levels of conservation of numerousness and to I.Q. groups. The subjects were grouped into levels of conservation by a pretest administered prior to the main test of problem solving in…