In this paper the author proposes a learning model for basic mathematics based on measurement concepts. By analyzing mathematical concepts and citing related psychological and educational research, he develops and justifies this model. The basic premise on which the model is based is the notion that measurement provides an approach to number…

This is a report of an experiment performed to evaluate the effects of the teaching of non-decimal numeration systems in grades four and six. Eighteen classes consisting of 430 students comprised the sample. The students were divided into four randomly assigned treatment groups for each level. Tests were given before a teaching session of five to…

Twelve culturally disadvantaged 4-year-olds of borderline normal intelligence were subjects of this study. Its primary purpose was to test further the cognitive learning theory previously developed, as well as the reinforcement system, the facilities, and the experimental-longitudinal methods of research. The study did not include a control group…

This curriculum bulletin is one of a planned series of bulletins designed to meet the needs of teachers and supervisors who are working to improve the achievement level of mathematics in the schools. The eighty sequential units of this bulletin are organized into 3 categories - (1) Sets, number and numeration, (2) Operations, and (3) Geometry and…

This pamphlet is designed for use as enrichment material for able junior and senior high school students who are interested in mathematics. No more than a clear understanding of basic arithmetic is expected. Students are introduced to ideas from number theory and modern algebra by learning mathematical ways of coding and decoding secret messages.…

The material in this booklet is designed for non-professional mathematicians who have an interest in the theory of numbers. The author presents some elementary results of number theory without involving detailed proofs. Much of the material has direct application for secondary school mathematics teachers. A brief account of the nature of number…

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…

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…

Performance objectives are stated for this secondary school instructional unit concerned with introduction to the stretcher and shrinker approach, solution of simple equations, factoring composite numbers into primes, definition of prime numbers, and communication skills with computational concepts. The course of study is intended for students…

The teacher's guide for Unit 8 of this SMSG series covers the two chapters on the real number system and on area, volume, and computation. 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 objectives are stated,…

Topics covered in the first chapter of Unit 13 in this SMSG series include mathematical models, methods of solving systems of equations, and graphical solution of systems of inequalities. The second chapter of this unit deals with properties of exponents, exponential and logarithmic functions, computing with logarithms, and the slide rule. For…

This is the second of four guidebooks on minimum content designed to strengthen fundamental concepts which are basic preparation for Algebra I. This booklet covers integers, rational and irrational numbers, real number properties and operations, graphing in one dimension, and open sentences. The overall course goals are stated, then, for each…

Forty kindergarten children at the Stephen Bull School in Racine, Wisconsin were tested to determine the effects of a sequence of 12 experimental lessons on the ability of kindergarten children to recognize and conserve numerousness. Subjects were 40-low-to-middle socioeconomic level children divided into treatment and control groups. A specially…

The study attempted to trace the relationship between facility with cardinal-ordinal aspects of number; attention to dimensions of number, length, and density; and the presence and absence of number conservation. On the basis of performances on the standard test for number conservation, 25 nonconserving kindergarteners, 34 conserving…

This document is a collection of mathematics pretests and posttests for grades 3 and 4 on the topics of sets, place value, addition-subtraction, multiplication, division, multiplication-division, and fractions. Two forms for each test are provided plus answer keys. This work was prepared under an ESEA Title III contract. (DT)