This study reports a factor analysis of the data resulting from a 3-year longitudinal investigation into conservation of number and related mathematical type concepts. Conservation of number, which represents a subset within the concept of conservation, was measured by use of a 20-item, criterion-referenced testing device. The subjects, who were…

Reports on the development of a course in modern mathematics for elementary school teachers. The subject matter for the course is concentrated on whole numbers, integers, and rational numbers. Ideas of logic and set theory are brought into the discussion incidently as needed for developing the number systems. Part 1 of the course is a brief essay…

Reported are the results of a study designed to determine the most efficient learning sequence appropriate for preschoolers in learning three set relations. The efficiency of a particular ordering of the relations, equivalence (E), greater than (G), less than (L)) was evaluated in terms of time required to reach criterion, and amount of transfer.…

These materials were written with the aim of reflecting the thinking of the Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. This report deals with some seventh grade mathematical concepts taught at Cambridge Friends' School. The discovery approach was utilized by the teacher in order to…

Provided is an introduction to the properties of continued fractions for the intellectually curious high school student. Among the topics included are (1) Expansion of Rational Numbers into Simple Continued Fractions, (2) Convergents, (3) Continued Fractions and Linear Diophantine Equations of the Type am + bn = c, (4) Continued Fractions and…

This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms, sets, and…

This investigation sought to determine the effect of emphasizing mathematical structure in the acquisition of computational skills by seven- and eight-year-olds. The meaningful development-of-structure approach emphasized closure, commutativity, associativity, and the identity element of addition; the inverse relationship between addition and…

The objective of this study was to assess the ability of a previously prepared diagnostic test to detect the need for remediation in preschool children and then to assess the effectiveness of specially designed remedial materials. The subjects consisted of 47 boys and 25 girls from four private kindergartens in Nashville, Tennessee. All subjects…

The teacher's guide for the fourth unit of this SMSG series covers the two chapters on the rational numbers and geometric congruence. 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, and…

The purpose of the study was to gain information regarding the interaction between ten mental factors selected from Guilford's Structure of the Intellect Model and learning, transfer, and retention of a mathematical concept studied with and without a physical model. The meaning of place value in different number bases was studied by 202 seventh…

Two experiments were conducted to examine the possibility that numbering might have an effect on learning of lists composed of more meaningful and highly available materials, words, and to further explore the possibility that different strategies may be employed in learning the two types of lists. In Experiment 1, 40 female students from…

One hundred seventy-six seventh grade students underwent a recorded interview where each was given a set of computational exercises and asked to say aloud his thinking as he worked them. The most frequently used strategies in computations with whole numbers and fractions are described in detail, an analysis of the nature of wrong answers is…

The relationship between children's performance in solving open sentences and the factors of sentence type, number size, and context was investigated. The study also identified and classified the methods of solution used. Thirty-two third graders were individually given an orally administered test on open sentences. Four types of open sentences…

This guide continues instruction of the three guides in SE 012 723 and of the two guides included in SE 012 724. Counting skills, appreciation of pattern and order, and understanding of place value are extended to numbers up to one million, and the associative, commutative and distributive laws are made explicit. Manipulation of equations is…

There are at least two situations in which the behavioral scientist wishes to transform uniformly distributed data into normally distributed data: (1) In studies of sampling distributions where uniformly distributed pseudo-random numbers are generated by a computer but normally distributed numbers are desired; and (2) In measurement applications…