The development of number concepts from prehistoric time to the present day are presented. Section 1 presents the historical development, logical development, and the infinitude of numbers. Section 2 focuses on non-positional and positional numeration systems. Section 3 compares historical and modern techniques and devices for computation. Section…

The child's ability to identify numerousness as a property of a set, distinct from all the other properties of that set, may be a prerequisite to conservation of numerousness of sets. To test this theory, 11 lessons designed to develop the ability to identify properties of objects and of sets of objects and to represent length and numerousness…

Conservation of a property is the ability to recognize that the property in question hasn't altered, even though other properties have been varied. It is Piaget's view, confirmed by empirical evidence that children are not able to conserve length until age 7 or 8. Recent concern over confounding variables led to the present study in which the…

The research reported dealt with the ability of first, second, and third grade students to understand the topological concepts of solids, sheets, lines, networks, and of order and betweenness. The concepts were presented through the use of manipulative materials. The instruction was conducted by the regular teachers for a period of three weeks…

The task analysis for Developing Mathematical Processes, Arithmetic, Book 2: Writing Mathematical Sentences is presented. The major objective of this text is to have children write and validate mathematical sentences which represent the results of the compare-and-equalize process. The major components of the task analysis of Book 2 are Writing…

This study sought to determine whether a number of specific counting and numeration behaviors emerge within children in a fixed developmental sequence; at what point in the development of mathematical behavior the use of numerical representations normally appears; and what relationship holds between development of counting skills and development…

This book deals with the teaching of mathematical concepts through the use of the psychology of human learning. In the first part of the book, the thought processes which people adopt when they do mathematics are analyzed psychologically. Interpersonal and emotional factors affecting the learning of mathematics are discussed. The second part of…

This paper describes and evaluates a corrective mathematics program designed to meet the needs of approximately 25,000 Title I eligible pupils attending non public schools. The major objectives of the program were to improve the mathematical competency of pupils in computation, concept development and problem solving. Approximately 10,000 pupils…

A project for the teaching of mathematical concepts such as tessellation, algebra, and symmetry through artistic form is discussed. (MN)

Geomathematics is a developing field that is being used in practical applications. Classification is an important element and the dynamic-cluster method (DCM), a nonhierarchial procedure, was introduced this past year. A method for testing the degree of cluster distinctness was developed also. (MA)

Several examples of concrete mathematical models are discussed along with suggested criteria for good heuristic models. (MN)

Quarks are elementary particles considered to be components of the proton, the neutron, and others. This article presents the quark model as a mathematical concept. Also discussed are gluons and bag models. A bibliography is included. (MA)

The vast majority of people are most familiar with arithmetic in base ten. This article presents a follow-up on a problem with several divisibility tests valid in base ten which are related to Freitag's general test and which follow directly from it. Base 13 is also explored. (Author/MA)

The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)

This paper discusses ways of discussing limits in the secondary classroom. Particular attention is paid to showing that hypothesized answers are not limits to given sequences. (SD)