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…

The study was designed to investigate the effects on immediate acquisition, retention and transfer of two methods of presenting selected geometry concepts to sixth grade students. The effects of immediate acquisition and of transfer were measured immediately after presenting the lessons. The effects of retention were measured 1, 11, and 21 days…

This booklet was written for elementary school teachers who want suggestions of the type of activities suited to a mathematics laboratory. The emphasis is not that of a thorough survey of the available activities. Instead, the author uses selected examples to describe the spirit of a laboratory environment. The suggestions include arrangements of…

It is extremely difficult to extend in a natural way the concepts developed in high school geometry to motivate the concepts of trigonometry. To solve this difficultry, the author defines "sensed angles" as ordered pairs of rays and makes appropriate definitions which yield the familiar angle properties of plane geometry. He then shows how this…

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. These materials are intended to provide children with a variety of informal activities in intuitive geometry in the elementary school. Opportunities are provided…

A 1-year postdoctoral research training program prepared one trainee in early childhood education during 1966-67. Flexible arrangements allowed this mature trainee to plan and follow his own program in consultation with the staff of the Research and Development Center in Educational Stimulation at the University of Georgia. Experimentation in…

This bibliography serves as a guide to teachers and librarians who want to select books to supplement the elementary school mathematics program. The selections give an indication of the wide variety of topics which may include mathematical concepts. They reinforce or develop concepts about number and size, present material on the application of…

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…

Scientific Method rather than trial and error methods should be used to search for instructional algorithms. The Scientific Method is discussed with implications for this purpose. Suggested is the inclusion of theoretical and technological foundations in formulating instructional theory. Conditions needed for adequate instructional research are:…

In evaluating the two-course sequence in mathematics for prospective elementary teachers at the University of Texas in Austin, a study was included to determine whether there was a significant gain in knowledge of selected recommended mathematical content by students completing the course. A 46-item multiple choice test was developed and used as a…

A 12-part paradigm for testing level of concept attainment was used to construct items covering the topics of sets, division, and expressing relationships. Within each topic the concepts presented in the middle elementary grades were identified; ten concepts were randomly selected for each topic; and, for each concept, items matching the tasks in…

An investigation of student proof behavior in a complex computer-assisted instruction (CAI) setting is presented. Using 125 logic derivation problems, the responses of 23 students, enrolled in the Stanford Logic-Instructional System, were evaluated to determine the amount of variation occurring in the structure of their proofs. By assigning the…

The objective of this study was an attempt to clarify the nature of number conservation with number conservation tasks using variations in length, area, and volume. According to Piagetian theory, conservation is attained successively for number, length, area, and, finally, volume. It was hypothesized that success on the number conservation tasks…

CERTAIN TYPES OF INTELLECTUAL ABILITIES WHICH DEFINE THE MATHEMATICAL APTITUDES OF NINTH-GRADE STUDENTS AND WHICH RELATE TO ACHIEVEMENT IN SPECIFIC MATHEMATICS COURSES WERE DEFINED AND EVALUATED. ANALYSES OF VARIANCE AND COVARIANCE INDICATED THE RANGE OF VARIATION IN EIGHT TEST SCORE DISTRIBUTIONS OF VERBAL AND MATHEMATICAL APTITUDES AMONG FIVE…

Using mathematics as an example, the nature of the confusion between "knowledge" and "coming to know" is elucidated. The range of curriculum choices available to structuralists once the distinction is clarified is larger, and teaching a body of knowledge and teaching by discovery are compatible. (Author/MLF)