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)

After a unit on Euclidean geometry which stresses both the development of intuition and the use of deductive methods, non-Euclidean concepts are introduced by having students read and consider science fiction stories. (SD)

Referring to several examples, the author argues that more time should be spent developing statistical concepts such as randomness and independence before developing mathematical models for statistical computations. (SD)

Various sequences of characterization and exemplification of concepts, and use of examples versus nonexamples, are compared for their effectiveness in teaching inclusive and disjunctive concepts related to algebra and geometry. (SD)

Exercises integrating mathematical concepts and reading are explained.

After considering the mathematical system common to various types of measure, the author argues that instruction needs to reflect the common aspects of measure systems as well as the distinctive attributes of different systems. (SD)

Activities involving rolling dice and recording results in diverse ways introduce children to a variety of basic mathematical concepts. Several games and activities are described. (SD)

Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)

College students read passages describing quantitative relations among elements, and answered either 12 numeric (A=20C?) or 12 comparative (A .gt. C?) questions. When they received both types of questions, subjects performed better on the type they had received previously. Information stated as meaningful stories resulted in better performance…

A report of two investigations using different instruments and concerned with student understanding or lack of understanding of mathematical terms is presented. (MN)

The author cites observations of his own children that reflect their concept of fractions and analyzes their conduct in each case. (MN)