The processes and products involved in discovery learning are analyzed, some of the relationships among the terms involved are established, and a framework for the identification of these terms is set up. (DT)

This paper discusses the process of investigating a mathematical situation, making conjectures, formulating an equation, then using mathematical induction to show the result is valid. Several examples appropriate for secondary school level are given. (DT)

Seven different views of geometry are identified, and for each of the views, guidelines for designing individualized curricula are developed. (DT)

An analysis of methods of teaching children to solve verbal arithmetic problems is presented together with transcriptions of interviews in which children solve problems by reference to problem types. (SD)

The author argues that the emphasis on logic and set theory in the school mathematics program is unnecessary and possibly harmful. He discusses briefly the relationships between semantics and logic. (SD)

A computer-based college course covering the exact and complete theory of logical inference is described. Student's performance and their evaluation of the course are discussed. (SD)

The concept of infinite divisibility is shown by this research report to be intuitively contradictory. This intuition remains unaffected by age and the teaching process. (MP)

The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

Several general aspects are discussed. These include the role of mathematics in scientific and technical progress, some deficiencies in training, the role of mathematics in engineering faculties, and methods of improving mathematical training. (MP)

Topics discussed include: reasons for strategies; the use of a hierarchy of spaces from topological to Euclidean in teaching; structural strategies; pedagogical strategies; and mathematical strategies. (MP)

An instructional program is described involving six booklets on descriptive statistics and four computer programs on statistical tests. (MP)

Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

The nature of insight is discussed as it relates to mathematical models. Intuition and the intuitively obvious are argued to have no necessary connection with models. (MP)

Discussed are difficulties which occur while the student is using mathematical induction as a tool to prove theorems. An appropriate approach is suggested. (MP)

The iconographic means of illustrating mathematical facts is discussed along with several examples of graphical solutions to descriptive mathematics problems proposed by pupils. (MN)