This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

It appears extremely advantageous for highly gifted children if their parents can work in close collaboration with education authorities. How an individualized education program for one child was devised, and comments on preschool and tertiary education are given. (MNS)

Provided is an overview and analysis of recent progress in applying electronic information technology to creation of new environments for intellectual work in mathematics. Describes the impact of numerical computation, graphic computation, symbolic computation, multiple representation of information, programing and information, and artificial…

Described is an article that describes an adaptive computer tutor for arithmetic entitled "Shopping on Mars." The purpose of the tutor is to help children develop an extensive repertoire of information techniques for performing arithmetic in everyday situations and to learn to formulate shortcuts in problem solving. Results of…

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

This paper is an attempt at clarifying the concept of "problem," in order to improve the teaching of problem solving. Four categories are employed in the analysis: formulation, context, solutions, and methods of approach. Examples are included. (MNS)

Proposes that the learning of mathematics requires that the socially developed mathematical form, as well as the concepts it represents, become the property of the individual student. Indicates that the distinction between the form and content of mathematics, together with interrelationships between the two, is of crucial importance to effective…

Results obtained when a procedure for assessing the questions on uniersity mathematics examinations to see what skills were needed for their solution are given for a sample of 1400 questions set during 1976 in 10 British universities. The method is a way of focusing rational argument. (MNS)

Explores meanings of "generic" and "generality" as they are found both in everyday language and as they confront mathematics students. Considers everyday occurrences of the idea of generic (leading to the notion of a generic example of a class) and some ramifications in elementary algebra. (JN)

The geometry curriculum at the elementary school level is discussed. Details of five different units on geometry, each stressing space orientation, are given. (DT)

Examined is what radical constructivism in connection with Intuitionism might mean to mathematics instruction. Implications for mathematics education, especially the potential consequences for the teaching of mathematics of a relativist view of mathematical knowledge, are suggested. (YP)

Reports on a study of possible differences in interaction patterns between a sixth-grade teacher and different groups of students. Results showed consistency in the interactions studied, but important differences occurred in the quality and quantity with students perceived as "best" and "weakest" and boys and girls in…

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)

A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

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