This paper discusses what the theory of abstraction is about, the need for a theory of abstraction in mathematics education, and the requirements that such a theory should meet. All three are reconsidered from a personal point of view. (KHR)

In this paper we report on a research aimed to identify and characterize secondary school students' reasoning and proof abilities when working with 3-dimensional geometric solids. We analyze students' answers to two problems asking them to prove certain properties of prisms. As results of this analysis, we get, on the one side, a characterization…

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…

This paper presents a cognitive theoretical framework for the learning of mathematics which has generic implications for other disciplines. The framework has been developed using a combination of established theories about learning and the authors' research into the understanding of some specific types of learning. It is based on the integration…

Informal interviews and naturalistic observations indicate that the child often invents novel ways of doing arithmetic and that some type of individualized instruction is necessary. (Author/WM)

Punisher effectiveness and generalization of an aversive stimulus, a rationale, and a combination of the two were investigated in a laboratory analog designed for punishment research, with 80 first and second grade subjects. Significantly greater suppression of deviant behavior and punishment generalization occurred when the punisher consisted of…

Article considers the forms of poetry and painting found in the talents of artists, such as Pound and Kandinsky. (RK)

Reprinted from the November 1971 issue of the Journal of Thought.'' (DD)

Author analyzes Walden in terms of his own semantic reactions to it which in turn sheds some light on Thoreau's semantics and author's teaching practices. (MB)

Outlines a teaching sequence to help students move from finger counting to abstract levels of computation. (Author/SP)

Experiment to determine whether the use of realistic materials would improve performance in a deceptive reasoning problem. (Authors)