Discusses some aspects of the defining process in geometrical context in the reference frame of the theory of "figural concepts." Presents analysis of some examples taken from a teaching experiment at the sixth-grade level. Contains 30 references. (Author/ASK)

Analyses several examples of tacit influences exerted by mental models on the interpretation of various mathematical concepts in the domain of actual infinity. Specifically addresses the unconscious effect of the figural-pictorial models of statements related to the infinite sets of geometrical points related to the concepts of function and…

Investigation of the presence and effect of intuitive obstacles to the concept of irrational number in (n=30) ninth-grade, (n=32) tenth-grade, and (n=29) college students found that only some students manifest genuine intuitive biases. Most students were unable to classify numbers as rational, irrational, and/or real. (Author/MKR)

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…

The main thesis of the paper is that geometry deals with mental entities (the so-called geometrical figures) which possess simultaneously conceptual and figural characters. The paper analyzes the internal tensions which may arise in figural concepts because of their double nature, developmental aspects, and didactical implications. (Author/MDH)

Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)

Discusses the problem in the relationship between schemata and intuitions. Analyzes the hypothesis that intuitions are always based on certain structural schemata. Concludes that intuitions, even when expressed as instantaneous guesses, are in fact manipulated behind the scenes by schemata. Contains 27 references. (Author/ASK)

Analyzes the relationship between intuitions and structural schemata. Indicates that intuitions are generally based on structural schemata and the transition from schemata to intuitions is achieved by a particular process of compression. (Contains 38 references.) (Author/ASK)