Primary and secondary intuitions in the introduction of probability


Book: 
The Intuitive Source of Probabilistic Thinking in Children
Authors: 
Fischbein, E., Barbat, I., & Minzat, I.
Editors: 
Hintikka, J., Cohen, R., Davidson, D., Nuchelmans, G., & Salmon, W.
Type: 
Category: 
Volume: 
85
Pages: 
138-155
Year: 
1975
Publisher: 
D. Reidel
Place: 
The Netherlands
Abstract: 

The main objective of our research has been to study the intuitive biases corresponding to certain fundamental concepts and methods of the theory of probability. This is not simply a question of the general concepts of chance, or randomness, on which there are data already available. Research which has already been done by psychologists indicates the existence of a natural intuition of chance, or even of probability (cf. Fischbein et al., 1967, 1970a, b). However, A. Engel, a mathematician, has written: "...we have a natural geometric intuition but no probabilistic intuition". In order to elucidate this problem, we decided to go beyond the notion of chance, and try to follow the course of what, in fact, happens during the systematic teaching of certain concepts in the theory of probability. We therefore decided to study the intuitive responses of subjects to certain concepts and calculational precedures which were introduced during some experimental lessons on probability, viz. chance, and probability as a metric of chance; the multiplication of probabilities in the case of an intersection of independent events, and the addition of probabilities in the case of mutually exclusive events. Reprinted from Educational Studies in Mathematics 4 (1971), 264 - 280.