E. Fischbein (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel.
E. Fischbein, Ileana Pampu and I Mînzat (1967). The child's intuition of probability. Enfance, 2, 193-206. Reprinted in Fischbein (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel. p. 156-174.
The discussion may be summarized thus: the synthesis of the stochastic and the determined, which the concept of probability theoretically presupposes, is to a certain extent prevented by the fact that schools, and the whole intellectual environment of the child, concpire to favour only one of these terms - that of explanation by strict necessity - and create a 'cognitive set' in this direction. The child is gradually and fundamentally convinced that to fully know and understand a phenomenon means referring it to u unique causal relationship. This is a belief which has, in fact, dominated modern scientific thought for centuries, and which is still cultivated in schools. [p. 171]
The synthesis of the possible and the necessary, of the indeterminate and the determined, which is presupposed by the understanding of probabilistic phenomena, is in reality handicapped by a structural disequilibrium in the mental development of these two components. Under the influence of the teching process, chance events are rejected as being inexplicable and beyond human control, while univocally determined relations are accepted, sought, even imposed in the form of different attempts to 'rationalise' phenomena. [p. 173]
This piece of research touches on two kinds of problems in achievement testing: the tendency for test questions to have a 'closed' character, and the kind of phenomenon exhibited by the the-age-of-the-captain problem: children autonatically performing what they have learned in the (informal) curriculum.
Jenni Way (2003). The development of young children's notions of probability. European Research in Mathematics Education III Proceedings of the Third Conference of the European Society for Research in Mathematics Education 28 February - 3 March 2003pdf
Jane M. Watson and Jonathan B. Moritz (2002). School students' reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology. abstract