A Study on Symbiogenesis of Probabilistic Conception
2011 Volume 17 Issue 2 Pages 25-33
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2011 Volume 17 Issue 2 Pages 25-33
The aim of this paper is to characterize a construction of children's conception on the elementary concept of probability. Firstly, three dualities on classical probability and frequentistic probability are identified. A construction of children's conception on the elementary concept of probability is accomplished as a cooperation of these dualities.
table 1: Dualities on classical probability and frequentistic probability
Secondly, a model of a cooperation of dualities on two concepts of probabilities is elaborated, using analogy with "symbiogenesis" which is a concept for interpreting cooperation on evolution of living things in the theory of evolution. This model is laden with three points of Table 1. Phase 1 indicates the condition of learning classical probability or frequentistic probability. Phase 2 indicates the condition of learning two probabilities and of occurring some misconceptions. Phase 3 indicates the condition of understanding two probabilities.
Figure 1: A model of symbiogenesis of probabilistic conception
Finally, it is suggested that a conflict between dualities in phase 2 of Figure 1 is implicit in the present curriculum on probability in Japan, and then that a means for leading phase 3 is insufficient.
