Structure of mental models, problem solving, and learning of probability
Yuji Itoh (Dept. of Psychol., Keio Univ.)
In this paper, the structure of non-mathematicians' knowledge of
probability is argued. Based on the analysis of the conceptual model
(teachers' model) of probability, it is hypothesized that the mental
model (non-mathematicians' model) of probability might consist of
three different understandings (views), the case view, the frequency
view, and the subjective view. In people's explanations of
probabilistic statements about some concrete events, the hypothesized
views are identified, and it is shown that an indivisual's
explanations are often based on two or more views. The relationship
between mental models and problem solving processes is discussed. It
is demonstrated that the view that a problem solver took influenced
problem solving processes. There are some cases where the frequency
view has advantages in problem solving. The implication of multiple
views of probability for mathematics education is also argued.
Keywords: mental models, problem solving, learning, multiple views,
probability