数学的ミスコンセプションのモデル化 : 小数の法則を事例として

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In prior studies, it has been pointed out that misconceptions play important roles in processes of mathematical teaching and learning. The research objective of this article is the development of the theoretical framework in order to inquire misconceptions from the viewpoint of conception model. Regarding to this objective, the model of condition of conception is constructed. This model is "tetrahedral model of static aspect of conception", which consists of "object / reference context as 'event'" (O), "sign / symbol as 'event'" (S), 'notion' (N) and 'conviction' (C). This is based on Steinbring's framework "the epistemological triangle" and on Mizoguchi's model "the C(C,N,E) model" (these letters C and N have different meaning from those in the tetrahedral model), and shows that O, S and N are nothing but connected indirectly by C. N means learner's concept, ambiguous idea, knowledge, or mental model. C means learner's attitude towards mathematics or mathematical knowledge. 'Event' means learner's practical experience which is laden with N and C. Then, O is object / reference context which is laden with N and C, and S is sign / symbol which is laden with N and C. The tetrahedral model can identify relatively misconception, because this model can describe context of mathematics teaching and learning through N. [figure] There is probability misconception of "the law of small numbers". This misconception makes learners believe that a small sample will be representative of a large sample. The misconception of the law of small numbers is characterized as Fig. 2. "Small sample" and "fraction numerals as probability based on equiprobability" cannot be linked by "classical probability and frequentistic probability". They are connected by determinism. This argument is justified by interpreting history of probability and resilience of misconception. [figure]
全国数学教育学会の論文
2012-00-00

数学的ミスコンセプションのモデル化 : 小数の法則を事例として

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