| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1996: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1994: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Research Abstract |
In this project, four experimental researches were conducted to elucidate the role of cognitive contradictions in the acquisition of logico-mathematical knowledges. Research tasks concerning ratio-comparison, reversibility of artithmetic operations and interpretation of disjunctive sentences were administered to elementary school children and one research task concerning conditional reasonings to high school and colledge students. Main results of this project were as follows.
(1) Two qualitatively different types of cognitive contradictions are identified in a cognitive system making possible logico-mathematical knowldges. One type of contradictions is external to this system and imposed by contingent situatoins and the other is internal to this system and sensed as such.
(2) When contradictions are confirmed externally to a cognitive system, it is easy for a subject to identify their existence itself but difficult to clarify their origin and their reason because of their externality. So
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, to eliminate them, the cognitive system is obliged to have recourse to trial-and-error. As a result, these external contradictions cannot have enough power to reorganize the cognitive system.
(3) When contradictions are internal to a cognitive system, the sensitivity to these internal contradictoins is dependent on subject's cognitive level and if the subject is in a lower cognitive level, he or she cannot even realize their existence. In other words, cognition of cognitive contradictions is the product of cognitive development. If the subject senses contradictions as such, the cognitive system is already implimented with the cognitive instruments (conceptual schemas) enough to detect contradictions. In this case, these internal contradictions could be a facilitative factor for reorganing the cognitive system.
It is possible to facilitate the acquisition of logico-mathematical knowledges, profiting from cognitive contradictions, but some guide for orienting reorganization of a cognitive system will be needed in an instruction-learning setting, because contradictions do not in themselves ensure the cognitive system for leading to a better organization. Less
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