Developmental Study on the Role of Cognitive Contradictions in the Acquisition of Logico-Mathematical Knowledges

认知矛盾在逻辑数学知识获取中的作用的发展研究

• 批准号: 06451021
• 负责人: NAKAGAKI Akira
• 金额: $ 1.6万
• 依托单位: National Institute for Educational Research (NIER)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06451021/
• 关键词: Cognitive contradiction; Logico-Mathematical knowledge; Conditional reasoning; Disjunctive interpretation; Ratio-Comparison; Arithmetic operation; 条件型命題論理; 論理的推論; 4枚カード問題; 可逆性; 演繹順序; 演算の可逆性

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 … More , 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

在该项目中，进行了四项实验研究来阐明认知矛盾在逻辑数学知识获取中的作用。对小学生进行了有关比例比较、算术运算的可逆性和选言句子解释的研究任务，并对高中生和大学生进行了一项有关条件推理的研究任务。该项目的主要结果如下：(1)在使逻辑数学知识成为可能的认知系统中识别出两种性质不同类型的认知矛盾。一种矛盾是系统外部的、由偶然情境强加的，另一种是系统内部的、被感知的。(2)当矛盾在认知系统外部得到证实时，主体很容易识别其存在本身，但由于其外部性，很难澄清其根源和原因。因此，为了消除它们，认知系统必须求助于试错法。结果，这些外部矛盾就没有足够的力量来重组认知系统。（3）当矛盾是认知系统内部的时候，对这些内部矛盾的敏感性取决于主体的认知水平，如果主体处于较低的认知水平，他或她甚至无法意识到它们的存在。换句话说，认知矛盾的认识是认知发展的产物。如果主体本身感觉到矛盾，那么认知系统就已经使用了足以检测矛盾的认知工具（概念图式）。在这种情况下，这些内部矛盾可能是重组认知系统的促进因素。从认知矛盾中获益，有可能促进逻辑数学知识的获取，但在教学环境中需要一些指导认知系统重组的指南，因为矛盾本身并不能确保认知系统导致更好的组织。较少的

项目成果

中垣啓: "演算順序の可逆性に関する発達的研究" 国立教育研究所研究集録. 第32号. 31-51 (1996)

Kei Nakagaki：“运行顺序可逆性的发展研究”国立教育研究所论文集第32. 31-51号（1996）。

中垣啓: "割合比較課題にみる認知システムのダイナミズム" 国立教育研究所研究集録. 第34号. 31-51 (1997)

Kei Nakagaki：“比率比较任务中看到的认知系统的动态”国家教育研究所会议记录第 34. 31-51 号（1997 年）。

Nakagaki, A.: "Developmental Study on Reversibility of the Order of Arithmetic Operations" (in) Research Report of NIER. No.32. 31-51 (1996)

Nakagaki, A.：“算术运算顺序可逆性的发展研究”（载于 NIER 研究报告）。

中垣啓: "割合比較課題にみる認知システムのタイナミズム" 国立教育研究所研究集録. 第34号. 31-51 (1997)

Hiroshi Nakagaki：“比率比较任务中的认知系统的暴虐”，《国立教育研究所杂志》，第 34 期。31-51 (1997)。

Nakagaki, A.: "Dynamics of Cognitive System in Ratio-Comparison Tasks" (in) Research Report of NIER. No.34. 31-51 (1997)

Nakagaki, A.：“比率比较任务中认知系统的动力学”（见）NIER 研究报告。