认知的历史发生原理及其教学工程化——以数学学科为例

Historical-genetic Principle of Cognition and Its Educational Implication——Taking Mathematics as an Example

生物发生律认为个体发生是种系发生短暂而迅速的重演.迁移到教学领域,这条法则意味着个体知识的发生过程遵循人类知识的发生过程.有效的学习要求学习者追溯正在学习的主题在历史中演变的主要步骤.围绕这条法则,人们展开了经验的论述、实证的检验、理论的探讨.这条法则为用教育取向的数学史发展教师的学科教学知识奠定了理论基础.以教育取向的数学史为指导,教师可以更好地发展学科教学知识,进行教学设计,从而实现认知的历史发生原理的教学工程化。

The biogenetic law is that ontogenesis recapitulates phylogenies. This law states that in a brief period the development of the embryo of an animal recapitulates the historical development of its ancestors. Transferred to the realm of pedagogy the law implies that the genesis of knowledge in the individual follows the same course as the genesis of the knowledge in the race. Many discussions have stated on this law. There are experiential points, empirical tests and theoretical studies. This law is the basis of educational orientation to the history of mathematics which can improve teacher＇s pedagogical content knowledge. Guided by the history of the history of mathematics, the teacher can do a good teaching design and develop pedagogical content knowledge.