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根据认知心理学的有关理论,知识的表征是指人在自己的工作记忆和长时记忆中,对信息的储存、表示和再现方式.陈述性知识的表征有三种基本形式:命题网络表征、表象表征和线性表征.由于数学主要研究数与形以及它们彼此之间的关系,因此数学陈述性知识的表征常表现为命题网络和表象表征的相互交织与融合.数学概念属于陈述性知识,能否对数学概念进行不同形式的表征,实现各种表征形式的融合,形成相对完善、精致的概念网络是学好数学概念的关键.那么在实际教学中,如何对数学概念进行表征,学生头脑中概念表征的状况如何?笔者围绕“等差数列”这一重要数学概念的表征进行了一次调查,并做一些探讨.1 调查工作的安排
According to relevant theories of cognitive psychology, knowledge representation refers to the way people store, represent, and reproduce information in their own working memory and long-term memory. The representation of declarative knowledge has three basic forms: propositional network representation, Image representation and linear representation. Since mathematics mainly studies the number and shape and their relationship with each other, the representation of mathematical descriptive knowledge often appears as the interweaving and fusion of proposition networks and representational representations. Mathematical concepts are declarative knowledge, and Whether to carry out different forms of mathematical concepts, to achieve the integration of various forms of representation, to form a relatively complete and refined concept of the network is the key to learning the concept of mathematics. Then in the actual teaching, how to characterize mathematical concepts, the concept of student minds What is the status of characterization? The author conducted an investigation around the characterization of the important mathematical concept of “equal difference sequence” and did some research.1 Arrangements for investigation work