函数思想主题教学的意涵建构与构型分析

Connotation Construction and Configuration Analysis of Function Thought Theme Teaching

从函数思想的文化源流、价值意蕴及内涵导向入手,构筑以教学要素、知识结构、心理结构、思维范式为支点的函数主题教学结构。采用文本分析和案例法,以发展、辩证、动态的视角分析了函数思想教学过程中的几重关系,构建了系统化、智能化、结构化的函数思想教学观。函数思想的源流经历了不断精练、深化及丰富的动态发展过程,既显示了哲学的辩证思维,又体现了数学的抽象思维。在思想方法应用上,它凸显了模型法、构造法、计算法、映射法等关键特征。运用多元化视角建构了三种以函数思想为主题的教学构型,以此促进学生更好地理解函数概念、函数知识以及函数思想内涵与应用过程,从而搭建学生科学合理的数学认知结构。

A teaching structure of function theme based on teaching elements, knowledge structure, psychological structure and thinking paradigm is constructed from the perspective of cultural origin, value implication and intension orientation of function thought in this paper.Text analysis and case method are employed to analyze several relations in the process of function thought teaching from the perspective of development, dialectics and dynamics, and systematic, intelligent and structured teaching concept of function thought is constructed as well.The origin of function thought has experienced a dynamic development process of continuous refinement, deepening and enrichment, which is an embodiment of both the dialectical thinking of philosophy and the abstract thinking of mathematics.In terms of thinking method application, the key features of model method, construction method, calculation method and mapping method are highlighted.This paper has constructed three kinds of teaching configurations with function thought as the theme from multiple perspectives for promoting students to better understand the concept of function, function knowledge, the connotation and application process of function thought so as to build a scientific and reasonable mathematical cognitive structure for students.