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也谈高中数学形式化及其教学 被引量:5

Also on High School Mathematics Formalization and Its Teaching
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摘要 有关数学形式化及其教学曾在20世纪90年代引发广泛讨论.伴随着中国高中数学课程标准从2003年实验版到2017年版及其2020年的重新修订,革新教学内容、改革教学方式成为时代发展的必然要求,重新认识和探讨新时代数学形式化及其教学具有十分重要的意义.基于文献研究和思辨性分析,提出数学形式化即是数学内容的抽象化与数学概念的符号化.数学形式化具有过程性、层次性及关联性等特点.与科学数学相比,学科数学重在传承、生长和理解,其形式化有所淡化.新的高中数学课程标准有关形式化内容表述的修订并非舍弃形式化的学习要求,而是力求更客观、更具体,体现适度性.改进高中数学形式化内容的教学要遵循“注重过程,渐进导入”的教学原则,运用情境化引入,降低形式化门槛;渐进性铺垫,搭建形式化平台;符号化呈现,揭示形式化内涵;巩固性训练,促进形式化理解. The formalization of mathematics and its teaching have aroused extensive discussion in the 1990s. With the revision of the mathematics curriculum standard of senior high school in China from the experimental version in 2003 to 2017 and its revision in 2020, the innovation of teaching contents and teaching methods has become the inevitable requirement of the development of the times. It is of great significance to re-understand and explore the formalization of mathematics and its teaching in the new era. Based on literature research and speculative analysis, it is proposed that mathematical formalization is the abstraction of mathematical content and the symbolization of mathematical concepts. Mathematical formalization has the characteristics of process, hierarchy and relevance. Compared with scientific mathematics, subject mathematics focuses on inheritance, growth and understanding, and its formalization has been diluted. The revision of the formal content expression of the new mathematics curriculum standard in senior high school is not to abandon the formal learning requirements, but to strive to be more objective, more specific, and appropriate. To improve the teaching of formal content of mathematics in senior high school, we should follow the teaching principle of “paying attention to process and gradual introduction”, using situational introduction to lower the formal threshold, gradually paving the way and building a formal platform, symbolizing presentation to reveal formal connotation, and strengthening training to promote formal understanding.
作者 段志贵 张雯 DUAN Zhi-gui;ZHANG Wen(School of Mathematics and Statistics,Yancheng Normal College,Jiangsu Yancheng 224000,China;School of Teacher Education,Nanjing Normal University,Jiangsu Nanjing 210023,China)
出处 《数学教育学报》 CSSCI 北大核心 2022年第6期60-64,92,共6页 Journal of Mathematics Education
基金 江苏高校哲学社会科学重点课题——《乡村教师支持计划(2015—2020)》下的乡村教师身份认同与专业成长研究(2017ZDIXM151) 江苏省教育科学“十三五”规划课题——数学学慢生“慢学习”的实践研究(B-b/2020/02/217) 盐城师范学院教育教学改革重点课题——师范类专业认证背景下的数学教学论课程教学改革的探索和思考(2018YCTUJGZ011)。
关键词 高中数学 数学形式化 教学策略 注重过程 渐进导入 high school mathematics mathematical formalization teaching strategies process-oriented progressive introduction
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