两种公理化思想的比较对数学教育的启示

Revelation of the Comparison between Two Axiomatized Ideas to the Mathematics Education

从实质公理化和形式公理化两种思想的比较出发,提出真正的数学课程是非形式化和形式化二者的统一,进一步阐述关注形式数学知识与所联系的实体对象的重要性,然后提出对"淡化形式、注重实质"的新的看法。

Based on the comparison between the two essential axiomatization and formal axiomatization, this paper points out that actual curriculum of mathematics is the unification of formalization and non-formalization; it illustrates the importance of focusing on formal mathematic knowledge and related substantial object, and derives new opinions from 'Taking form lightly and Attaching importance to substance '.