关注高等数学中的形式和意义

On the meaning and form of advanced mathematics

数学形式可以看作是表达个体头脑已有数学意义的工具,更为重要的是能用形式来建构数学意义,这是数学家基本的数学活动,也是数学思想产生的重要源泉。高等数学大都是从已知的性质建构思维对象,正是这种建构给学生的学习造成了很大的困难。针对数学系大三学生进行了问卷,结果表明学生总是倾向于单独地考虑意义或是单纯地关注形式,而没有真正把数学意义和形式结合起来,也就是很少同时关注到句法和语义知识。

The form of advanced mathematics can be regarded as a tool for expressing the meaning that exists in an individual＇s mind, and using the form to construct the meaning is not only an important activity for mathematicians, but also a source of mathematical ideas. Advanced mathematics is characterized by constructing objects from properties, which is very difficult for students. The questionnaire shows that the students are intended to use the meaning or form separately, they seldom combine the meaning with the form, that is, they seldom show concern for syntactic and semantics aspects simultaneously.