数学本质:何谓、为何与何为

The essence of mathematics: what it is, for what and what it is to do with?

深刻理解数学本质是教师灵活进行数学教学的根基,对教师开展数学教学具有根本性的指导意义.因此深入分析“什么是数学的本质”“为何要实施突出数学本质的教学”以及“如何实施突出数学本质的教学”,具有重要的现实意义.基于“多元数学本质观”,提出了实施突出数学本质的教学的五条原则:现象与本质并重,形式与内容并重,过程与结果并重,绝对与可谬并重,感性与理性并重.

A profound understanding of the essence of mathematics is the foundation for a teacher’s flexible control of mathematics teaching,which is of fundamental guiding significance for teachers to carry out mathematics teaching.It has an important realistic significance to have a thorough examination of“the essence of mathematics”,“why it is necessary to implement the teaching highlighting the essence of mathematics”and“how to implement the teaching highlighting the essence of mathematics”.Based on the plural essence view of mathematics,five principles are put forth for the implementatation of the teaching that highlights the essence of mathematics:“equal importance placed on phenomenon and essence,form and content,process and result,absolutism and fallibilism,sensibility and rationality”.