数学“老三高”与“新三高”的发展及教学创新

The Development and Teaching Innovation of the Mathematics between “Lao Sangao” and “Xin Sangao”

根据数学“老三高”（高等数学、高等代数、高等几何）与数学“新三高”（近世代数、泛函分析、拓扑学）的关系及应用,必须更加强化“数学老三高”的教学,推动“新老三高”的应用与数学创新,为学生可持续发展奠定雄厚的基础。以数学新课程理念与数学方法论为指导确立数学“老三高”教学的目标,按照数学新课程理念的教师观、教学观、学生观的教学方法组织教学,对培养学生的数学才智及逻辑思维能力、应用创新能力等各种能力,有着非常重要的作用。

Based on the relations and applications between the mathematics ＂Lao Sangao＂-advanced algebra, advanced calculus and higher geometry-and the ＂Xin Sangao＂ -modern algebra, functional analysis and topology, the teaching of mathematics ＂Lao Sangao＂ should be far intensified. In order to lay the foundation for students＇ sustainable development in mathematics, the applications and teaching innovation in both ＂Lao Sangao＂ and ＂Xin Sangao＂ need to be developed. On the guidance of the new curriculum ideas with teachers＇ and students＇ thoughts and mathematics methodology, this paper will introduce the teaching goals of mathematics ＂Lao Sangao＂, and the significance to cultivate students＇ mathematics intelligence, logic thinking and innovative abilities.