对中学生数学“无限”观念的教育庶谈

Education Study of the Middle School Students’ Mathematics “Infinity” Concept

中学数学教育教学务必要重视学生对“无限”的认识,思考如何在教学中结合教材内容,实施数学“无限”思想的教育.中学数学教学中,教师应让学生了解数学领域中“无穷”概念的基本类型;让学生了解数学上塑造“无穷”的基本方式;让学生搞清“数学中的无穷与现实中的无穷的区别,‘任意大’与无穷大、‘任意小’与无穷小,点与线的关系,无穷大之间的层次有别,有限与无限的辩证关系”等关系.

Understanding ＂infinity＂ and forming the correct conception of it was not only consolidate the high school students＇ foundations for their further study of advanced mathematics, but also was of great significance to their philosophy and methodology. Some surveys showed that the correct rate of the high school students＇ understanding of ＂infinity＇ was rather low. Especially that they didn＇t thoroughly understand the expression of ＂infinity＂ displayed by cycle. Although the mathematics of high schools involved much in ＂infinity＂, the textbooks indicated it unclearly. Therefore, the students need their teachers to steer them purposely to investigate and grasp ＂infinity＂, as well as to construct and develop the concept of ＂infinity＂ on the foundation of correct understanding of it.