数学化对学生学习数学概念的影响——以“小数”概念学习为例

The Influence of Mathematics on the Students Learning of Mathematical Concepts:Taking “Decimal” for an Example

"数学化"这一概念最初是由荷兰数学家和数学教育家弗赖登塔尔(H.Freudenthal,1905—1990)提出的。"数学化"既是数学教学的过程,也是数学教学的结果。以"小数"概念学习为例,将数学化的过程呈现在数学概念的教学中,第一次学习是水平数学化,即由现实问题到数学问题的学习;第二次学习是垂直数学化,即由具体问题到抽象概念的学习。在这两次教学实践过程中,生活经验、模型支撑、多种表征都对学生"小数"概念数学化有一定的帮助。

The concept of ＂mathematician＂ was originally proposed by Freudenthal （H. Freudenthal, 1905--1990）, a mathematician in Holland. ＂Mathematics＂ is not only the process of mathematics teaching, but also the result of mathematics teaching. Taking the ＂decimal＂ concept learning for an example, the process of mathematics in the teaching of mathematics concept, mathematics learning is the first level, from the reality to the mathematical problem of learning; second learning mathematics is vertical to a specific issue, from the abstract concept of learning. In the two course of teaching practice, life experience, model support, and many kinds of characterization are helpful to learn the mathematical concept of ＂decimal＂.