基于范希尔理论提升几何思维水平——以“圆周角定理”教学为例

Improving the Level of Geometric Thinking Based on Van Hill Theory—Taking the Teaching of the “Circumferential Angle Theorem” as an Example

几何内容的学习长期以来都是存在一定的难度和挑战性的,这是因为几何具有一定的抽象性和严密的逻辑性,学生常常对一些几何证明题感到困难,而如何提升学生的几何思维水平一直是一个热门话题。荷兰范希尔夫妇提出的范希尔理论在几何教学领域有着广泛的影响,其核心内容之一的几何思维的五个水平,对于教师课程的开展具有重要的借鉴意义。因此,本文以“圆周角定理”的教学为例,讲述如何基于范希尔理论的五个水平来依次提升学生的几何思维水平。

The learning of geometric content has long been difficult and challenging, because geometry has a certain abstraction and strict logic, students often feel difficult on some geometric proof problems, and how to improve students’ geometric thinking level has always been a hot topic. The Van Hill theory proposed by the Dutch Van Hill couple has a wide influence in the field of geometry teaching, and one of its core contents, the five levels of geometric thinking, has important reference significance for the development of teacher courses. Therefore, this paper takes the teaching of the “circumferential angle theorem” as an example to describe how to improve students’ geometric thinking level based on the five levels of Van Hill theory.