中学数学中的证明

Proofs in Secondary Schools

证明是检验方案的一种类型,证明有构造性证明与非构造性证明之分.信息时代的中学生需要熟悉各种不同类型的检验方案,目前的中学数学中涉及到的大多数证明都是构造性的.在很多情况下,许多检验方案与古典类型的构造性证明相比更有效,概率论方法就是这样的检验方案之一.将一些不同于经典证明的检验方案应用到中学数学教学中去,用以培养学生新的数学观是十分必要的.

In the information age, we needed various types of scheme of verification. We noted that only one type of verification scheme that was usually called 'proof' was in the current curriculum for secondary school mathematics. In this article, we surveyed a variety of types of verification schemes that would be useful in real life. We proposed some types of verification scheme that need to be in our secondary school mathematics curriculum. We emphasized that probability plays an important role in this proposes schemes of verification.