论数学猜想在数学探究活动中的思维形式

On the Thinking Forms of Mathematics Conjecture in the Activity of Mathematics Exploring

数学猜想作为一个动态的思维过程,是数学探究活动的核心.数学猜想在数学探究性活动中的基本思维形式主要有以下3种:(1)直觉判别,这种判别通常在经验判别和审美判别2个层次上具体进行;(2)直觉想象,它实质上是思维的内插法,即在一系列已确定的事实之间填补空白,它主要表现为物理直觉想象与几何直觉想象;(3)直觉推断,它是指由一个或几个直觉判别,直接推出另一个直觉判别的思维过程.

In this paper, the author took the mathematics conjecture as a developmental thinking course and discussed the three principal thinking forms running through the course intuition inferences, intuition distinguishes, intuition imaginations.