例谈直觉思维与数学解题

Case study of intuition-oriented thinking and solution to mathematical problems

数学教学是数学思维活动的教学,直觉思维在数学思维活动中有着特殊的地位和作用。文章通过对直觉猜想、直觉洞察、直觉类比、数形结合、直觉归纳和审美直觉这六个方面举例论证直觉思维在数学解题活动中的作用。同时也分析了运用直觉思维解题需要注意的问题,并介绍了调控这些问题所必需掌握的知识,如数学观念、学习本质以及逻辑思维与直觉思维的互补作用。

Teaching of maths is the teaching of activities related to mathematical thinking. Intuition-oriented thinking has a special position and role in activities related to mathematical thinking. Through case study of intuition-oriented guess, intuition-oriented insight, intuition-oriented analogy, combination of mathematics and forms, intuition-oriented summary and aesthetic intuition, the article endeavors to expound and prove the role of intuition-oriented thinking in solving mathematical problems, while analyzing points of attention in the course of solving mathematical problems through applying intuition-oriented thinking as welI as introducing knowledge to be acquired as a must in adjusting these issues,such as mathematical concepts, nautre of study and the complementary role between logical thinking and intuition-oriented thinking.