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数学思想是人们在长期的实践经验和社会生活中得出的有关现实世界的数量关系、空间结构等科学意识的反应,是人类思维活动的结晶.数学思想在漫长的历史演变中逐渐发展,帮助人类掌握学习知识的技巧,提供最优质的解决方案,常见的数学思想包括数形结合、分类讨论、换元思想、函数与方程、等效思想等等.函数思想是高中数学中的重难点,但是在高中解题中运用广泛.在高中数学解题过程中引导学生积极运用函数思想有利于提升学生的解题速率,培养学生思维的缜密性和严谨性,锻炼学生的思维拓展能力和创新实践能力.本文阐述函数思想在高中数学解题中的实际应用.
Mathematical thinking is the reaction of people’s long-term practical experience and the social relations about the real-world relations of quantity, spatial structure and other scientific consciousness and is the crystallization of human thinking activities.Mathematical thinking has been gradually developed in the long historical evolution and has helped Humans master the skills of learning knowledge and provide the best quality solutions. Common mathematical ideas include the combination of numbers and forms, the discussion of categories, the thought of commutation, the functions and equations, the equivalent thoughts, etc. The function idea is a heavy and difficult point in high school mathematics, However, it is widely used in solving high school problems.Guiding students to actively use the function ideas in high school mathematics problem solving is helpful to improve students ’problem-solving rate, cultivate students’ thoughtfulness and rigor, train their thinking ability and innovative practice Ability.This article elaborates the practical application of the function idea in high school mathematics problem solving.