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任何事物都存在着对立与统一的两个方面,数学问题也不例外.因此,在数学解题教学中,教师应加强引导学生用辩证思维思考问题,并合理地将辩证思维运用于数学解题中,这不仅有利于提高学生的解题效率,而且也利于提高学生的辩证思维能力.下面结合实例,浅析辩证思维在高中数学解题中的运用.1.陌生与熟悉在解决一些陌生问题时,我们首先要认真、细致、深入地观察和联想,尽可能找出已知或熟悉的东西,对其进行转化,使之变为我们熟悉的问题来处理,达到化难为易的效果.例l设P为AABG内的一点,P点到AABC三边BC,CA,AB的距离分别为x,y,z若BC=a,CA=b,
Therefore, in the teaching of mathematics problem solving, teachers should strengthen the guidance of students to use dialectical thinking to think about the problem and apply the dialectical thinking reasonably to solve the problem of mathematics , Which is not only conducive to improving students ’problem solving efficiency, but also conducive to improving students’ ability to dialectical thinking.According to the following examples, the application of dialectical thinking in high school mathematics problem solving is analyzed.1.The strangeness and familiarity in solving some strange problems We must first of all, carefully and in-depth observation and association, find out what is known or familiar as much as possible, transform it into something familiar to us, and achieve the effect of making it difficult for us to cure. l Let P be a point within AABG, the distances from point P to the three sides of AABC BC, CA, AB are respectively x, y, z if BC = a, CA = b,