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由于一题多解既可激发学习兴趣、理清知识脉络、拓宽解题思路、提高课堂效率,又对培养学生的求异思维、发散思维大有裨益,因而深受师生的偏爱.那么在解题教学中如何探究一题多解呢?本文力图基于建模思想,从常见的基本图形中找到创造之源,提炼经典的几何模型,引导学生多方位、多角度地考虑问题,由此产生多种解题思路,从而激发学生学习数学的兴趣,提高学生的数学素养.本文以探究一道几何填空压轴题的多种解法为例,谈谈如何引导学生添设辅助线构建模型解
Because the multi-explanation of a topic can stimulate interest in learning, clarify the context of knowledge, broaden problem-solving ideas, and improve classroom efficiency, it is also helpful to train students to think differently and diverge their thinking. Therefore, they are deeply loved by teachers and students. How to explore a problem and multiple solutions in problem-solving teaching? This article tries to find the source of creation from the common basic graphics based on modeling ideas, refine the classical geometric model, and guide students to consider problems in a multi-faceted and multi-angle manner. A variety of problem-solving ideas to stimulate students’ interest in learning mathematics and improve students’ mathematics literacy. This paper takes a variety of solutions to the problem of inquiring into a geometrical fill-in-offline problem, and discusses how to guide students to add auxiliary lines to build a model solution.