解题教学中,低效或无效的恶习有三:一是用一些看似高明却极其不自然的技巧让学生眼花缭乱,学生在击掌叫好的同时,只能感叹“数学看上去很美”;二是用极其繁难的思路与方法让学生晕头转向,学生在解题的百转千回中迷失方向;三是只以追求正确答案为目的,单纯为解题而解题,忽略了反思提升这一高效解题的重要手段.数学家庞家莱说:“数学的优美感不过是问题的解答合乎我们心灵需要产生的一种满足.”简单、自然、直接、明快地解决问题正是我们追求问 In the problem-solving teaching, there are three kinds of inefficient or ineffective bad habits. One is to dazzle the students with some seemingly brilliant but extremely unnatural skills. When the students clap their hands, they can only lament that “mathematics looks beautiful”; The second is to use extremely difficult ideas and methods to make students dizzy, students lose their directions in solving problems, and the third is only to pursue the correct answer for the purpose of solving problems and solve the problem, ignoring the reflection of the promotion An important means of solving problems efficiently. The mathematician Pang Jialai said: “The beauty of mathematics is but a solution to the problem in line with the satisfaction of our spiritual needs.” "Simple, natural, direct, and neat solutions to problems are precisely ours. Asking for questions