一、案例背景在学习等差数列以后,对于一类关于两个等差数列前n项和比值的问题,学生由于认知结构的原因,求解常常出现错误,怎么帮助学生正确认识等差数列的性质与概念,抓住问题的本质?笔者在教学过程中,按照自己原有的教学设计,利用等差数列的性质,给出“巧妙”的解法,但是学生普遍反映自己想不到采用这种 First, the background of the case After learning the arithmetic progression, for a class of questions about the first n terms and the ratio of the two arithmetic differences, students often find mistakes due to the cognitive structure and help students to correctly understand the arithmetic progression Nature and concept, to grasp the essence of the problem? In the teaching process, according to their own original teaching design, the author uses the nature of the arithmetic sequence to give “clever ” solution, but students generally reflect their own unexpected use of this