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1.问题的提出笔者在“合情推理”新授课中发现,学生对归纳推理题做得相当好,正确率高,而对类比推理题一筹莫展,乱做一通,正确率很低.如作业中有一道题:在平面几何中有如下结论:若正三角形ABC的内切圆面积为s_1,外接圆面积为s_2,则S_1/S_2=1/4,推广到空间几何体可以得到类似结论:若正四面体A-BCD的内切球体积为V_1,外接球体积为V_2,则V_1/V_2=____.答案为1/8的同学占绝大多数,究其原因是:大多数学同
1. The question put forward In the “reasonable reasoning ” new lectures found that students do a good job of inductive reasoning, the correct rate is high, but do nothing to analogy reasoning, chaos do a pass, the correct rate is very low. There is a problem in the work: The following conclusions are made in plane geometry: if the inscribed circle area of a regular triangle ABC is s_1 and the circumscribed circle area is s_2, then S_1 / S_2 = 1/4, which can be extended to the space geometry to get a similar conclusion: If the volume of the inscribed sphere of positive tetrahedron A-BCD is V_1 and the size of the external sphere is V_2, then V_1 / V_2 = ____. The majority of the students who answer 1/8 have the following reason: most of them agree