著名数学教育家波利亚说:“一个专心地认真备课的教师能够拿出一个有意义的但又不太复杂的题目帮助学生发掘问题的各个方面”.在高三立体几何复习时,我给学生布置了这样一道常见习题:四面体 ABCD 的棱长 BD 是变量,其余各棱长都等于3,问 BD 为何值时,该四面体体积最大?通过检查,发现学生由有多种不同特色的 The famous mathematician educator Polya said: “A teacher who is dedicated to preparing lessons seriously can come up with a meaningful but not too complex topic to help students explore various aspects of the problem.” In the third grade geometry review, I gave students A common problem has been laid out: the length BD of the tetrahedron ABCD is a variable, and the rest of the lengths are equal to 3. When asked about the value of BD, is the tetrahedron the largest? Through examination, it was found that students have a variety of different characteristics.