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在一节高一习题课上,笔者安排学生探究了10道习题。其中前9道属于基本题,由学生展示自己的解题思路和过程,虽有小火花,但总体上波澜不惊。到了第10道题,笔者向学生提出了较高的要求:争取用两种以上的方法来解答。下面是第10道题的教学片断。题目:已知点P(0,5)及圆C:x~2+y~2+4x-12y+24=O,求过点P的直线在圆C上截得的弦的中点的轨迹方程。此时离下课还有17分钟。停顿了大约1分钟,学生1率先举起了手。学生1:(参数法)设过点P的直线方程为l:y=
In a high one class, I arranged the students to explore the 10 exercises. Among them, the first nine are basic questions, and students show their own ideas and process of solving problems. Although there are small sparks, they are generally placid. To the first 10 questions, the author put forward to the students a higher requirement: for more than two methods to solve. The following is the tenth piece of the teaching piece. Title: Known point P (0,5) and the circle C: x ~ 2 + y ~ 2 + 4x-12y + 24 = O, the trajectory of the midpoint of the chord equation. At this time there are 17 minutes from get out of class. Paused for about a minute, student 1 took the lead in raising his hand. Student 1: (parameter method) set point P over the linear equation l: y =