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错误是一种可以利用的教学资源,它有着正面教育所不可替代的功用.有些错误的经历则会在学生心中产生巨大的冲击波:既使学生知识中的缺陷一下子暴露无遗,又让学生经过了这样的错误的洗礼,他的思维也会在瞬间得到升华.所以,教师对课堂上学生发生的某些错误,常常要考虑如何利用它来教育好学生自己的问题.本课从一个普通例题的小小错误引发,竟想到了一大类的问题:与两个定圆都相切的圆的圆心的轨迹问题.这两个定圆有各种不同的位置关系,而相切又有三种不同的切法:一种外切,两种内切;还有一些特殊情况.这里有着丰富的内涵:从一声自然的叹息唤出了一个大胆的猜想,从辩证的类比到最后的质疑.同学们在用统一美,奇异美审视数学,用和谐的辩证的数学思想窥视问题,出错者的无心之举,就这样演变成了一堂生动活泼的研究性学习课.
Errors are a kind of teaching resources that can be used. They have the irreplaceable function of positive education. Some wrong experiences will have a huge shock wave in the hearts of students: Even if the flaws in students’ knowledge are suddenly exposed, students are allowed to pass by. With such a wrong baptism, his thinking will also be sublimated in an instant. Therefore, teachers often consider how to use it to teach students’ own problems in the classroom. The small mistakes that were raised led to a large class of problems: the trajectory of the circle’s center of circle that is tangent to both circles. The two circles have different positional relationships, and there are three different tangencies. Different cuts: one kind of outer cut, two kinds of cuts; there are some special circumstances. Here is a rich connotation: from a natural sigh beckoned a bold conjecture, from the dialectical analogy to the final question. They examine the mathematics with unified beauty and singular beauty, peep into the problem with the harmonious dialectical mathematics thoughts, and the inadvertent actions of the errant ones, and thus they have evolved into a lively research-based study class.