发现法教学

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目前加拿大的教育工作者们推崇一种名为“发现法”的教学方式,具体如何操作,我没有领教过,只是从一些学生那里得知一二。

Raymond现在上十年级的Pre-IB。他们班上二次方程已经一月有余;每次测验,老师总是出一些还没有教过的题目他也是后来才发现的,所以他每次考得都不好;于是找到我,要求给他提前教。我问他们老师是如何教的,他给我的描述是这样的:前两周,每个学生都拿一个图形计算器去画二次多项式的图,让找出顶点和对称轴、X轴交点,Raymond觉得这有意思;然后是做二次方程的文字题,要求学生去列方程,这让Raymond头都大了;再接着是教因式分解,用所谓的拆分法,Raymond通过模仿,总算掌握了;最后是配方法,这就让Raymond丈二和尚摸不着头脑了!老师至今也没有教过二次方程的求根公式。另一个学生Edward跑去问老师,什么是平方和公式?什么是平方差公式?老师回答说:我从来不在课堂上教那个东西。

看来他们的发现法教学就是让计算器或电脑展现出别人早已编程实现了的东西,对那些抽象的算法、公式则不屑一顾。我问Raymond, 你想知道那是怎么编程的吗?他说,我才不想知道呢!他今后既不想参加数学竞赛,对物理、化学、DECA竞赛也嗤之以鼻,说是只参加科学竞赛!至于什么是判别式呀,他一辈子都不想知道。可惜的是,他现在连二次方程都不会解,又怎么去谈科学竞赛,看来他连什么是科学都还没有搞清楚。

这是要把学生们引向何方?严谨的东西弃之不用,却把肤浅的东西当宝贝;名曰发现,却扼杀创新:凡是与老师所讲不一样的东西,通通判为错!尽管老师自己连该学科的逻辑关系都没有弄清。如果我是Wilson,我就要对学校当局提起诉讼了!

Wilson2009年就上了大学,之前我给他辅导过两个月的函数。半年后,他被大学踢了出去,回到一所社区学院去上十年级的东西;一年后,重新申请了另一所大学,所幸被录取了。每学期选两、三门课,不到一个月就又全部放弃;年年如此,至今2015年都快过去了,他连微积分的考试都还没有通过;以至于完全丧失了自信心,患上了严重的忧郁症,得去看医生!是谁害了他?他的老师们!包括我在内,要是早点给他辅导就好了:学习的方法对一个人一生的影响太重要了!

近日,我的一个外甥女在准备高考了,可她总是害怕数学;她妈妈让我说几句,让她不再害怕数学。我就说,其实,数学家们很无能,就连许多基本问题都解决不了;中学数学里教的那点东西,简直就让人笑掉大牙!

老师们,你可以花上一辈子去发现、去探索,我也可以在一夕之间给你讲清整个数学的结构;可是在教别人的子弟之前,能不能先弄清楚该学科的目的、方法和任务,还有别人的需求,然后再来谈什么教学法好吗?我求求你们了!

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