## 伍鸿熙对因式分解及分式化简教学的一点看法

内容摘录自他的一份手稿 Introduction to school Algebra.

There is no denying that beginning students ought to acquire some facility with decomposing numbers into products. It is also important that they can eortlessly factor a simple quadratic polynomial $x^2+2x-35 $ as $ (x+7)(x-5)$. But it sometimes happens that

if a little bit of something is good, a lot of it can actually be bad for you. This seems to be the case here, when the teaching of a small skill gets blown up to be a major topic, with the consequence that other topics that are more central and more substantial (such as learning about the graphs of linear equations or solving rate problems correctly) get slighted. The teaching of algebra should avoid this pitfall. Please also keep in mind the fact that once the quadratic formula becomes available (see Section 12), there will be a two-step algorithm to accomplish this factorization no matter what the coefficients of the quadratic polynomial may be.

伍鸿熙认为因式分解这一技巧在正常代数教学中不宜过分看重，不然可能会妨碍其他关键代数内容的教学。毕竟教学时间有限。（不过这一技巧是代数变形技术的重头戏，掌握熟练了还是有好处的。）

后面他还质疑了花大代价将分式（分数）化简到最简的必要性。看来美国和中国的内容安排还是有点相似的。要是分式化简不过分强调，那因式分解也不必过于重视。

In beginning algebra, often there is too much emphasis on simplifying rational expressions. This is a left-over from the questionable practice of teaching fractions by insisting on the reduction of all fractions to lowest terms at all costs.