# Quod Erat Demonstrandum

## 2007/11/24

### [初中] Algebraic computation

Filed under: Junior Form Mathematics — johnmayhk @ 1:23 下午

After the uniform test, I’m really sad to see the poor performances made by my F.2 boys. We, teachers, keep on asking WHY, WHY, WHY: for certain kinds of questions, it is a MUST that students will make mistakes. During the discussion of paper, I said, ‘I knew many of you may make mistake here…’, then a student, Ho, replied,’ then why you set up this question?’ Oops.

What is the question in the discussion? It is a M.C. question.

$\frac{1}{x - y} - \frac{1}{x + y} =$

A. $\frac{-2}{x + y}$
B. 0
C. $\frac{2y}{x^2 - y^2}$
D. $\frac{2x}{(x - y)(x + y)}$

Yes, I intentionally set this question to test whether students could perform algebraic computation correctly. And we, teachers, knew that some students may make mistakes. Hence, I let students practice questions of similar types beforehand. But, according to student Ho’s comment, should I stop setting this kind of question instead?

Students asked what are techniques of doing mathematics? Teachers may reply that “practice more", but students just turn a deaf ear to this and want to have the painless short-cut. I try to clear up the concepts and show common techniques during lessons, but it is insufficent if students have no studying and drilling. Undoubtedly, we have tricks, but the effort takes the lead.