Is giving hints a good way to help students in solving mathematics problems? Urm, sometimes it may not.
Here is a common m.i. question in recent F.4 additional mathematics regular test:
Show that is divisible by 3 for any positive integer .
(Note, it is quite a stupid question, because, , i.e. is a product of 3 consecutive integers, and of course, it is divisible by 3. Also is divisible by 3 trivially. Hence is divisible by 3, Q.E.D.)
To HELP students to get some marks, I’d posted the question like
(a) Show that for any value of .
(b) By using m.i., show that is divisible by 3 for any positive integer .
Do you think that part (a) is a helpful part? At the beginning, I think it is helpful in terms of getting marks. BUT, the real case is, many students (esp. those were not in my class) did the part (a) wrongly! Why F.4 students did not know how to cope with this F.2-standard question? Because, they tried to do it BY M.I.
Oh, my! M.I. is invalid in solving (a).
I come across similar things (not helping, but hurting) sometimes. May be, it is not a fault to set up ‘hint-giving’ steps, but the problem is, the so-called hints were inappropriate and irrelevant.
I think I need to learn more in setting up good paper.
Another thing could be interesting about the recent additional mathematics regular test. Some arguments in “exist or does not exist".
Here is a part of the question I set:
Write down the coefficient of in the expansion of .
It is easy to answer because ,
and there is no term in involving odd power of , hence the coefficient is ZERO.
BUT, some students gave the answer : “does not exist"
Quite an interesting reply! Do you agree with the students?