[jmilloy]

When are practising skills in school, sometimes we practice creativity and sometimes we practice techniques. Both are useful, and it's clear which is which.

Secondly, a student that knows the difference between different techniques and can call them up at will (such as the difference between 5 sets of 3 and 3 sets of 5) is better off than a student that only knows how to produce a particular answer for a particular question.

[Someone]

I seriously doubt this student "only knows how to produce a particular answer for a particular question". Are you claiming he could compute 3 times 5 but not 5 times 3?

On the contrary, I think this student may be showing that he knew the two techniques, and that he is smart enough to pick the easier computation.

But yes, if your goal is to kill any creativity in intelligent should punish kids that deviate from the lines hard.

If a teacher asked "compute 1000 x 1", no sane kid would do "1 plus 1 equals 2; 2 plus 1 equals 3;...; 999 plus one equals 1000".

This teacher would have failed Carl Friedrich Gauss, too, for computing sum(1,100) in seconds.

[maxerickson]

A student that sees a multiplication sign and reads it as "sets of" is not better off than one who reads it as multiplication.

[jmilloy]

Maybe, maybe not; I'm not sure.

But I am sure that a student who understands and can apply a specific process when required as well as produce a correct result is better off than one who can only produce a correct result.

Obviously I don't think that all of school should be rote application of techniques. But I've found that when you want to make sure your students have learned a specific technique, you sometimes have to create a somewhat artificial request. Have you taught enough to have found otherwise?

[maxerickson]

Nope, I'm not a teacher.

(I tutored math in college and did have the experience of helping people understand math...)