[pohl]

It certainly is a repeated addition strategy, but is it the repeated addition strategy given to the students?

The definition of the algorithm given to the student may involve language like "take the first number and..."

The steps are the steps.

[ryandrake]

"The steps are the steps". Great advice if the purpose of school is to train people for rote factory work (we have robots for that). Not such a great way to prepare future leaders or creative problem solvers.

[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...)

[maxerickson]

The steps ought to be a bridge to understanding the arithmetic as an abstraction.

Teaching and requiring that a commutative operation be ordered doesn't seem like it is going to contribute to that.

[jmilloy]

I agree with you. The learning objective is stated as "I can use multiplication strategies to help me multilpy", but it's important that the question asks about a specific multiplication strategy, and marks the question as partially correct because the specific multiplication strategy desired is used only partially correctly.

[chris_wot]

The steps are either being taught incorrectly, or they are wrong. Very worrying!