Here’s some discussion of (primary) maths education from off the usual mathsblog trail. It’s the this post from John Holbo at Crooked Timber. He offers this excerpt from his daughters homework:
3. What do you get if you add two ODD numbers together? – an even number
4. Do you think this is always true? – yes
5. Why do you think so? My MoM Said So
The question is what she could possibly be expected to have put that would be better. Could a child so young be taught even a vague understanding of a better reason? Some informal “first draft” of what a proof is? Is it worth the effort to try?
On a side note, sorry for the not posting for a while.
Epsilonica 
April 2, 2009 at 3:39 pm
It’s good that she’s being asked the question – it’s certainly an attempt to teach Maths rather than How To Do Sums, which is always pleasing to see.
I can’t see how one could expect a small child to answer any better, but whatever the kid writes, at least (s)he has been encouraged to think about the question. I’d guess that a lot of kids work out the answer in their heads but then can’t articulate it, especially given such a small space to write their response.
(I had a Pushy Maths Dad who was always asking me this kind of thing when I was a littl’un. I think it helped.)
April 2, 2009 at 5:43 pm
It is indeed good just to ask.
Reading down the comments at CT it sounds like she had been taught a “right” answer to why it is true in general, though. Something like: “You have an even number of things if you can put them pairs and an odd number if there is one left when you try put them pairs. If you add odd to odd you can pair the the two ‘spare’ ones (and leave the rest paired as before)”.
On the one hand having an early familiarity with this sort of general argument seems like a Good Thing but on the other I’m not sure how useful it is to just have them parrot back “the spare ones pair off” (all they could hope for in that space).