On Jan 20, 2013, at 8:48 PM, GS Chandy <firstname.lastname@example.org> wrote:
> Joe N. was not talking about any specific algorithm that could be formally written down, I believe, but about 'algorithm building in the mind', which is a horse of a different colour entirely, a rather mysterious process that goes on in our minds (about which science and scientists still know very little). The child's scratch papers surely would have helped the teacher to understand what might have been going on in that child's mind, which is fairly important in the process of 'teaching' (or 'helping to understand') - or at least so some of us believe.
Given that this problem takes very little time to solve (especially in a group), and that the students had considerable time to solve it, and didn't, all the scratch work will show is that the students where lost at step 1. Or, in your words, most students "guessed" wrong, and a couple students weren't exactly "guessing".