Date: Jan 21, 2013 8:21 AM
Author: GS Chandy
Subject: Re: To K-12 teachers here: Another enjoyable post from Dan Meyer

Robert Hansen (RH) posted Jan 21, 2013 10:15 AM:
>
> On Jan 20, 2013, at 8:48 PM, GS Chandy
> <gs_chandy@yahoo.com> 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
> d 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".
>
> Bob Hansen
>

So in what way is your 'response' actually responding to any of the substantive issues about learning that had been raised? A copy of the points raised is pasted below my signature for ready reference.

GSC
("Still Shoveling!")
Copy of issues raised:
>>A: 'Organization of mind'
>> ====
>>
>>The way one's mind is 'formally organized' (some small part of which possibly may be written down) is almost certainly NOT what "enables one to see". It may help a bit, true, in 'triggering' other ideas, which help one "see".
>>B: Algoritthm building in the mind
>> ====
>>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.


>>My own response to Joe N. (http://mathforum.org/kb/thread.jspa?threadID=2430190) was in reference to this mysterious process of 'algorithm building in the mind'. The teacher I referred to insisted that we do our 'scratch work' not on different bits of paper, but in a broadish 'rough work' column along the right side of each page of all our math work. I believe this simple discipline helped us all enormously, then and later, in this mysterious process of 'algorithm building in the mind' - though we never wrote (or very rarely would have written) down any 'formal algorithms'. Those 'formal algorithms' that we might write down are, I daresay, only a minor fraction of what goes on in our minds.