[plt-scheme] Re: HTDP - evidently not for everyone.

On Wed, Feb 10, 2010 at 05:20:32PM -0800, Jordan Johnson wrote:
> On Wed, 10 Feb 2010, Raoul Duke wrote:
> >>it. Then I ask them to define a time data structure and write
> >>something like time=? and some of them can't write the template (none
> >>of them managed to write the program). There is a complete inability
> >>to see the similarity between the way the different data structures
> >>they have been shown have been manipulated. After about 80 hours of
> >
> >i'm curious about this.
> >
> >what it tells me is that to reach those folks, one has to go "further"
> >and explicitly demonstrate the inventive behaviour a few times, all
> >the while explicitly saying "i am now demonstrating how to apply what
> >we've seen in a new situation".
> >
> >in other words: http://en.wikipedia.org/wiki/How_to_Solve_It
> 
> YES.  More generally, in teaching math classes I've found it's usually 
> *well*
> worth the time spent teaching metacognitive skills, because many students
> haven't ever really spent time analyzing their process of solving a problem
> (or even answering basic academic questions like, "How do I decide what to
> write in my notes?" or "How can I be confident I understand what happened in
> class today?").  I don't have the research handy, but I remember 
> encountering
> some work a few years back that seemed to corroborate my experience.

I think a good deal of math consists almost entirely of metacognitive 
skills.

-- hendrik