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Re: [xmca] a minus times a plus

Thanks for the wonderful picture! Will take a closer look.

As to "the child's natural curiosity", I am sure that something like that leads the child to ask all sorts of questions about Why? things are set up as they are in our mathematics. But I am not sure that children have any natural drive toward abstract synthesis for the sake of consistency and coherence. In any case, what counts as an acceptable synthesis is at least in large part culturally defined, though individuals may still want more or settle for less.


Jay Lemke
Educational Studies
University of Michigan
Ann Arbor, MI 48109

On May 3, 2009, at 7:33 AM, Ng Foo Keong wrote:

Jay Lemke wrote
This idea of organizing all the representations, or realizations
in Sfard's terms, of the system of the integers into one coherent
scheme is of course attractive. But we should ask WHY it is
attractive? and to whom? Culturally it has been argued in our recent
history, by postmodernists, that such Master Narratives are part
and parcel of a particular ideology.

I thought it's just a child's natural curiosity (instinct?) to try to
make sense of the world.  Maybe when people grow up, they get more
erm ... complicated.  What do we tell the child then?  "Shut up!  and
calculate!" like we tell the physicists?

Jay Lemke wrote
Forgive me, but I find myself nearing the limits of language as a medium
here. I need some pictures, if not an animation!

What ever happened to the plans for a next-generation xmca where we could
have more than text??

But still, somebody has to do the donkey work of hanging the bell on the
cat.  OK, OK, I get the hint.

  do, do, do, doodledy dooooo. ...
  converting to pdf ...
  trying to attach it to this message ...

did you guys "get it"?
<Negative times Negative.pdf>_______________________________________________
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