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Re: [xmca] a minus times a plus

So the negative sign in -2 × 3 is being interpreted as a /process/
whereas the negative sign in 3 × -2 is being interpreted as an
/end-product/ (i.e. after taking away the blue chips from the
zero-pairs, you get 2 red chips; -2 = 0 - 2).  as an advanced learner
i don't feel that these are different, because (using Anna Sfard's
theory) i have /reified/ the process, compressed it as it were
until i can treat it like an object without any problems.  for
a beginner, there is still a very wide gulf between the process
and the end-product.

is there another way out?  is it the representation that is the
problem, or should educators put more focus on the learner's
learning experiences?


2009/5/1 David H Kirshner <dkirsh@lsu.edu>:
> Foo Keong,
> Yes, you can increase the semantic span of this approach by changing the media, as you suggest. But the basic semantic limitation still applies. The negative sign in -2 × 3 is being interpreted as a subtraction [-2 × 3 = 0 - (2 x 3)]--very different from the negative sign in 3 × (-2). Thus the lack of a commutative interpretation of multiplication in this representation is not completely solved by arraying markers in a rectangular configuration.
> David
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