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These files are maintained strictly for historical reference, research, and recordkeeping purposes, and the content has not been altered or updated since archiving. Content on this site may not meet current digital accessibility standards. If you require an alternative, accessible format of any information found on this site, please contact Bruce Jones, bjones@ucsd.edu to request an accommodation.
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? F.K. 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 _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca