On Apr 27, 2009, at 9:49 PM, Andy Blunden wrote:
Why is a number line easier to understand than the symmetries of topological or rhetorical transformations? I don't know, but intuitively I think it is. But different people think differently. Maybe the Linda's rhetorical explanation is easier for a verbal thinker than a spatial thinker? (is this mumbo-jumbo?)
Andy, although I do think the Mirror is the most powerful and generalizable way to introduce the idea, one that is probably more "ready-to-hand" would use a coin or a card. Now the transformations are "leave it alone"/"turn it over", and there is nothing esoteric or even particularly "geometric" about them (the pattern is pre-numerical AND pre-geometric). Turn-it-over twice in succession has same result as leave-it-alone. Not done with mirrors, or numbers. ;)
But the importance of the pattern is its ubiquity! Even within the realm of numbers, before the child tackles the "less than zero" stuff, it's customary to learn the "Evens" and the "Odds". Well, consider how the Evens and Odds behave under addition: E+E = E; E+O = O; O+E = O; O+O = E. Adding an odd number "flips" (reflects) what (some of) us grownups would call the "parity" of the number, whereas adding an even number "leaves it alone". Kind of like what multiplying pos & neg numbers do to the sign of their product.
Jerry _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca