I certainly think modern mathematics instruction must include discrete mathematics.
I'm concerned that the mobius strip is used as an activity with no connection to other topology ideas... and as math I think of it as a one of a series of classified surfaces, that it's interesting as something that has different invariants... I'm not expressing this very well.... and my question is just that... how does one express the mathematical importance, how does one convey this?
The hexaflexagons (and other flexagons) boggle my mind. But that and the results of slicing mobius strips is not what mathematics is about. If math is mind boggling only, then it's just magic and belongs to the world of those strange nerdy magicians.
I want to convey to others that mathematics gives us power. For example, showing that minimal trees can show how to minimally brace a structure. Or that finding the maximum time on a graphed path can show the minimum time of a schedule.
It's my bias, I know. And I'm ignoring the "gorgeous" sort of mathematics like fractal images..... but where is the power in having my mind boggled unless I know what's going on?
P.S. Yes mobius strips have been used in power belts to keep them wearing evenly. Some dot matrix printer ribbons are too.
Some of the public programmers I work with think it's enough to have practical uses as answers to the "so?" question. I'm not convinced of that either.
Cathy Brady Math Specialist/Education firstname.lastname@example.org Maryland Science Center Opinions are my own "Beyond Numbers" exhibit or something I overheard Baltimore's Inner Harbor