III

Beautiful Dreams and Horrible Nightmares

You’re an interesting species. An interesting mix. You’re capable of such beautiful dreams, and such horrible nightmares.

—Alien sage to Eleanor Arroway in the movie Contact1

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

—Edward G. Begle, twentieth-century mathematician, math educator, and a chief architect of the New Math2