perhaps there are two purposes to education:
-you need this for your life. this will help you as you navigate life.
-this is to make you a cultured person. you may not need it but it is beautiful and significant.
i feel like the majority of the mathematics i teach lies in a lukewarm, murky puddle between the rushing, vibrant, ever-changing stream of today's numbers, and the icy crystals (more beautiful yet upon magnification) of pure math.
i think i could be happy with either extreme. but this middle ground that at times masquerades as useful and other times as beautiful (and is mostly neither) just irritates me and bores my students.
there have been many situations where mysteriously beautiful mathematics has been discovered (years later) to have an amazing and unexpected application.
however when textbooks take a topic that has traditionally (for more than a century) been a part of the curriculum, and force an application to it, the laughably contrived "examples" that result are downright embarassing to the teacher. she has no choice but to skip over them, or to tell the students she thinks they are silly.
can math education ever change? i just had an idea driving home tonight of writing a book which shows a traditional approach to a topic on one page and contrasts it on a facing page with what might be so much more interesting, useful, or beautiful.
but stories about how many nickels and dimes Susie has! or perfectly parabolic supply and demand functions? please!!