With regard to J. Conway's article about lamenting having to strip off the fluff to get to the mathematics. Isn't this one of the strengths of mathematics, and one of those traits that one would like to inculcate in a student? I can not imagine anyone advocating a complete separation of mathematics from worldly aspects, though this is the argument of Hardy, was it not? The purity and sanctity of mathmatics, beauty in its self?
Having learned most of my geometry from Wentworth & Smith, I remember still many examples mostly of militaristic applications, that great source of much of mathematics, and of agricultural applications, that primary phaenomenon of rural America, and of sailing problems. As I recall there were no applications until the late editions of their geometry that incorporated examples from sports, whihc might have become the defining element of modern America.
I can not imagine teaching trigonometry without discussing at some point indirect measurement and giving examples, sometimes with appropriate equipment having students make the measurements in surveying, in determining within measurement of error confines distances and heights. Nor can I imagine teaching Diff. Eq. without discussing applications to growth-decay, springs, reasonance, etc.
However, thank goodness one does not still have to include "fabricated examples" such as "Mary is now twice as old as her sister Beth, prove that if they are twins then ... " or however that problem goes.
I can give many examples that I have used and seen used that have gone awry because of cultural ignorance or linguistic lacunae. I will never use the word "wench" again in a problem, I promise. I still use in pre-caluclus an example of a piston, because it is a good problem that most students make an initial incorrect hypothesis concerning the nature of the defining curve. And I expect my students to know the dimensions of a bsaeball field, and in the words of Robin Williams that "three up and three down" means half an inning, not a corporal or whatever.
With more and more students having English as their non-primary language, I find "reality problems" to be more a hindrance when lack of time is significant. (Isn't this a common malady?) But then I do wish for them to know that most of the world, if not all, can be thought of mathematically, from looking at music using groups and geometry, to analyzing the structure of poetry in through form (see Bronowski and Scott Buchanan). After all doesn't mathematics come from the greek word for "thought."
Enough, let me return to the green fields of paradise.