Reasons to learn math you'll never use

The film, "An Education", is about the experience of a teenaged girl (Jenny) growing up, meeting an older man, and making decisions regarding pursuing school versus marriage.  There is a passage near the end of the film that rather haunts me, especially the very last line (in bold below):
Jenny: Studying is hard and boring. Teaching is hard and boring. So, what you're telling me is to be bored, and then bored, and finally bored again, but this time for the rest of my life? This whole stupid country is bored! There's no life in it, or color, or fun! It's probably just as well the Russians are going to drop a nuclear bomb on us any day now. So my choice is to do something hard and boring, or to marry my... Jew, and go to Paris and Rome and listen to jazz, and read, and eat good food in nice restaurants, and have fun! It's not enough to educate us anymore Ms. Walters. You've got to tell us why you're doing it.

An Education
It strikes me that much of the frustration at all levels of education comes down to people having varying beliefs that are often contradictory, sometimes confused, and at other times missing altogether, about the purpose of education (and by that, I mean formal education in the school setting).

Some think education is for opening the mind of young people to the light of reason.  Some believe education is essentially career and job skills training.  Some think it is to "raise the kids" in the parenting sense, as though teachers are parents.  Many think it's more or less pointless, but essential as a child caring service while the children's parents are out making a living.  Some don't think about the question altogether, opting to do whatever the teachers say, as education is just traditionally "the thing to do".

The list of purposes ascribed to education by various people goes on...

These questions are especially difficult to answer in the context of math education.  Except for a minority of students who end up going to university [1], most students will never get the chance to have to use the calculus, geometry, formal logic, proofs, etc, that they learned in primary and secondary schooling.

In fact, even for those students who do end up going to university, many of them will never get the chance to use all the maths they've learned either, as they end up in fields that are either not science, not quantitative, or just not very mathematical at all (many in engineering don't use all the maths they learn either!).

This means that years of schooling is spent teaching a lot of students a base of knowledge and skills that they will never find any use for.  So why do we educate them, especially in the field of math and science, to the levels that we do?  There are multiple possible ways to answer this question, and none of them are totally satisfactory to everyone.

For instance, at the social policy level of discussion, it might be argued that by educating as many students as possible to as high a level of math and scientific knowledge as possible, it gives society a much larger base of science and engineering minded young people to choose from to make into mature scientists, doctors, and engineers — to the ultimate benefit of the rest of society. Actually, that's essentially the reason why relatively small countries with a need for a strong military force, like Singapore and Israel, have a draft. Compulsory education is like compulsory military training, only the result is not a strong military force, but a strong intellectual force.

But appealing to the good of the rest of society is probably not a very good way to answer an individual student's question of why he or she, in particular, is being educated in math and science to such a high level of knowledge.  This simply wouldn't fly: "Sally, you're being educated as you are being drafted into the intellectual work force, so that one day you can be economy fodder!"

Instead, I would suggest explaining the value of intellectual edification in math and science the same way you would explain why you went on a vacation to some exotic locale, why you went adventure traveling to some remote islands, or why you hiked up some tall mountain to a summit thousands have been to in the past.

That is, it's the challenge, the intellectual stimulation, the sense of adventure, the thrill of understanding eternal truths to the universe, the appreciation for beauty, etc, that makes learning math and science — even if it will never be used ever again — purposeful and meaningful.

It seems to me that these values listed here are what it means to have an interesting life — certainly to have an interesting intellectual life.  It's these values that makes it possible to "make school the foundation of an interesting life" [2].  Perhaps these values form the essential core to answering the challenge from Jenny: ie, it's not enough to educate students anymore; perhaps they have to be enculturated to also value what makes life interesting.

[1] It seems that only 47.9% of persons age 18 to 21 are in college in the USA (in 2007, per statistics in form 264 from US Census), and college seems to include all kinds of trades and technical colleges.  In Canada, only 26.3% of persons age 18 to 21 are in university (in 2006, per Statistics Canada figures shown over at HRSDC).

[2] See Learning to Love Your AP History Assignments for some tangentially related readings.

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