Validating the material. Justifying the curriculum.

I'm all for the real world. I live here, too. But not everything I do is directly related to what I'll be doing tomorrow. Sometimes, I'm just guessing. Most of the time I know what's useful and what isn't.

What I refuse to do is to always justify every topic and problem that I teach as being useful to every student for every day of their future lives. I won't even guarantee that every topic will be "useful" even just once for each student. I can never do that because I know that every kid is different and will have different needs. Some kids are losers who will grow out of being losers -- what you were sure was useless last year may suddenly become very useful tomorrow.

This question arose when f(t) posted about some circle theorems and asked "What are these good for?" One answer included the following: "On the other hand, there are millions of other problems/concepts that also do that AND are useful in 'real life.' So, why do we do these that are so disconnected?"

The problem with always requiring "a real-world application or you'll dump the material" is that all of math can be reduced to this absurd level if you try hard enough. As can poetry. And chemistry. and history. and art. (and grammar and writing, if you took my principal's example). Every topic can be eliminated by somebody.

"When am I EVER going to use this?" becomes a weapon instead of a question.

Why not teach it "just because?"

Why should my short-sighted, intensely hormonal, spring-addled students have the right of refusal over anything they don't immediately see a purpose for? I can see a couple of blue-collar uses for those circle and tangent rules above. If I can't convince a student that a machinist, draftsman or custom motorcycle builder would need at least an understanding of this stuff, should it be eliminated? I don't think so.

Sometimes they just need to follow the leader. "We're doing it because I think it's neat, it's part of the course, it fits here and we have the time."

As math teachers, we need to refocus the question and answer it ourselves. We need to take the question out of the mouths of the lazy and decide what does, indeed, make for a good curriculum. If something like those circle theorems can be used in any meaningful way either later in life or later in the week, then WE should decide. If they have no purpose other than intellectual curiosity, then they have that going for them, don't they?

Geometrical theorems are rarely useful in the raw as it were, but in combination with other knowledge, make a different problem solvable. It's a polygon inscribed in a circle -- or is it a bolt-pattern for a truck wheel? Tangents and circles, central and inscribed angles, external angles come together all the time in machining and manufacture.

To answer the original question:
Every time I see these theorems, I think of the guys on Junkyard wars who recited geometrical theory when building a go-kart. They won.

Some other comments:
"My take on it is that the people behind the unified 10-12 curriculum looked at circle geometry and asked these same questions of "why?", had no answer, and got rid of them. " The commenter didn't get rid of them but the powers-that-be did.

"I don't consider "it's interesting" a good enough justification, because there are plenty of things that are both interesting and relevant to what students will later see of pure mathematics." In other words, justify or get replaced.

"it's a mathematical dead end." and "but I can't even think of a later pure-mathematics connection. Shouldn't we be suspicious of anything that's a "stub" in the curriculum?" I can't think of a reason for it, so let's be suspicious of it?