"When do I ever need to use trig in real life" is an interesting question, because it points out certain flaws in the way our society approaches education. One of those flaws is the one you pointed out: the examples we use are not very interesting.

But there's another flaw that gets overlooked most of the time, which is that we're raising kids to believe that "why are you teaching me something that you're not 100% sure I will need in my day-to-day life" is a sensible question, when it really isn't.

Outside of my 2-year stint in the game development industry, I never really needed most of what I learned about trigonometry in my day-to-day life. But that doesn't mean it wasn't useful.

Yes, we should make the subject matter more approachable to kids, but we should also try to shift the paradigm so that kids are more open to learning new things.

When I was in third grade, I decided I want to make computer games to get more of them. Dad got me started with GW-Basic turtle graphics and I made pictures with them - usually non-functional title screens for my games.

At some point I had made a small space ship and was able to make it turn around with the wonderful angle command [1]. However, I could not figure out how to make it move "forward" regardless of the angle.

I was also attending an after hours computer graphics club, mostly about Deluxe Paint, taught by a 20-something student (who much later went on to found a GPU company and got acquihired by ATI/AMD). He would help me occasionally, and in this case he took a tiny slip of paper and wrote down a couple of lines about sin and cos. No questions, no explanations, no gatekeeping.

Just like that I internalized this foundational piece of trig - later when it arrived in school maths it was easy and obvious for me. I had a practical application, but even more I think was because it started as a need I had, and when given to me, felt like a gift and an enabler.

Still much later I studied Seymour Papert's pedagogy and understood I had lived it. I consider myself fortunate.

1: http://www.antonis.de/qbebooks/gwbasman/draw.html

If the subject matter isn’t something the kid has a natural aptitude or interest in, and it’s not practical, and it’s not being taught in an unusually captivating way, why wouldn’t kids push back? I don’t blame them. I think adults should be able to justify why we’re using what boils down to the threat of force (if we’re honest) to make them sit in classrooms and listen to us.

I asked my math teacher for applications and she just mumbled something, embarrassed. Took me until a while later to realize that most of my teachers had never stepped foot outside a school in their entire life.

Later at university I complained about the lack of applications in the textbook, and my classmates became very upset. One of them responded, "we are mathematicians, we do not concern ourselves with applications."

I agree this is a problem. The best reason I can come up with is “because it is fun/beautiful/interesting” (to some people).

But IMO that pushes you to making the curriculum more flexible and not forcing every student into the same sequence where math is the core IQ test for STEM. If a kid doesn’t find it interesting I struggle to justify forcing them.

Personally I also think trig and calculus are far inferior to statistics for most people. If you have an intuition for probability distributions, precision/recall, and a few other basic concepts, you’ll be guaranteed to apply them everywhere in your life.

Of course if you are interested in STEM then calculus must be available too, but it’s pretty specialized in practice.

It is also a fallacy. Interesting and practical are two different things, especially for kids. Kids will happily learn completely useless things and will dislike clearly practical and important subjects.

> One of those flaws is the one you pointed out: the examples we use are not very interesting.

I think the truth is a lot simpler. Most kids won’t use trig in real life.

There's also the distinction between "I know that X% of this will (not) be useful" versus "I know which X% of this will (not) be useful."

Especially when "useful" includes "to get a future job" or study something else much more useful and interesting later."