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."

> All the text books I've ever seen had practical examples in them. Like determining the height of a tree or a house simply based on trigonometry.

The trouble is a lot of those practical examples fall into the, "why would I care category". I had a high school physics teacher who described his university antics, one of which included a funny story of a bunch of his friends climbing on top of each other to measure the height of a flag pole. I guess the profs got tired of dealing with students scaling flag poles because I was measuring the height of mountains on the moon at the same university a couple of years later. The thing is nobody really cares about the height of a flag pole, while only a few would care about the height of the mountains on the moon.

The reality is the interesting applications are much more involved. They either require a depth of thought of process or a depth of knowledge that isn't appropriate for a textbook question. Take that trigonometry in games example. The math to do it was in my middle school curriculum, but it becomes obvious that computer graphics is more than trigonometry the moment you try to frame it as an example. I had linear algebra in high school. That will take you pretty far with the mathematics, but it will also be clear that a knowledge of computer programming is involved. Even knowing how to program isn't going to take you all of the way because few are interested in rendering verticies and edges ...

And that is just the obvious progression of knowledge in a simple application. Physics itself involves buckets full of trigonometry in extremely non-obvious ways, non-geometric ways.

> I see no problem with the examples being boring.

I'm in agreement with this point; the examples are boring, but that's not really relevant. After all, we're mostly talking about Maths ITT, not history or social sciences.

1. Some foundational study is needed before you get to the really interesting problems at a higher grade/level/school/university.

2. Who cares if they are boring? A spectacular facility to learn Maths which is demonstrated by high marks indicates better abstract reasoning skills, making it easier for specific trades to decide who is more suitable.

3. How will the kids know whether they like Maths or not if they skip trig in high school?

(Sidenote: Am I the only one who finds trig easy and everything else in Maths hard?)