[locococo]

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.

Your suggestion is interesting but I am not convinced that a student would be helped by aligning the examples with their interests. I could see a student asking how trig relates to computer games and the example the LLM generates becoming much more involved.

I see no problem with the examples being boring. The people that developed these techniques had such fundamental problems to solve and the wonder to me is the human mind that came up with these methods.

All this to say, maybe we lack appreciation for the fundamental sciences that underpin every aspect of our modern lives.

[II2II]

> 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.

[amluto]

I agree with your point in general, but I do find myself actually using trigonometry for fairly basic real-world purposes more often than one might expect. For example: how big of a piece of material fits in a particular position if it’s not parallel or perpendicular to the stuff around it? If a rope supports a load in the middle, how much tension does the rope need? How much of an angle should be cut into a door to comfortably clear the jamb? (If you’ve never contemplated this before: a door with a rectangular cross-section will have less clearance to the jamb when almost closed than when fully closed.)

[Terr_]

> If a rope supports a load

Rambling off-topic, but I remember being very impressed at how a uniform hanging rope makes a catenary [0] shape which is related to making strong structural arches.

So maybe if the students were somewhere where the class could design and make an igloo... :p

[0] https://en.wikipedia.org/wiki/Catenary

[amluto]

Fun exercise for the reader: if you have that uniform hanging rope support a uniform flat suspension bridge (via a bunch of closely spaced vertical ropes), and the bridge is much, much heavier than the ropes, then you get a parabola instead of a catenary. Wikipedia gives a derivation involving differential equations, but it glosses over the actual fundamental difference between these situations. But you can explain what’s going on with just trigonometry and no calculus, let alone differential equations: consider how much weight a small section of chain that isn’t right in the middle is supporting. You’ll end up with a drawing involving a right triangle and some numbers associated with the sides, and those numbers will line up differently with the opposite, adjacent and hypotenuses in the two cases.

So your off-topic rambling isn’t off-topic at all :)

[lovehashbrowns]

I think for me personally although I don’t use maths often enough in any practical sense, the one thing I think has stopped me progressing in life how I feel I want to has been my lack of maths knowledge. I don’t mean in a career sense but in an enjoyment sense. I watched a video about proving that the square root of two is irrational and that made me irrationally happy, and I’d love to keep going but a lot of the maths in other proofs or concepts gets absolutely insane. I don’t know how to express that to kids learning maths for the first time, though. It also almost feels like the world of math is so vast there’s something for everyone to enjoy casually. That feels like a video game analogy to me with all the different genres built around basic fundamental concepts.

[lelanthran]

> 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?)