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I am teaching some kids (ages 13-15) some basics of functions and trigonometry in a summer camp. I have noticed that 90% of the class is above average and quickly resolve most of the problems.

Soon I will have to teach sines and cosines. One of the school managers want to take the class outside on campus and sit on the grass and give them the problem of measuring the height of a building knowing the adjacent and the angle to the top. This will take half an hour, i.e., takes the kids outside etc...

I can do the same on a powerpoint slide, giving them the same exercise and seeing an image of a skyscraper instead. Most of them will do it in 2-3 minutes and we will be ready to move on.

What is best? I believe the second since this will give the kids the opportunity to play with some Mathematica code after. On the other hand, the organiser wants to be "softer" and "funnier" and always try to connect whatever we do to some "real life situation" or "problem".

When I was 14 or 15 in my country, most of the problems were already "proof" like.

In the country I am doing this the school (and university) maths level is extremely low. I think being so soft, avoiding any kind of formalism, presenting everything is fun and connected to "real life" poses a problem for the mathematical literacy of the young students. They are not "allowed" to solve a problem for the shake of solving it, for curiosity etc if we teach the way they want us to teach.

What is your view on this, first for the trigonometry lesson and later for the teaching style?

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    $\begingroup$ This is probably better for the math educators SE than here. But my two cents: this is a very boring application of trig, the most rudimentary and obvious thing one can do -- since it follows immediately from the definition in terms of lengths in a right triangle. Come up with a more powerful, less trivial application, such as triangulation: maplesoft.com/support/help/maple/… $\endgroup$ – symplectomorphic Jun 21 '16 at 14:09
  • $\begingroup$ So you agree with my general spirit? That indeed it is a waste of time. Unfortunately this is an application that we "have to do", I just prefer to do it in 2 mins rather half an hour. $\endgroup$ – Marion Jun 21 '16 at 14:13
  • $\begingroup$ Which country are you in? I am in the UK, where the last 50 years has been an absolute disaster for maths education pre-university, starting with the New Math in the 1960s. Everything has been dumbed down etc. $\endgroup$ – almagest Jun 21 '16 at 14:23
  • $\begingroup$ I am in a country very similar to UK, I would say extremely similar (I would rather not say more) but in discussions I have have had the problem is exactly the same. I have studied also in the UK and indeed everything is dumbed down even in university level. In this country they try to raise mathematical literacy and their policies is as the ones described above. I can see that children can learn and understand harder topics than the ones they are asked to complete. $\endgroup$ – Marion Jun 21 '16 at 14:29
  • $\begingroup$ A bit late, and I'm not a math teacher. But I think the fun way make trig useful is... music and art -- making sounds with wave forms, cancellation, drawing interesting shapes, etc. $\endgroup$ – Ubuntourist Apr 17 '18 at 15:28
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The approach you use will depend on your audience. You may want to teach at a higher level, but your students may be unprepared. What you may do is to give them some diagnostic at the beginning of the term and then adjust your teaching based on the results.

You can find some advice on teaching trigonometry here: https://ekswhy.com/on-teaching-trigonometry-introduction/.

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