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?