RE: A: When and how do schools outside the United States teach geometry?
Here is an interesting story.
When I was in college, I made a transition from polytechnics to mechanical engineering.
In order to be able to continue from second year instead of first I had to prepare and undergo some entry exams in various subjects.
Not a problem for most topics involving maths but the one that I feared was technical drawing as I didn't have the one year experience in the subject other students had. This was a 'practical' topic that was quite alien to me.
My dad was a carpenter and offered to help since he was used to deal with technical drawings.
I was stunned to see how he could solve geometric problems without the use of trigonometry...
He never had a math education but was able to determine angles and lengths without a single formula.
He used traditional methods involving compass, ruler and pencil and simple arithmetic. Probably the result of thousands of years of practical engineering without the knowledge of any advanced maths.
That was a great lesson for me.
Knowledge takes various forms and where I had learned the mathematical shortcuts to calculate answers through formulae, my dad had a better and deeper understanding of geometry than me with 2 years of engineering training.
So much for the 'old' school way of thinking!
I know a couple of people who are like that. I was like that once. I was in scouts when I was younger and we have a pretty serious scout program in my country. We learned a lot about geometry, maps, azimuths, angles etc. but not in the way it presented in schools. It was fun to see different approaches to the same thing :) You were lucky to have your father to help you. Knowledge really does take various forms.
Enjoy your weekend 💚