Let me preface this by saying that I want to become good at posing problems. By good I mean able to produce problems of varying difficulty that are insightful and read well. I understand this is quite general so lets focus on pre-universtiy maths (similar to a-level for those familiar with the uk system) so things like u-substiution, polar coordinates, hyperbolic functions, solving 1st/2nd order DEs.
How do people do it? It seems so difficult to create these seemingly random scenarios and expressions that you want students to prove. Even then, they must not be too challenging and not too easy. For example: https://imgur.com/tuOeaOv
How can I become good at posing such problems?
How “able” should I be mathematically speaking to be able to come up with good problems?
This is all very broad I know, but I just want some guidance. any advice at all is highly appreciated 🙂