Sorry, am I suddenly in that shitty class with bayrak? What is problem solving? It's solving a fucking problem. Do you need a definition of the words?
according to google problem solving is "the process of finding solutions to difficult or complex issues."
Problem is "a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome." or "an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law."
to solve is "find an answer to, explanation for, or means of effectively dealing with (a problem or mystery)."
Anyway. Problem solving is solving a problem. Finding a solution to a problem. In math, finding THE solution.
How do I approach problem solving? IDFK. Um. I ask google. Or I look in the relevant math book if I have one. Solving engineering problems I think comes down to experience. Maybe. How did I think of repairing the blinds with tape? I don't remember. I remember about the coaster holder. I first thought of a rubber band but I thought it would be too easy for them to roll over it. I thought it needed something taller but then it would have to be looser to make room for the coasters and I thought of the headband thing. I needed experience to even think of rubber bands and headbands. I also needed supplies. I don't remember exactly how the phone case came to me either. Sometimes I have to think and sometimes things just pop into my head.
I don't really remember solving math problems but I remember that I did, and I remember thinking that I relied on experience. I tried things that had worked on similar problems before. Or I just tried random things if nothing seemed to fit, until it led somewhere familiar. If it takes too long, where "too long" is subjective, look it up, and after a while give up.