For years I have used this story to explain my mathematical philosophy.
Imagine you and I want to go to the movies on Saturday. We talk and decide which movie, what time, and what theater. We then go to our own homes. It just so happens that our movie starts at noon on Saturday at a theater in a nearby city. We both must decide for ourselves when to leave our own homes. As long as we make it to the theater on time, and we aren’t being chased by the police for breaking the law, then we are both happy. Even if one of us had a longer trip, all that really mattered was that we were both there when the movie started.
Usually, my students get the analogy. Follow the mathematical laws and we will get to the answer and be happy. You may have to give me directions, but as an educated person, I should be able to follow you.
My job as an educator is to look at your directions and help you discover any “shortcuts” that might make your trip easier. Your job as a student is to realize I have taken the trip before and know where the shortcuts are.
I just hope Sean Connery is in the movie.