Maybe you do, but some arrive at the answer using the wrong techniwue that doesnt work when the equation is altered. There is no way you are doing calculus and functions and relations in your head. Process and method is the important part.
By you, I mean plural you. Like a prof has a class of people to ensure they grasp the fundamental underlying concept, not just running through the paces. For a personal example, I had a Descriptive Geometey course in college. Early stuff is easy, later techniques for finding shortest distance between two topologies in 3d space based of 2 flat images are complex. I was working 50 hours a week and just had a kid, so my level of focus on this course was too low. For the exam I did not know all the mulitprojection methods well enough to solve them, so I just used my ability to imagine the spatial shape, and sketched them down. Turned out my guesses were good and got highest mark. Prof gave me kudos in front of class on how well i had completed it. But in fact I really had no clue hoe to solve the complex topologies properly. Had he asked for the staging projecrtions to be turned in I would have failed the course. This is what I meant by getting the right answers doean’t test that “you” know the underlying concepts.
Maybe you do, but some arrive at the answer using the wrong techniwue that doesnt work when the equation is altered. There is no way you are doing calculus and functions and relations in your head. Process and method is the important part.
If Im getting it correct every time it is altered then clearly it isn’t an issue.
That is an assumption you aren’t really in a position to make.
By you, I mean plural you. Like a prof has a class of people to ensure they grasp the fundamental underlying concept, not just running through the paces. For a personal example, I had a Descriptive Geometey course in college. Early stuff is easy, later techniques for finding shortest distance between two topologies in 3d space based of 2 flat images are complex. I was working 50 hours a week and just had a kid, so my level of focus on this course was too low. For the exam I did not know all the mulitprojection methods well enough to solve them, so I just used my ability to imagine the spatial shape, and sketched them down. Turned out my guesses were good and got highest mark. Prof gave me kudos in front of class on how well i had completed it. But in fact I really had no clue hoe to solve the complex topologies properly. Had he asked for the staging projecrtions to be turned in I would have failed the course. This is what I meant by getting the right answers doean’t test that “you” know the underlying concepts.