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If I arrive at the correct answer every single time then I clearly understand the principles.
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.
There is no way you are doing calculus and functions and relations in your head.
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.
It’s endlessly amusing to me that people come into a post about adhd and then downvote anyone who explains their experience.
I struggled all through school with math classes (which I still passed) and it turns out Im actually extremely good at math. I just didn’t realise it until I was programming video games.
I was working on machine learning in games in 2009.
All this to say, the education system doesn’t deal well with people who think differently.
Looking back through the comments the downvotes aren't about denying experience. The topic raised was no need to show work if answer is right...but there is a reason the work should be shown and it is for the future course / work setup. If people have trouble doing that, your school can setup an IEP (individualized Education Plan).
If anyone had taken my explanation as insult to experience that was not my intention. Two of my kids have ADHD. They both had wildly fluctuating math scores. Working with them on techniques to work through the method and not jump right to answering, helped them steady their grades. They were often done first out of everyone, but rounding error or just plain old transposition often messed things up, so part of showing work reasoning was "OK, you have 1/2 hour left till test is over, go through your steps backwards, does it still make sense" and often they'd find their errors, but you can't do that with an empty page with only an answer.
Until the system has multiple types of learning and testing setup, which could take decades, working with the system is really the only way to get through it. Finding the students currency often helps provide a reward system to counter what the executive function and impulse system aren't coordinating on
i typed a bunch, but it disappeared. I will try again. For example I had a topology descriptive geometry solving exam, I had not had time to learn how it was done due to job/life events.
I used my spatial sense to sketch up the solutions, because I didn't know the methods well enough to actually solve it. Got a great mark on the exam, prof gave me kudos in front of class. So while my faked end solutions passed the check, had the prof asked for the projection stage sheets to be turned in (showing how you work through the problem) I would have failed.
Right answers don't mean you know the material. And by you I mean the plural you, not you personally.
The profs are aaking to see work to see if you know the principles. People can arrive at an answer that looks right by doing the wrong things