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How do you not get discouraged after messing up math assessments?

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I remind myself that it's a hard subject, well known for being hard, and that struggling isn't a sign of doom but rather a sign of growth. Every failure is a chance to make a comeback. Attitude is the number one thing that will affect progress in math, followed closely by effort.
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Take it from someone who just graduated with an engineering degree. It’s hard stuff man. The best way to get better and learn is simply to keep doing it. Math is like a sport. I’ve had so many frustrations like yours I can’t count em. Just keep at it and you’ll be fine
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Andrew Wiles messed up in his proof of FLT but he didn't get discouraged but kept working for many more months to fill the gap in his proof, so it's totally normal to mess up and you should expect it and learn to cope with it.
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We've all been there OP. It's ok to be bummed about it, but don't let it get you down in general. We've all had bad quizzes/exams. Work through the problem(s) that gave you trouble, and don't hesitate to go to the teacher for clarification. Maybe ask for a couple of extra problems so you can get more practice before the final.
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Listen to angel by the wings and let the discouragement fade, even better, practice Calculus while listening to it.
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You learn the most from your failures, and I think this is even more true in Math. You can do dozens of the same type of problem, get them all right, and still make a mistake when you change one aspect of the problem. It's that change, the mistake it leads to and the recognition of your mistake after the fact that teaches you the most.

It sucks when it happens on an assessment of course, but just look at it as a learning opportunity.
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Been there. Math is fucking hard. And on top of it, the pressure to excel and compete can be intense.

I've been working on degrees in math for 7+ years now and I have failed a lot. And I mean tanked a midterm exam. Got a 40% and begged my professor to let me do extra work to make up for it. I withdrew from my advanced math program because the pressure was too high and I was killing myself to keep up. I'm not the brightest. I didn't get amazing internships like my classmates, and I got rejected from PhD programs my first try.

But here is the amazing thing. Through the struggle, all the math you are learning accumulates. It piles up in your brain, regardless of failures.

Math is like this at every level. Always pushing you in some new way. Making you uncomfortable and confused. And you will stay confused until you put in the work to solve problems on your own. And because you are so wrapped up in the difficulty of learning, and comparing yourself to your peers, you don't ever see the huge pile of math skills you have stored up.

Right now, you are learning calculus. That is amazing! Think back to how much you knew about integrals/derivatives a year ago. I bet that you know so much now. See! You are accumulating math skills!

It's not easy. Institutional benchmarks and gatekeeping get in the way of the learning process and cause a lot of fear and uncertainty. But you can navigate them if you are patient.

Be present with the feelings of fear and anxiety and acknowledge to yourself that this feels important to you. Then take a breath and give yourself some room to be imperfect. You will get there eventually.
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You're human, and it is important to remember that. You're an imperfect being, and therefore you will produce imperfect work. We all make mistakes. What is most important is understanding why you were wrong so that you don't make that mistake again in the future. If you can do that, you will continue to make fewer (or I guess newer) mistakes as you go along.
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I just do not see the point of being discouraged, if I do mess up, it simply means I need to learn more
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My enjoyment of maths in school was more an enjoyment of recreational maths books. Sometimes the school maths was good, sometimes it wasn't.
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