I love math, and I used to be very good at it. The correct answers came fast and intuitively. I never studied, and redid the demonstration live for the tests (sometimes inventing new ones). I was the one who answered the tricky questions in class (8 hours of math/week in high school)… You get the idea.
As such I used to have a lot of confidence in my math abilities, and didn’t think twice about saying the first idea that came to mind when answering a question.
That was more than 10 years ago, and I (almost) haven’t done any math since then. I’ve graduated in a scientific field that requires little of it (I prefer not to give details) and worked for some time.
Now I’m back at school (master of statistics) and I need to do math, once again. I make mistakes upon blunders with the same confidence I used to have when I was good, which is extremely embarrassing when it happens in class.
I feel like a tone deaf musician and an ataxic painter at the same time.
One factor that probably plays a role is that I’ve learnt math in my mother tongue, and I’m now using it English, but I wouldn’t expect it to make such a difference.
I know that it will require practice and hard work, but I need direction.
Any help is welcome.
I think the key to your problem is in your first paragraph. You say, “The correct answers came fast and intuitively. I never studied.” This is the classic high school con that can lead one to doubt one’s own abilities as soon as the going gets more challenging.
No matter what your abilities, to do worthwhile work in mathematics you will need to study and work hard. You say in your last paragraph that you know it will require practice and hard work, but I do not think you have fully taken this on board.
When you do, you will stop worrying about making mistakes. They are an essential part of the learning process and not something to beat yourself up about. Forget the belief, instilled in high school, that you should be able to come up with the correct answer straight away. Those questions were crafted to have short, snappy answers within the reach of rote learning.
Your mathematical career has now gone beyond this stage. So get down to study and make as many mistakes as you like on the path to a deeper understanding, and enjoy!