Ever since high school, I've had a serious problem with math classes. Be it discrete math, algebra, calculus or linear algebra, I seldom have trouble understanding the texts or lectures, but when it comes to executing calculations on homework and exams, I can never do it: I keep making mistakes. It's been a constant source of frustration, and right now, I'm on the verge of failing linear algebra and second year calculus (which I've been avoiding for as long as I could).
I'm currently going through all the exercises and videos on Khan Academy, beginning with one-digit addition, working my way back up to integrals. I was making a lot of mistakes with multiple digit subtraction and multiplication, so initially, I was hopeful that maybe with enough practice in those two things, I'd be good to go again. But it turns out that my mistakes aren't confined to any one task, and the number of mistakes I make per exercise just accumulates as the tasks become more and more computationally involved:
- Thinking that 7 + 5 = 13
- Neglecting negative signs when transcribing
- Carrying in multiple-digit addition when a digit hasn't surpassed 10
- Multiplying instead of adding
- Using the wrong exponent laws, log laws, limit laws etc.
- Mixing up trigonometric function properties
- Forgetting to reverse signs when expanding negated expressions of multiple terms
A typical page from my notebook:
I've tried everything: going for walks, ensuring that I have good sleep, writing out every step with almost hilarious verbosity, changing rooms, starting with fresh notebooks, reviewing everything I write, trying different notations, heck I even spent a month refining my handwriting and posture for good measure.
I'm certain I spend about twice as much time as other people practicing too. I avoid taking other courses in the same semesters that I take math courses.
As far as personality goes, in general, I'm not exactly OCD, but I'm not careless either. I probably have more patience than most people -- a bit too much, as my friends would tell me. I'm sure you can also tell from my adequate grammar, punctuation and spelling that I probably don't have any kind of learning disability that would prevent me from following symbolic rules. I've gotten near 100% in a first order logic course too.
Yet when I do math, I always screw up. It's been this way for over a decade, maybe more.
I don't know what I'm doing wrong anymore, and I'm losing hope.
What could I do?