I had a very bad experience with maths when I was younger, generally doing very badly and as such taking the sensible option of hating it. I even dropped my study of maths at A level, in spite of my huge love of Physics and desire to study it at University.
I was eventually convinced that I really should take maths, so after a year out I did. I personally found the difference in the topics being studied to be drastic. No longer tedious mental arithmetic and boring calculation, but far more interesting things like calculus and mechanics! I suddenly found that things made sense, which had rarely been the case before. Perhaps you have a similar issue, and find calculation difficult?
I, like you, find that I make very many "silly" mistakes. This is something that continues to plague me. I have developed techniques to compensate for these weaknesses, so while it might take me longer to go through the "grunt work" of solving a problem, I can quite happily end up with the right result. I suppose my point is, while it is not an advantage, it doesn't have to be too great of a disadvantage!
I have also been diagnosed as dyslexic, though I don't really know how true that is. Perhaps this is something you might look in to.
I can see that this is a good thing to do (though I will need to spend some time working out how to find interesting things on github). However, will this be enough to learn things like - design patterns, and when to use them? How to properly test code? I suppose these things are not so much of a problem; I have heard of them, so I can find out about them. I am more worried by finding out about things that I am thus far unaware of!