Mistakes are not nice - at first sight, at least. They mess up results and stuff in general. Sometimes they are big and they're easy to spot. Other times, they're so small, it's just annoying to try look for them - so how about moving on? Hmm... not a good idea. Definitely, not in math.
I suspect lots of people don't like math because it is merciless. You make a little mistake - boom! your whole work goes down the drain. All that calculation and the function graph still doesn't look right - probably because you messed up a sign, plus instead of minus. Or it said "find total" and you did subtraction. Blast. And that's just the theoretical part. What about the practical stuff?
You may have spent an hour to figure out how to cut the wood for the fence (yep, you have a complex fence structure) - and after you cut and start assembling, you realize it's not enough: you made one or two mistakes. Now, that's annoying, to say the least: more money, more time, more figuring out. Sucks. These days though, when computers help us with everything, maybe you find an app to calculate all that wood. That's nice. Still, you realize that instead of taking only two trips to the store to get the wood, you did four - just because you didn't optimize the spacing in the car. Oh well. Yeah, it adds up to that lost time and some gas. A little bit here, a little bit there. What are credit cards for? By the way, do you understand the concept of "interest"?
So yes, math is part of life and there is no way we can avoid it. We'd better embrace it, try figure out how to go about it and hopefully it will help us advance instead of coming back to bite us (which it always does, haha!)
I've made my mistakes. Tons! No, I don't like them. And of course I don't like having done them! There were times when I've cringed at my negligence or my shallowness. Ah well. I can sit cry about it (which I also did lots, make no mistake!) or I can go search for the problem, find it and deal with it. My tip to go about mistakes then is this: be courageous, thorough and organized in everything you do. It pays off. When you register all the steps, it's easier to go back the trail and find where the problem is. Sometimes, there are more mistakes than one, so you might need to start at the beginning and reconstruct the whole thing - provided, of course, that you actually know all the drills.
That brings me to when it's good to make mistakes. Early. As early as possible in life. We are wired to make connections between cause and effect. Mom says "don't touch that stove, it's hot" - well, you'll get burned if you don't listen and next time you'll refrain from touching a hot stove. Teacher says "you need to learn the multiplication table by heart" - as soon as you get to simplifying fractions, you won't get what to divide by 'cause you'll have to search hard in your non-existent data base. Never mind that high-school math will be a complete mystery and you'll only be able to enroll in social studies for university. Who will ever know you have the brain of an engineer?
Mistakes may not be nice, but each one of them is a little great lesson. They play their role in shaping us into our better selves. Do them if you can't avoid it, and then acknowledge them, fix them, learn what there is to learn and move on. Don't let your stuff unsolved - it's also a good idea not to let others solve your stuff because you don't want to deal with the consequences. Clean up after yourself - and be thorough about it. You don't wanna do this? Fine. Not my life. Just don't be surprised if history repeats itself. Better not, though - don't you think?
Bottom line - dig into math. Early! You make mistakes? So what? Keep going - you'll get it, you have a good brain. Is it tedious? You bet. Nothing that is worth it in life is actually easy - but again, doesn't it pay off, boy! Math is one of those harsh friends who never leave you when the going gets tough. And if you need some help, let me know. I certainly don't have all the answers but we can try figure out stuff together while making (healthy!) mistakes. Oh, and we laugh about it! Seriously.