I dread mathematics, and I believe it’s because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the epitome of evil. She would take any opportunity to yell and scream at me when I struggled to comprehend the problems given. She approached the kids in my class as if their struggling wasn’t a result of a misunderstanding, but rather from a lack of discipline, one that she could solve by being some sort of mathematics drill sergeant. This was when I was a small child, which obviously left an impression on my mind that probably wouldn’t have existed had I been older.
Now that I am older, however, I need mathematics. I also have a growing curiosity and interest for it. Right now, I am planning to move out of my parent’s house and live elsewhere. However, I have a fear in the back of my mind that my understanding of mathematics is not sufficient enough to do all of this; to handle a job; to handle expenses; to handle day-to-day life. Even the idea of becoming a cashier and having to handle money frightens me into avoiding those jobs; which leaves me (having no formal education) with virtually no options for employment. It’s pretty intimidating. I seem to have some problem grasping even the simplest mathematic questions. Come up to me and ask me “What’s 8 + 6?” and my mind wanders for the answer as if blindfolded. I would probably resort to sticking my hands behind my back and counting it off on my fingers or counting one at a time in my head. This just doesn’t seem normal.
I want to conquer my fear of mathematics and educate myself. I want to approach the field as an absolute beginner, and by that, I mean go back to the very basics and work my way up, no matter how reassured I am of my abilities at times. I know it’s impossible to conquer the entire mathematic field, but I want to conquer what is necessary and then some. I need the bare minimum, though I want a sufficient understanding. Are there any approaches or, what I am specifically requesting, books or courses, that would allow me to to teach myself in such a manner?
Sorry for the history lesson and/or if this is not a legitimate question.
This is a difficult question to answer, mainly because any advice must be very personal to be useful for you. I’ll try anyway.
Before learning mathematics, one has to learn how to learn mathematics.
Concerning the contemporary school system, it simply does not do a good job at what it is supposed to do. The range of children who learn successfully from it, or rather in spite of it, is quite narrow. You simply fell through the cracks, as many others, but that does need to have any relation to your general ability to learn mathematics. (I once instructed someone who taught himself programming after dropping out of college. He was very capabable, though he lacked methods to learn efficiently.) You are simply outside the way too narrow scope of the school system.
Still, the best advice for learning mathematics is to find a good teacher, but these are very hard to come by, so that this advice may be useless. (That’s basically the same advice as for learning to play the piano.)
Then, there is the issue that school does not even teach proper mathematics, only some nonsense that they label “mathematics” but which is better described as “rote arithmetics”.
Two of the sins of the rote arithmetics as taught in school are the notions that 1) every problem has a definite answer and 2) that you should be able to come up with that answer instantly or you’re stupid. Both are wrong. The book Thinking Mathematically dispels these myths and presents a proper way to learn mathematics. However, note that learning how to learn mathematics from a book is quite difficult. It is easy to miss the point, for instance by not doing the exercises. A good teacher would be preferable.
That said, “simple” questions like “what is 8+6” are also a matter of rote learning. This is something that can be learned in the school system at least, but again, it’s equally easy to pass the school system and never learn how to do rote learning properly. Learning a foreign language, in particular vocabulary, is usually a good way to exercise rote learning.
Another sin of school teaching is 3) the notion that learning is no fun. It baffles me how the key ingredient to learning, fun, is entirely absent from the school system. (I don’t know any mathematician who is doing mathematics for reasons other than that he/she loves it and that it’s a lot of fun.) Fortunately, since you are motivated to learn mathematics by yourself, this should be no problem for you. Every moment of understanding is a tremendous amount of fun, and if you have enough of these moments in the beginning, you’ll be hooked for life.
Concerning the process of learning, there is another problem that might or might not apply to you, namely the issue of genuine medical conditions that can inhibit learning. (“Inability to concentrate”, undiagnosed food allergies, …) However, given all the things above that can go wrong before that, I’m hesitant to put blame on medical conditions. Still, it may be worth keeping in mind, though personally, I’m not convinced that current treatment options actually help (and don’t just accidentally fix some of the 3 problems mentioned above). In case you have a medical condition that can be fixed, fix it, otherwise you’re kinda screwed anyway, though not necessarily when it comes to learning mathematics.
After these general but very important considerations of the process of learning itself, there is the problem of finding good materials for the actual mathematics. Fortunately, this is a much easier problem, largely solved by the videos from the KhanAcademy.