Again and again, I find that the trickiest thing in getting a handle on math, be it elementary foundations or calculus, is getting an handle on the language. Most of us don't talk about inverse variations, derivatives, summations, or reciprocals on a regular basis. Or do we? Actually, we do! We just don't use those words. But math books aren't written in those words, so often what we need is a math translator.
Most people think that a teacher's job is to present new material to you. After ten years as a teacher, I have come to agree with a line of thought that says that each one of us already possess the knowledge and skills; a good teacher is one who can help students realize what they already know. That light bulb moment when suddenly an idea makes sense to you is really just your brain going, "Oh! I knew that!"
When I sit down with a new student, I spend some time trying to figure out how they think, what they connect with, what they know they already know. I make analogies and tell stories and draw pictures to take an idea the student thinks they don't understand and help them see how it actually is an old familiar friend. All those words that throw most of us off when we look at math problems, we don't need to be scared of them! We just need to make friends with them, to see that these big words are really just simple ideas we already know in disguise. Just in time for Halloween.
Fractions, too! I used to start sweating when I saw fractions -- like when my mom told me I had to clean my room! Ah, so messy! I didn't want to deal with it. So instead, I told myself that I was just a messy person. Or I told myself I was just bad at math. But that was a lie to get myself off the hook. It was easier to put myself down than to do the work I didn't want to do. Or was it?!?! All those years of fighting, avoiding, and feeling stupid just so I didn't have to deal with something that intimidated me. It was years later when I learned the secret: simply doing one step at a time. Just fold a shirt; that's not so hard. Put the book on the bookshelf; I can do that. Just divide by seven; not really so bad.