I do not really understand where I was suppose to learn this kind of stuff. I am always told that my algebra knowledge is the biggest reason I am so bad at math. But I do not understand where I was suppose to learn it. I started math with pre-algebra and I learned basically no algebra in that, just arithmetic. After that was college algebra and I was told constantly that the biggest reason people fail that class is because of a weakness in algebra.
That doesn't make any sense to me, isn't that where I am suppose to learn algebra? Anyways I will have a semester off of math, where is it that I can actually learn algebra? All the math books before pre-algebra are incredibly basic and problems I can mostly do in my head. Where do I learn those incredibly complex trick, formulas to memorize (pascal's triangle stuff, quadratic formula and all that other stuff?
It just seems like people expect you to either be good at algebra or be bad at it.
Best Answer
Key to learning algebra? I think it depends on what you mean by algebra. To me, algebra is just arithmetic where we're allowed to use symbols that aren't exactly numbers (variables), or represent numbers that are difficult to write (e.g. $\sqrt{2}$ and $\pi$.) I say "just arithmetic" because all of the old operations and distribution works exactly the same way. I have found many students struggle because they never even mastered the basic arithmetic rules. I think if they did, doing it with $x$'s would make no difference.
Incredibly basic exercises I obviously have no idea what's going on in your head about these exercises, maybe you're exactly right in all or some of your thinking about algebra problems. The problem with this is that this isn't useful to anyone unless you can write it down.
I'm not saying you are this type of student, but I have seen some students fall to a sort of overconfidence where they think they understand something, but it's clear they don't, because their work and answers are completely wrong. The only antidote for this is practice and validation of your answers. The clearer your written solutions are, the clearer it will be in your mind.
Memorization Memorization is an extremely blunt tool, and yet many students treat it as their main weapon. Memorization is too often used to avoid or delay thinking about things that really ought to be understood. My wife would say I have an awful memory, so I can probably attest that math is not so much about memory.
Certainly there are some things that need to be memorized, and there is no sense in spending time "understanding" them, like adding and multiplying single digit numbers. The quadratic formula on the other hand is a borderline case that is good to have memorized, but it's also good to understand where it comes from (completing the square on a quadratic equation!).
Contrary to popular belief, we use mathematics to simplify problems. I would casually argue that a core tenet of math is: "You just find the right way to look at it (or represent it) so it becomes simple".
Edit Dejan Govc inspired another thought with his comment about a student being uncomfortable with what exactly a variable is. This is true: it makes people uncomfortable when something new/ambiguous is introduced, like this. This is because the student hasn't "made the jump" to that new way of thinking yet. Being able to make these jumps is important, because as they learn to abstract further, they will encounter this feeling of disorientation all the time. The best thing to do is simply admit to yourself that you don't get it totally, but trust that through practice you will finally gain a feel for the idea.