I can't do math?

Question

So after failing another math test today I have realized that I can't do math on my own. For whatever reason when I get to a test I just can't do math without extra resources. I think this is because when I do homework there are many problems that I just can't do on my own so I need help or I have to look at the answer. Once I get the answer I try to work it out again, and then when I go to review I make sure to go over those problems again. Unfortunately I think I am just learning how to do those problems and not learning how to do that kind of problem.

How do I stop myself from learning like this? I am not meaning to just learn processes to do math homework, I am trying to learn the math but it seems like I am not actually learning anything when I study.

Answer 1

Jordan

Maybe what you need is a coach or a mentor. If you don't believe you can do this yourself, you never will do it. That happens to most of us in Maths at some stage. But if you have someone telling you the answers or "how to do it", you'll never actually learn how to do it for yourself. I used to sit in front of problems until I could solve them (I was bloody-minded in that kind of way). My dad could have helped me if I'd asked, but he knew I had to solve it for myself.

A couple of years ago I helped someone who hadn't even got their basic qualification in maths and had failed two or three times and was on her last chance. Basically I showed her how, if she'd put all her knowledge together, she would have passed every time - how she did know what she needed - nothing but confidence, actually. She flew through well ahead of any marginal grade (and someone who hoped she'd fail, and didn't believe I could help her in the time available, had a problem to deal with).

Answer 2

There are perhaps 4 distinct stages in Mathematical understanding, and a lot of people never get past the first (and indeed may never need to).

The stages are:

1. Applying specific recipes to solve specific problems.
2. Analysing problems to work out which are the right recipes to apply.
3. Analysing recipes to understand why they give the right answer, and proving that they will always work (or alternatively, understanding their limitations).
4. Exploring interesting (often artificial) scenarios to see whether it leads to anything interesting. Sometimes this might lead to the creation of new recipes, or even whole new fields of mathematics.

The point is that if you're limiting yourself to solving specific problems, then you are missing the stuff that really makes maths interesting – and it is no wonder you are having trouble retaining information. Why these things work is far more interesting than what steps you need to follow to reach the solution, and I found it much easier to remember.

Make sure you read around the topic in your text books, and understand the reason for stuff. Work out reasons and connections – make up stuff for the time being if you need to – make up crazy poems or rude acronyms or whatever you need to do to make connections.

A good teacher can help – but so can a site like this...

I remember the relationship between Sine, Cosine and Tangent because of a rude poem about one of my teachers, that the teacher himself taught me. It isn't really something I can post on the internet under my own name, though! I learned it 30 years ago, and I still remember it.

I know other people who simply recite S-O-H C-A-H T-O-A.

Answer 3

There is a book which title is «How to solve it» by G. Polya. It tries to understand the process of solving problems and its typical mental operations. You can download the entire book as pdf.

From that book:

First. You have to understand the problem

Second. Find the connection between the data and the unknown. You may bo obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution

Third. Carry out that plan.

Fourth. Examine the solution obtained.

Answer 4

I believe that all the above answers are quite splendiferous. (I do not use that adjective lightly. :)) I'd like to provide my own input, though it might be slightly Socratic:

What do you care about? Ask yourself this and answer honestly. Does mathematics happen to be one of the things you care about? Or do you find mathematics to be a torturous beast that has no soul? Hyperbole aside, this matters.

It is very easy to be good at math even if you don't care about it. That applies to all subjects, really. Nearly anyone can sit down, go over a text, and learn the associated processes and patterns of it. But, here is my point: It is so much easier if you care about it.

I can't convince you to do this; it is your own task. But let me clarify that caring about an exam grade or your math grades does not necessarily mean you care about math itself. To care about math involves doing things that most people think are crazy or odd. For example, I spend my spare time doing mathematics and felt literally sad when I learned that $\int x^x dx$ cannot be expressed in terms of elementary functions. Do you have this same amount of interest in mathematics? Note that I'm not saying you have to be like this, I'm just saying that it helps immensely to actually care about what you're learning.

Now, I would not say I am near the caliber of the majority of the users here, but this is what I have learned about learning math so far:

• Be patient. You can't learn everything at once. Even Goethe, one of the smartest humans to live, was aware of this fact. (He made a play, Faust, that expresses this fact.) I like to take pointers from people like him.
• Don't lose hope or give up early. I've realized that it's not my intelligence that causes me to be decent (I don't really think I can call myself "good") at mathematics, but rather my perseverance. I literally spent two weeks trying to solve one problem and I failed. But the point isn't that I failed: It's that I tried until I could do no more. I exhausted every thing I could think of and then acknowledged that this problem was simply beyond my current understanding. I like Edison's quote along these lines: "I have not failed. I've just found 10,000 ways that won't work."
• Learn at your own pace. I can't emphasize this enough. I had a really interesting experience a few months ago with a friend. I was showing him how to solve quadratic equations. I tried to show him how to use a general approach and see the inherent process behind why a particular method works. This failed miserably. But, I did learn something: This was beyond his pace. So, instead of using this method, I illustrated it with concrete numbers. Then, I showed him how the general method is underlying these numbers. He had a lot of trouble with the general idea, but he did eventually solve it. Let me tell you, though: This wasn't a stupid person, by any means. He just hadn't learned this yet.
• Don't take your grades too seriously. One of my favorite people in the world and one of my greatest teachers told me this, "It's just a number. You can't reduce a person to a number." This is one of the wisest pieces of advice I have ever heard. But be careful: My teacher here was not saying that grades are irrelevant, he was saying that your grades should not be the Gospel. They shouldn't be definitive concrete that roots you to a particular level. Too many people fall victim to this. I see it everyday, sadly.

Now, let me try my best to give you some specific and exact advice:

• Pinpoint precisely why you fail. I'm not saying you are a failure, or anything to that extent. I'm saying that you, as a human (like us all), fail to some extent. Everyone fails somewhere. What's important is figuring out where, exactly, that you are failing. You cannot fix a problem without knowing what it is. For example, I struggle with English and particularly grammar. It pains me. But, once I realized where I was failing, I did a lot better. I realized, "Wow... My understanding is so elementary and inaccurate that it's no wonder I can't understand what a prepositional phrase is." I realized that, the very base of my understanding was horrible and inaccurate. I also noticed that I was failing because I was trying to put out a fire with an ice cube. My method of learning grammar was inherently lacking: I tried to understand the concepts of grammar based solely on their definitions and how they function, rather than trying to understand them intuitively and inherently by analyzing them in specific sentences. I learned that, to my surprise, a word's function and classification depends entirely on its use in a sentence.
• I looked over a few of your questions and I think your issue is that you've skipped into waters too deep without any way of floating. That is to say, I think your class(es?) have went beyond your mathematical understanding. They are not at a comfortable level. Don't be embarrassed or upset over this: You can fix this. It has already been suggested, but I'd really recommend khanacademy. I recommend taking a week or as long as you need to work past the elementary exercises involving addition, subtraction, division, etc. It is best to do an exercise until you get a streak, which usually tells you to move on. I personally would not focus on the word problems, but that is a choice of preference. If you need help with any of the exercises, there are up to three videos explaining the concept. I find Sal to be impressively great at illustrating complex ideas. (It may help to learn about the concepts you're covering in class by using khanacademy while you work your way up to those concepts as a side project. That may complicate things, but it should help.)
• Consult Wikipedia profusely. This is something that has helped me greatly in some of the most bizarre ways: I learned about Louville's proof involving the thing about integrals like $\int x^x dx$. Now, I in no way am at that level of mathematics to fully understand what Louville was doing, but I get the point he made. (There's a subtle difference between those two: If you fully understand, you can reproduce the result yourself. If you get the point, you can use the result to your advantage literally or as a supplement to how you view other concepts.) P.S. Don't be surprised if Wikipedia makes you feel stupid. It does this to me all the time. There is a profuse learning curve to the mathematics on that site, but you can get bits here and there that make a significant impact on how you understand things. Even one sentence can enlighten you a lot sometimes.

I have wrote you a book that could be even longer (I apologize if I am in any way verbose, but I have written this all in my best attempt to help), but I'd like to end on one final point:

• Participate in the lovely community here. I've been using this site for a few days now and I find that it's one of the most interesting ways to learn about mathematics. Helping other users here is also a great way of enhancing your own understanding. Be careful, however. Do not try to answer a question unless you feel comfortable with what you are submitting. That is, you would put this confidently on an exam if the question came up in school. At the same time, try not to strain the denizens here with too many questions. Try to give as much as you take. Now, I have a feeling this is difficult at your current stage, but try to follow this guideline as much as you can. Hopefully the users here will be understanding about this fact and help you. They seem to be doing that, judging from this question and others. :)

Again, sorry for the book.

EDIT: I now see that I am quite late to answering this question. (I have a horribly bad sense of time. . .) I hope that is not too heavily frowned upon and Jordan actually has a chance to benefit from this.

Answer 5

About your question: I think there is nothing wrong with looking at the answer and asking for help /after/ you've attempted the problem yourself and thought about it extensively. I find that when I do this, and finally see the correct answer (be it calculation or proof), the solution reaally sticks. Unless you're extremely skilled (and clearly skill can only be achieved through a lot of practice), nobody's expecting you to be able to solve all the problems in your textbook on the first try.

As a fellow student, to remedy my weaknesses in a subject, there are usually four things I do.

• I simply solve a lot of problems. If I can't solve a problem, I try my best to understand the solution and the general solution pattern of the problem type. I believe practice makes perfect in mathematics.
• I try my best to ask a lot of questions. Of the lecturer, of my fellow students, basically anyone available. I can't overemphasize the importance of this. If there is something I don't understand, I note it down, and usually approach my lecturer when he has time, so he could explain things to me thoroughly. I prefer private sessions where his attention is focused on me, because I find that when asking questions in class I often get "half an answer" (and understandably so, we need to get on with the material).
• I carefully think what exactly are my difficulties in the subject. Why am I having a hard time understanding, say, multivariable calculus? Is it because the explanations in class were unclear? Maybe my foundation in single-variable calculus is not strong enough? Maybe I just haven't had enough practice?
• I look for supplemental material. Sometimes the way things were explained in class simply aren't enough for me. There are a lot of excellent, free resources online that can enrich my understanding.

Answer 6

I agree with all the above, Math is just a bunch of rules and understanding how to put the rules together to solve the problem. Most rules have to be done in a certain order.

-The thing that makes these rules stick when you do the test is every problem you do write the base equation down. Even write the rule you use for each step in the margin or at the top of the page. This will help commit the rule to your memory so when you take the test you have already written down the "lookup" many times it will be more like hand memory.

Answer 7

@Jordan May I suggest that you stop solving problems altogether? I think that helps a lot. Problem solving might have its advantages late in the career but when beginning I find it to be completely counterproductive especially when it is too much. I think it is much more important to be be able to read the standard mathematics texts first - line by line - make sure you understand every line written in the text. Just doing a hell lot of problems is hardly going to teach any mathematics. It can help to get the subtle points across ONLY if you have first read the text thoroughly. By standard texts I mean things like - lets say Artin for algebra or Apostol for Calculus etc. (I am not sure as to what is your level)

OR

Many good students are known to take the approach of reading the text itself like a problem. They basically read the stuff written between the proofs and then they try to prove the theorems on their own. If they can't only then they might look at the "standard" argument. This can be an exciting way to do stuff unless speed of learning is a concern.