Course choice - bad at arithmetic

[Lord Satin]

Greetings.

I've come with yet another issue which is causing me some distress. So I took everyone's advice and started self-teaching calculus (or at least I started trying... Limits are still confusing). However, my problem doesn't stem there. I decided to review my algebra before year 10 starts in September. What I found is truly an unpleasant discovery. I suck at it. A lot.

I have a great book of mathematical problems. It's made for year 6-9, and yet I can't solve the problems on the first page! I'll be honest, I'm terrible at mental arithmetic. I get lost, I'm slow. Just better off using a calculator for even basic operations.

So here is one problem that I can't solve no matter what I do. I thought I got the negative signs wrong; didn't work. I tried some stuff with the brackets; no luck. It's supposed to equal "6.3" I think, but I keep coming up with answers like 22, 27, 11, or even -5. I've gotten everything but the correct answer.

3.5^2 + 2 * [2.7 - (-0.5 + 0.3 * 0.6)]

I can solve problems similar to this one, but still very inconsistently. I am not forgetting to switch signs inside the bracket, I'm not forgetting to square the 3.5 first, got the order of operations down perfectly. Yet these problems still confuse me. Would anyone know what I might be doing wrong? I do have ADD (I am revolted even just typing that), so lack of focus, perhaps?

I can do linear equations mentally, I can use trig functions, solve quadratics, graph functions, do rational expressions; everything on my level. But I can't do 8*7.

So I suppose I won't be doing applied mathematics? From my abilities (and lack of abilities), do you think pure mathematics could hold a place for me? I enjoy working with abstract numbers... What about physics?

I'm total trash at chess, even though I try really hard to win. Suppose it means I have a short-sighted mind and I can't think properly? IQ of 125, but I don't think that means anything. I feel tired constantly, just totally burned out. So maybe I could attribute my atrocious mathematical abilities to that, but I feel as though that would be a shameless excuse.

TL;DR (and I won't blame you for it):

I'm bad at arithmetic and tend to forget a lot of algebra, I'm terrible at chess and I feel like I'm losing my mind lately. Which course, if and when the time comes, would you recommend? Or is there even any point in trying?

 

[micromass]

You really need to practice these basic mathematics stuff. If you go on to studying mathematics, then you will encounter situations where you are forbidden from using a calculator. And sometimes you will need to do these basic stuff in order to make some simple tests.

Don't say pure or applied math is not for you. That's silly. That's like giving up without really trying.

Focus on these arithmetic stuff right now and keep practising every day. The good news is that it's mainly memorizing that is involved, so if you practice long enough, you will get there. For example, make small cards with time tables, and practice them every day for some time. It might take a while, but you'll know them eventually.

 

[Lord Satin]

Thanks. I really appreciate the answer.

I suppose you're right... It's all in the practice. I've admitted this countless times before, but it's just so much easier to say I'm not mathematics material. But when I do that, I just feel even worse. So I suppose practicing problems every day is the most painless way to go.

You're right. The whole thing with the calculator pretty much ruined the next year of my life. I failed entry exams for the school of my dreams. I got 20/50 points in the maths test because I relied too much on a calculator -> got stuck on very basic problems -> lost confidence -> gave up. So now I'm in a dying engineering school which is losing its prestige by the year.

You know, I'm looking at your signature, and I think I will indeed drop a PM. I could really use some help with that calculus stuff, since my dead engineering school doesn't teach it 'till year 13 (I can't be bothered to wait that long. Since I'm not very good at algebra, I want to give calculus a go before it's too late).

 

[symbolipoint]

Since I'm not very good at algebra, I want to give calculus a go before it's too late).

Learning about Limits and Calculus places strong stress on knowledge of the properties of numbers, or in other words, ALGEBRA SKILL AND KNOWLEDGE - Arithmetic using variables.

...Suppose it means I have a short-sighted mind and I can't think properly? IQ of 125, but I don't think that means anything. I feel tired constantly, just totally burned out. So maybe I could attribute my atrocious mathematical abilities to that, but I feel as though that would be a shameless excuse.

Check your sleeping habits, and that you get enough sleep, or of good quality. Maybe habits with foods interfering? Time for a medical doctor?

I can do linear equations mentally, I can use trig functions, solve quadratics, graph functions, do rational expressions; everything on my level. But I can't do 8*7.

Basic multiplication table facts need to be both understood AND memorized.
Learn to estimate as a way of checking how closely a value is to a numeric expression which you wish to compute.

 

[Lord Satin]

Yes, I believe I should see a doctor. Perhaps a brain tumor. But then again, I am an absolute hypochondriac, so it's probably just bad sleep.

Anyway, I can do 8*7, only it takes me much longer than it should. I never learned to memorize it. And there rests my problem. I don't seem to have very good long-term memory. Suppose that's why I do bad at tests. I can't memorize things, I need to thoroughly study and understand them before I can use them. Maybe this can be fixed with practice. I'm actually really good at estimating the results of maths problems, or so my teacher always told me. I was always a few hundredths away, but it was close enough. Unfortunately, getting the one true answer can prove time consuming.

Thanks for the reply!

 

[symbolipoint]

Yes, I believe I should see a doctor. Perhaps a brain tumor. But then again, I am an absolute hypochondriac, so it's probably just bad sleep.

Anyway, I can do 8*7, only it takes me much longer than it should. I never learned to memorize it. And there rests my problem. I don't seem to have very good long-term memory. Suppose that's why I do bad at tests. I can't memorize things, I need to thoroughly study and understand them before I can use them. Maybe this can be fixed with practice. I'm actually really good at estimating the results of maths problems, or so my teacher always told me. I was always a few hundredths away, but it was close enough. Unfortunately, getting the one true answer can prove time consuming.

Thanks for the reply!

Try daily review and practice. That should help with long-term memory.

Computing accurately can take more time than estimating. You have opportunity for mistakes in either goal; but the idea of estimation is to know approximately what answer to accurately compute, as a way to check the results.

Multiplication Tables:
Maybe you do not always memorize all of the grid for 12 by 12, but you should know most of the table, and you can use your UNDERSTANDING to find what else you need which might not yet be memorized.
8*7, ... within one or two seconds, I recognize "56".
If you have memorized 7*7=49, then you may understand that just ONE MORE of 7 would be what you want.
What then is 49+7?
49+7=49+(10-3)=49+10-3=(49+10)-3=59-3=56, and yes, many of us can do this all in our head; and we might also write the steps on paper, since doing that is not a bad thing.

 

[Lord Satin]

That's how I do it, yes. I set a reference point that I have memorized. For example, I use the squares of numbers to help with the multiplication. If I were to solve 11*12 I'd do 12^4-12=144-12=132. With addition and subtraction, I've unconsciously developed a rather slow but functional system. The simplest way to add 74 and 89 for me is to do 70+80+9+4=163. But that still takes me way too long to do.

Honestly, now that I look at it, the 5+ multiples of 8 and 7 are the only ones I have failed to memorize! 8* anything over 5 and under 8 takes me ages, same for 7, only it's everything over 5 and under 9 except for 7.

These strategies do help, but with bigger numbers, I find that I just get distracted immediately. I need to work on my focus.

I try to practice maths every day with my book. In fact, I find the bizarre problems that require experimentation quite entertaining, but I need to stop straying towards those when I make dumb mistakes in polynomials.

Edit: Maybe my lack of focus could be blamed on the existential depression caused by total boredom I've been slipping into these past few months (summer holidays are long, broken laptop graphics card, and now I can't even do maths anymore). But I don't think so. I've always been bad at revising age-old material.

 

[axmls]

Do you write down every step? Do you rewrite the line every time you calculate a new part of it? For instance, after you've computed the value in those parenthesis, do you rewrite the problem with that value plugged in? It's important not to rush.

 

[Fancypen]

My old math teacher has a website with an amazing Elementary Algebra class on it. It's a proof-based class and will help with linear algebra if you decide to take that class. Anyways, you will be a solving machine if you take the course. Read the PDF > watch the lecture videos (take notes, write down all the axioms) > work the problems in the HW handouts. Don't worry about the tests/quizzes.

 

[Lord Satin]

I'd like to believe that I do, but since the problems have become so 'trivial' (obviously they aren't, since I'm struggling with them), I confess to skipping my rewriting habits sometimes...

Thanks for the tip! I'll be sure to check it out if you have a link!

 

[Fancypen]

I'd like to believe that I do, but since the problems have become so 'trivial' (obviously they aren't, since I'm struggling with them), I confess to skipping my rewriting habits sometimes...

Thanks for the tip! I'll be sure to check it out if you have a link!

http://daabz.com/home.html?coursenid=Z

 

[axmls]

I'd like to believe that I do, but since the problems have become so 'trivial' (obviously they aren't, since I'm struggling with them), I confess to skipping my rewriting habits sometimes...

Thanks for the tip! I'll be sure to check it out if you have a link!

There's no shame in writing down a problem in its full detail and taking your time solving it like that. Getting the right answer is the key.

 

[symbolipoint]

There's no shame in writing down a problem in its full detail and taking your time solving it like that. Getting the right answer is the key.

Actually the key is doing the correct steps. The correct answer depends on doing correct steps. Trying to hold all the steps in one's head is not often good to do.

 

[axmls]

Actually the key is doing the correct steps.

Of course, that the methods used are correct and that the intermediate answers are correct is absolutely necessary, but I meant in the sense that the OP shouldn't really worry about the time it takes to complete a problem provided that they're working it correctly. Of course, at some point speed is necessary, but that should come with good practice.

Remember, practice does not make perfect. Practice makes permanent; so worry about speed after you've practiced enough to consistently get the correct answer.

 

[Lord Satin]

That's great advice from all of you.

In fact, your words changed my point of view completely. Practice makes permanent... I never thought of it that way, and yet it is absolutely true. I'll never forget how to do linear equations, since we did so many in 8th grade. I'll never forget trig functions, since I used them so much. It's all about repetition... A shame, really, since I'm a person who doesn't really like repeating the same step over and over again.

Don't know how much weight these tests hold. I personally don't assign them any. Still, however, it seems that I am what is called an "INTP", whatever that may be. It gives me an excuse and an explanation for my apparent inability to keep up with skill development. At least I know it isn't a mental disorder.

 

[Fancypen]

Actually the key is doing the correct steps. The correct answer depends on doing correct steps. Trying to hold all the steps in one's head is not often good to do.

I agree with this too, but just keep in mind there is usually more than one way to solve a problem, thus different correct steps. Answers are cheap, is what my calc professor used to say everyday. Understanding is key.

However, it's not a waste of time to copy a problem already solved, if you use it as a guild to understanding. It's okay to have your hand held, especially with math!

 

[symbolipoint]

Of course, that the methods used are correct and that the intermediate answers are correct is absolutely necessary, but I meant in the sense that the OP shouldn't really worry about the time it takes to complete a problem provided that they're working it correctly. Of course, at some point speed is necessary, but that should come with good practice.

Remember, practice does not make perfect. Practice makes permanent; so worry about speed after you've practiced enough to consistently get the correct answer.

TWO Keys are finding correct steps, and practice. Correct answer is the goal. Regardless how each of these is classified, all of them are important.