Re: Can't Understand Math

Not wired. Absolutely not. At the very worst, we have no short term memory. This just takes more physical notes - maybe LOTS of physical notes.

In some cases, we simply cannot be motivated to learn some things. It is not a matter of ability. Just say "plumbing" around me and I will run away very quickly. I do not believe I can't learn some plumbing. I do believe it is very easy to hire a plumber and be done with it. I have no motivation and likely will not.

I doubt you have had sufficiently capable instructors with your well-being in mind. Many professors and tutors have more students than one and the time to spend with the one may not exist. Back in my early college days, I spent a lot of time with a mathphobic. He was afraid and seemingly incapable. I actually spent more time with this one student than my employers in the Math Lab would have wanted. He began to learn. Truth be told, he later switched his major to Mathematics! The right situation, the right person, the right motivation - many things can happen.

Re: Can't Understand Math

Thanks for your answer TKH! I just wish I had someone that could help me learn math; someone that had a lot of patience. I think that folks get frustrated with me because I have a hard time understanding the apparently easiest concepts, such as adding two fractions together. Perhaps I will attempt to find a local tutor that would be willing to teach an old man how understand math. I have a real desire to learn math, but I am not sure that I have the intelligence to do so.

Re: Can't Understand Math

Socrates and Plato, who were much smarter than I, believed anyone was capable of understanding mathematics.

Personally, I think what separates one person from another is the amount of time and assistance they need to come to grips with the subject matter.

Temperament is important too.

Math is not a race or a competition, as long as you are willing to give yourself the time you need and can put it down if you feel frustrated (to return later), and with luck to find someone who can help, you will get there.

Re: Can't Understand Math

Thanks Adam12, I agree that temperament is important, especially when learning new things. I have had a couple of individuals try and teach me basic algebra but they just got frustrated with me (I think I ask too many questions). I found a website called Khan Academy that has some really helpful math videos that seem to dumb it down nicely for people like me. I think if I just keep watching the videos over and over I will eventually begin catching on.

Jim

Re: Can't Understand Math

Quote:

Originally Posted by

**jlpiii** but they just got frustrated with me

Jim

Jim,

That is their problem, not yours. Quite honestly. Teaching is an ability quite independent from mathematical ability. (lol)

PS - try also __TTC__

Re: Can't Understand Math

my guess is that things started to go wrong for you long before high-school. more than likely, in 2nd or 3rd grade, but children are not very likely to be held back a year just because they are struggling with arithmetic.

you're not alone in questioning the validity of negative numbers. as late as the 3rd century AD, Diophantes (sometimes regarded as the father of number theory) regarded the solution to 4x + 20 = 0 as "absurd" (it is negative, if you're wondering). now he was one of the finest mathematicians of his time, so it's not like he was "too slow" to be able to understand the concept.

and fractions are hard. in abstract algebra, many college students are introduced to an imposing topic called "the embedding of an integral domain within a field". and many struggle with it, and i tell you in all sincerity, it is the very same struggle you have with fractions. fractions aren't nice and simple, like good, wholesome "round numbers", they're icky, and messy. you have to factor things and multiply and add, and then factor again, and reduce...it's a lot of work. and if your grasp of addition and multiplication, and prime numbers wasn't razor-sharp to begin with, it's not surprising you have no fondness for them.

i can't say whether or not, at this point, you ought to re-learn these things, but what i CAN say, is that you can, if you wish to. the best place to start is with simple things. the rules that were chosen as the important ones to study, these choices were not made arbitrarily. they were chosen because of their utility. here is a simple example (one i hope isn't too difficult or frightening for you):

for (suitable numbers....i won't get into the technical details of what "suitable" might be...just trust me when i say this encompasses most numbers you'll ever be on a first-name basis with) two numbers a and b:

a+b = b+a.

now, what is the utility of such a rule (which has the tedious to type name of "the commutative law of addition")?

well, for one thing it saves time: if you know what 2+3 is, you don't need to remember what 3+2 is, you can just switch them around. if you learned your sums "by rote" (memorization), this means you only need to remember half the sums. if you have a long list to add together, this also means you can put "the nicer numbers first": if you are adding 100 + 6 + 50 + 4, you can add the 100 and 50 together first, then the 6, then the 4.

now, proving this is true for (number set such-and-such), is perhaps a more difficult task. but if you are willing (for the sake of this discussion) to allow it is more than likely true, surely you can see why it is a helpful rule to know. the other rules of number that are distinguished enough to have names, are of a similar value...they allow certain problems that have come up time and time again (in commerce, construction, mixing stuff, estimating, navigation, and so on) to be solved, with reliable results.

by the way, the Khan Academy videos are really good. they are meant for "everyday people", and his explanations are usually well-paced, and thorough.

one advantage to being older, is that although the rate at which one learns may be slower, the efficiency is usually better. you have years of practical experience to test your intuition against. one drawback, however, is that often, because you have so many acquired ways of looking at things, it is easy to become distracted by all the questions that spring from one simple question. because of this, i recommend you try to learn (if you are inclined to do so) in a quiet, calm place, where you can contemplate in relative peace.

as for negative numbers, here is a way of looking at them that might make more sense to you (if not, no big deal, ok?). i agree that "negative numbers" can seem a bit nonsensical. after all, if i only have 3 sheep, how can you steal 5 of them? so let's agree (for the time being) that numbers are really only positive (or 0). however, we can assign a direction to them (growth or profit is "up", shrinkage, or loss is "down"). now, 3 - 5 in this kind of context makes more sense: it is 3 steps up, then 5 steps down. of course, this is the same as 2 steps down.

now, what we do (and this is purely for notation, so we can keep track of which way is which), is pick one direction and put a "-" in front. it is somewhat arbitrary which direction we choose, but there are certain social conventions which you might want to follow if you plan on communicating your calculations with other people. up is usually positive, down is usually negative. this is more of a convention than anything else...people who live in an upside-down world, would probably do the opposite. but all our numbers (distances, quantities, magnitudes, amounts, whatever you feel happy calling them) are positive things, just like you are hoping they are. -2 is just 2 "in the other direction" it's still a 2, but now we have a way of saying which 2 we mean. it's the 2 you owe me, instead of the 2 i owe you. there's no weird "anti-dollars" floating about, we're still talking about 2 bucks, but it does kind of matter which way the money is flowing, right?

Re: Can't Understand Math

In mathematics you don't understand things. You just get used to them.

-John von Neumann

Re: Can't Understand Math

Hi Deveno, and thanks for putting so much time and thought into your answer. I definitely do want to re-learn math because I have always just felt so dumb about it. I am now using the Khan Academy a little every day to get back into the swing of it. Unfortunately I am learning that I don't understand even basic math (or what the Khan Academy considers Developmental Math) that I had forgotten even existed. For example, I am currently stuck on one video that explains "Simple Equations" and I even feel a little lost with that (he is very good at explaining things; I just think I am questioning too much).

Here is what is confusing to me about "Simple Equations": the given equation is 3x = 15. He goes on to say that you just divide both sides by 3 and that gives you the answer of x = 5. It looks to me like the answer would be 1x = 5 because 3 divided by 3 = 1 (I think). I don't see how 1x can equal 5. Then my next question is do you always divide both sides of an equation by the number on the left side (like in the above equation), or am I missing something here? How would you know which number to divide both sides by?

Don't even get me started on Square Roots; it's like a different language to me.

I remember one of my teachers in high school trying to tell me that I should not question how math works, just use the rules and it will work. I believe that was one of the classes that I failed. I'm still amazed that my college professors let me slide through all those classes for my computer science degree. I just checked my transcript and I somehow passed the following required courses: Intro to Algebra, Intermediate Algebra, College Algebra, and Discrete Structures (whatever that means)! I guess it is true that universities are just in it for the money. I think all of those instructors just felt sorry for me and saw that no matter how hard I tried there was no way I would get it.

I do like your explanation of negative numbers; I have always thought of the "how can you steal 5 sheep if I only have 3" situation and therefore concluded that there can't be negative numbers. I like your "the 2 you owe me, instead of the 2 I owe you" way of looking at it. That helps me to look at negative numbers differently...thank you!

Thanks again for your help and explanations. I will stick to it and keep trying. Maybe I can do it enough to memorize how to do things.

Thanks!

Jim

Re: Can't Understand Math

things like + and * are called operations. the word "operation" derives from the latin "opus" meaning work. in other words, operations "do" something.

now, when something has been "done", to get back to where you were before, you have to "un-do" it.

here's a simple example: say you have a number, you don't know what is (it might be the amount remaining in your bank account, who knows?).

the tradition is to call such an unknown by a letter, usually x. so you make a deposit of $5. you've added 5 to x, so now you have x + 5.

at this point, it may occur to you to check your balance (perhaps online through the bank's web-site). you are told your current balance is $17.

so now we know: x + 5 = 17.

so, now suppose the question in your mind is: well, how much did i have in the account, before i made that deposit? to recover x, we have to "undo"

what was done. what was done? we added $5. to "undo" that, we have to do the "inverse" (which is like a sort of "reverse") thing, in this case, subtract $5.

now, a basic principle of math, is: "equals to equals are equal". what this means, in practical terms, is that if you have an equation; that is, you are saying

two things that look different are really "the same", if you do something to one side of the equation, you have to do the same thing to the other side.

the two sides have to move "in parallel", the two sides of the scale, must balance on the fulcrum of the "=".

so, we do this:

x + 5 - 5 = 17 - 5.

now....something wonderful happens. the two expressions 5 - 5, and 17 - 5, are simple arithmetic, and we can replace then with other numbers we know and love.

what we wind up with is:

x + 0 = 12. and 0 has a very special quality, when it comes to adding. it does absolutely nothing (this quality is called "the law of additive identity", if you really

MUST know). so x + 0 = x. and now, everything is clear: x must be 12. mystery solved, you had $12 in your account, before you made the $5 deposit.

now, there is a DIRECT analogy here with your problem, except that the operation has changed from "addition" to "multiplication".

and the "inverse" of multiplication is "division". so in the equation 3x = 15, what has been "done" to x, is that it has been tripled. to "un-triple"

we "divide into 3 parts" which is what dividing by 3 means. you are quite correct, however, 3x/3 = 1x.

the number 1 has, for multiplication, the same special quality that 0 does for addition, it doesn't change anything. that is, 1x = x.

this is called "the law of multiplicative identity". so when we divide both sides of 3x = 15 by 3, we get: 3x/3 = 15/3.

the left side simplifies to 1x (as you very correctly deduced), and the right side simplifies to 5 (it's a good thing 15 is evenly divisible by 3,

or you would have wandered into the land of the abominable fractions).

and this means x = 1x = 15/3 = 5.

so, how do you know what to "undo"? it depends on what has been "done".

and this is where "negative numbers" and "fractions" start to seem more useful.

if we allow the use of negative numbers, then instead of thinking in terms of "subtraction", we can think in terms of "adding the additive inverse":

that is, instead of subtracting 5, what we are doing is adding -5. by expanding our "number vocabulary", we can turn "adds" and "subtracts"

into all "adds". so, if we have negative numbers to play with, we can say that -5 is the UNIQUE number for which 5 + (-5) = 0 <--- the special magic number for +

similarly, if we have fractions, we can say that 1/5 is the UNIQUE number for which 5*(1/5) = 1 <--- the special magic number for *.

you can perhaps see the advantage of replacing "multiply" and "divides" with just "multiplies" more readily: multiplication is a LOT easier than division.

so, to answer your question: how do you know what to divide by? it's always the number x has been multiplied by. symbolically,

you might see something like this:

if mx = y, then x = y/m.

in english, this is something like: if we have m copies of an amount x, and we know what those m copies amount (or total) to, then our original amount

is an m-th part of the what the m copies amount to. although the english may be easier to conceptualize, you can see it takes up a lot more space.

the math symbols, on the other hand, are very concise, but you have to know what each symbol means, to decipher it. it's like a code, to speed up

the process of calculation.

Re: Can't Understand Math

Quote:

Originally Posted by

**jlpiii** Here is what is confusing to me about "Simple Equations": the given equation is 3x = 15. He goes on to say that you just divide both sides by 3 and that gives you the answer of x = 5. It looks to me like the answer would be 1x = 5 because 3 divided by 3 = 1 (I think). I don't see how 1x can equal 5. Then my next question is do you always divide both sides of an equation by the number on the left side (like in the above equation), or am I missing something here? How would you know which number to divide both sides by?

What you are missing is the meaning:

3x=15

means that x is a number when multipled by 3 gives 15. That is three copies of x sum to 15, or that x is one third of 15. That at least is what it means for positive integers, for other types of numbers we generalise from this.

The rules of manipulation derive from the behaviour of basic arithmetic entities

CB

Re: Can't Understand Math

Deveno, thanks again for taking the time to help with my silly questions! You make it much easier to understand! I can see that it is going to take a lot of work and practice on my part to get a good understanding of math.

Jim

Re: Can't Understand Math

they aren't really silly questions, they are questions of a basic nature. if you want to understand the more complicated things, you have to get a firm grip on the basic things. if something doesn't make sense...go no further! get it clear in your mind the "how" and "why" of it, so that you have a sound foundation to build upon.

i'm just guessing here, but if your education was anything like mine, the basics of addition and multiplication were probably based on memorizing "sums" and "times tables". well, that might give you a certain ability to get by (as long as the numbers involved are small), but by the time you got to algebra, you were probably already treading water.

however, don't get discouraged...it took humanity thousands of years to get to the point where an equation like 10x + 5 = 20 was widely regarded as "easily solved", and centuries more before it was considered "something everyone should know". even "the basic arithmetic entities" as CaptainBlack calls them, have yet to yield to us all their secrets.

i have to say that i feel your high-school teacher was dead wrong. i think everyone should question how math "works". mathematics is one of the few fields of knowledge, where it is possible to justify the rules, because they are not based on empirical observation, but logic itself. some mathematicians have even taken this to an extreme, claiming that math has an existence "more real than reality" (the term for these people is Platonists, after the Greek philosopher Plato). i personally do not subscribe to this view, feeling that mathematics is more "relatively true", in context.

be that as it may, as with almost anything, one of the most important parts of math is this: define your terms. a good definition, and one that you understand, is more helpful than a plethora of meaningless rules. when you get to the point where you think: of COURSE 6 is divisible by 2, it's EVEN, you realize that understanding the meaning of the terminology is much more valuable and useful than overloading your memory with a laundry list of mathematical trivia.

one thing that might help, especially with stuff later on, is to draw pictures, or use coins, or marbles..the idea is to get your eyes involved, to make it visual. the reason behind this, is that we are visually-oriented creatures, our eyes account for the vast majority of the information our brains process. one of my mottos is: something isn't true until i can prove it 2 ways, and one of them should be a picture. math isn't really about numbers, it's about ideas, and these ideas can be expressed in many different ways. the greeks were fond of using a compass and a straight-edge, on these forums there is a poster who uses "balloons" to express ideas about calculus. if you really get stuck on something, send me a message, the only thing in my inbox right now is love-letters from ackbeet.

Re: Can't Understand Math

im 25 and all my life ive struggled with math and hated it, cheat/con exams too, but my majors are CS/information systems and it involves algorithms and unfortunately math. after some time i realized its importance and that inorder to progress in what i like i gotta understand math, then after sometime time i found out that math is not just important in my field, its connected to everything and is at the essence of life.

i blame education systems, they make math very hard to understand and teach it in a way we cant relate to...if i understood its importance earlier i'd be a mathematician by now.