Thread: What is math to you?

I have always hated math because I don’t understand it. The other day I expressed to my sister I was worried that my trouble with mathematical concepts would eventually lead to trouble in understanding scientific concepts. In an effort to perceive any upcoming difficulties I may encounter, I started thinking about how it is that I grasp concepts in general. Upon reviewing my understanding of the universe I came to the conclusion that there is no room, no detectable bit that is missing from my understanding. Although I also understand that I wouldn’t notice whether or not I’m missing something if I had never known it to begin with….

Basically I want to how math is involved in your understanding of concepts. Is there something I’m missing in not understanding math?

Originally Posted by yickahey

Upon reviewing my understanding of the universe I came to the conclusion that there is no room, no detectable bit that is missing from my understanding.

Always good to start off with a display of modest self-deprecation.
Although I do wonder how, if there is no bit missing from your understanding, you also manage to claim "I don’t understand [maths]".

Basically I want to how math is involved in your understanding of concepts.

That would depend on what you mean by "understanding a concept". If it simply means you grasp the gist of it, then fine. But that's where your "understanding" comes to a halt.

Is there something I’m missing in not understanding math?

Yep. By not understanding the maths you lose the opportunity to grasp fully the concepts, and how it can be applied and explored.
Maths is a tool, probably the single most useful one the human race has in its possession.

Not understanding maths while claiming you understand the concepts in science is like claiming you understand driving and how a car works without ever having driven one or learnt what actually happens in an engine, or how to figure out how to design one.
"Well yeah, you turn the engine on and that turns the wheels and the car goes" - you might as well say "it's magic" for all the understanding you get from it.
Similarly, grasping the concepts of science without learning any of the maths provides no explanation of how those concepts are arrived at - they might as well be "magic".

And, maths, in and of itself, can be "fun". Exploring numbers and their properties can be quite fascinating.

Originally Posted by yickahey

I have always hated math because I don’t understand it. The other day I expressed to my sister I was worried that my trouble with mathematical concepts would eventually lead to trouble in understanding scientific concepts. In an effort to perceive any upcoming difficulties I may encounter, I started thinking about how it is that I grasp concepts in general. Upon reviewing my understanding of the universe I came to the conclusion that there is no room, no detectable bit that is missing from my understanding. Although I also understand that I wouldn’t notice whether or not I’m missing something if I had never known it to begin with….

Basically I want to how math is involved in your understanding of concepts. Is there something I’m missing in not understanding math?

Yes, you are missing a lot. As a simple example, without math you would understand gravitation as something like "what goes up must come down" or some simplistic rule like that. This may be good enough for your purpose, but it won't help you to understand how high something will go up, how fast it will come down, how the planets orbit the sun, and things of that nature.

Can you tell what the problem that you have with mathematics is? As a stab in the dark, do you understand the text but have trouble with word problems?

By the way I’m new to this so I don’t understand how to use the quote button…
Thank you for your reply. I feared that that sentence would come off as arrogance, but I didn’t mean it in that way. I meant so far as my senses could tell me (obviously I don’t understand the entire universe lol).

I see your point when you say that’s where your understanding comes to a halt. “By not understanding the maths you lose the opportunity to grasp fully the concepts, and how it can be applied and explored.”
Yet I still cannot picture what the world must look like through your eyes (assuming that you do easily grasp mathematical concepts). So far I have not hit a “wall” of understanding because, well I’m only still in high school. The concepts we have explored thus far in chemistry haven’t dealt with math greatly and I feel as though I’ve been able to understand the material thoroughly. I don’t know…

I think of mathematics first as a language which describes our observations of nature, and second as a tool to further our understanding of those observations, or even predict future or past observations.

Just like I use the English word love. I have a feeling, and I call it love. Then I can use the word love combined with it's meaning to record and explore things related to love.

Mathematics, like anything, takes time. It seems to me that qualities such as clear thinking (seeing things as they are rather than interpreted) and the ability to hold onto abstractions (a kind of concentration maybe) are useful. In the end however, exposure and practice are essential (for most). Imagine how long it took scientists to come to the mathematics we have today. As a student of the subject you must attempt to grasp all of this knowledge in but a single lifetime. If you try to reinvent everything it won't work. And if you are unsatisfied after only a short time (under ten years I'd say) it also won't work.

Think about it. You line up ten pencils and you don't even have to think about it being ten pencils, you just know. You're buying three six-packs of beer, and you barely have to think about it to conclude that you have eighteen beers. After a number of years you will look at a graph and without thinking that graph will not only represent a mathematical equation, but it will have meaning. Before you know it you are dinking around with electron microscopes and leaving notes of scribbled numbers and symbols for your research partner who comes in on Tuesday.

It takes time.

I would imagine it is more likely that you have not understood mathematics because you have hated it, rather than the opposite. I had the reverse phenomena. I hated literature and therefore was a slow reader, had an atrophied imagination, and a limited vocabulary. Now I have a degree in the literature of a non-native language. It just takes time and effort.

Can you think of another reason for hating something, besides no understanding it? Are you active in your studies? By that I mean, do you expect the concepts to come to you passively or do you actively practice them? Usually a healthy combination of both methods works well. Have you spent much time studying? This can be a difficult question because it is highly relative. Do you want to understand mathematics? Why?

Please feel free to tell me if my words come off as somewhat patronising, for it is not my intent.

Originally Posted by yickahey

I meant so far as my senses could tell me

There's another problem looming ahead of you then. Our senses are highly limited and, generally, a poor guide to seeing how the universe works. Although, as should be obvious, they're reasonably accurate for day to day life.
A favourite quote of mine is "Unfortunately, as will become evident later, common sense is often a poor guide to the real world" - Peter Coveney & Roger Highfield, The Arrow Of Time.

well I’m only still in high school.

In which case you have plenty of time.

Thank you for your response.
My problem with math seems to be that I cannot build upon my present understandings. I’m an online high school student, so I teach myself the material. I can understand it and get 100% on the quiz but by the time the later lessons come around I can’t seem to draw upon the earlier lessons to help with my understanding. And after an entire summer break…for get about it, I’ve forgotten everything I’ve learned. Currently I’m in algebra 2

So I’m not sure where the problem lies. What I can tell you is that I understand balance equations. I like doing it because I know what the purpose is. I’m not good with remembering formulas or the steps to solving specific types of problems.

Often it feels like it’s on the tip of my tongue. When I’m working with a problem where the first step is to use the distributive property. So I take A²(3+4) and make it 3A² + 4A². I can’t truly see and understand it. I know that it works our but I don’t know how. It has no texture to it, I can’t picture it.

Or even in simpler situations the other day I was trying to finger out what year someone was born. In my mind I pictured a number line with all the dates. As I was scrolling down the number line I kept losing my place, I couldn’t keep the figures in my head.

I don’t know how well of a picture of my abilities or disabilities this has drawn for you but I did my best. Thank you for your response.

Time! It's time and practice. Keeping things in your head is about concentration. It's a matter of practice. You're not disabled, or missing anything (as far as I can tell). Just go with it, and work at it. Review. 子曰：學而時習不亦說乎？ Confucius say: to study and review periodically, is this not enjoyable?

Originally Posted by yickahey

Thank you for your response.
My problem with math seems to be that I cannot build upon my present understandings. I’m an online high school student, so I teach myself the material. I can understand it and get 100% on the quiz but by the time the later lessons come around I can’t seem to draw upon the earlier lessons to help with my understanding. And after an entire summer break…for get about it, I’ve forgotten everything I’ve learned. Currently I’m in algebra 2

So I’m not sure where the problem lies. What I can tell you is that I understand balance equations. I like doing it because I know what the purpose is. I’m not good with remembering formulas or the steps to solving specific types of problems.

Well, there are two parts of learning and using math. The hardest part actually is learning what to do and especially why to do particular things in the first place. You seem to be doing this part well. The second part is that you don't want to have to reconstruct everything you use every time you use it. That takes too long and is darn annoying to you, so you have to remember formulas and techniques that you are going to reuse. There are three techniques that I have found useful in doing this. The first technique is just to work several examples of each principle until you don't have to think much about what comes next. Boring but essential. The second technique is to write an outline of each section of the material on your own. Put down the usable results in a reasonably logical order without all the material that is just there to help you learn it in the first place. Then review your outline periodically so that it stays in memory. No matter how well you know something, it will disappear if you never think about it again. The third technique is a branch of the second. I like to write down on one side of a sheet of paper a label for each thing I need to remember, and write down on the other side the statement or formula itself. Then for a few days I run through trying to reproduce the back of the sheet while looking only at the front. I'll write the formula or whatever that I am trying to remember if I need to, but eventually I can simply visualize it mentally. After I can do this, I'll check through it once every few days, and eventually get to once a month or so. It doesn't take that long after the beginning, because everything comes to mind quickly.

Originally Posted by yickahey

Often it feels like it’s on the tip of my tongue. When I’m working with a problem where the first step is to use the distributive property. So I take A²(3+4) and make it 3A² + 4A². I can’t truly see and understand it. I know that it works our but I don’t know how. It has no texture to it, I can’t picture it.

Not everyone thinks alike, but I do think pictures are important. They certainly do for me. All I can do here is to give you a sample of making a connection for the distributive property and hope it gives you an idea of what to do, which may be different in detail from what works for others. The idea is to make a connection with things you find obvious, so you can have confidence in the new principle.

Here I would make A² a number, since interpreting numbers is more familiar. I want that number to be different from 3 and 4 so that I can see what it is, and the next square is 9. So I want to see that

9*(3+4) is 3*9 + 4*9

Now I know that 9*(3+4)= 9*7 since 3+4=7, so 9*(3+4)=9*7=63
I also know that 3*9+4*9 = 27 + 36 = 63. OK!

If I really wanted to, I could go back to 9*(3+4) is 9 copies of three + four, so it is


1: xxx + xxxx = xxxxxxx = 7 x's
2: xxx + xxxx = xxxxxxx = 7 x's
3: xxx + xxxx = xxxxxxx = 7 x's
4: xxx + xxxx = xxxxxxx = 7 x's
5: xxx + xxxx = xxxxxxx = 7 x's
6: xxx + xxxx = xxxxxxx = 7 x's
7: xxx + xxxx = xxxxxxx = 7 x's
8: xxx + xxxx = xxxxxxx = 7 x's
9: xxx + xxxx = xxxxxxx = 7 x's
---------------------
63 x's in all; it doesn't matter which order I count them in.

Sometimes in a difficult problem, going that far back helps.

Originally Posted by yickahey

Or even in simpler situations the other day I was trying to finger out what year someone was born. In my mind I pictured a number line with all the dates. As I was scrolling down the number line I kept losing my place, I couldn’t keep the figures in my head.

I don't know all the details here, but in general if you can't remember something long enough to finish using it, you simply write it down. However, I don't see enough of what was going on here that you needed to use a number line instead of subtracting. At a minimum, in setting up an algebra problem you write down in an organized list all the numbers you know, all the quantities you want, and the formulas that apply to your problem. When the number of knowns equals the number of equations, you are normally ready to manipulate symbols.

Originally Posted by yickahey

I don’t know how well of a picture of my abilities or disabilities this has drawn for you but I did my best. Thank you for your response.

From what you have said, I think I do know that your abilities outnumber your disabilities. Learning online isn't all that easy. In particular I would recommend that you ask questions here [or PM me if you prefer] when you hit something you don't understand. On exercises that give you trouble, ask for hints, not answers. Hints do you more good.

I'm a maths tutor for students at your level.

Your big problem is that you think understanding what you learn, when you learn it, is enough. It isn't. You'll do much better if you treat learning maths the same as learning a sport. When your coach teaches you the right grip for serving a tennis ball, you don't nod your head and say, thanks I've got it now. You practice it with the coach at that session until they're satisfied you're on your way. Then you go home and you practice. Over and over and over again. More importantly, when you next see your coach, they'll check whether you've really got it - but they will never leave the topic alone. You have to demonstrate your skill with that technique every single time you play. The idea being that your skill and its reinforcement will mean that you can more often hit the ball just a little bit harder, just a little bit more accurately into that unreachable corner.

And for maths. Don't treat your education like a backpack in which you accumulate stuff. Even if it was a backpack everything in it has to come out to be used regularly and carefully maintained for future use. You don't notice yourself doing that with literacy and comprehension and vocabulary skills because you read all kinds of stuff all the time. With maths you have to do it deliberately, and it will feel like often.

Taking that algebra example you gave, that just shows me that you're not doing enough examples. It's a little bit like learning times tables. You learn them by heart and you use them just like a language. By that I mean that when you know, in your bones, that seven 8s are fifty six, you will see or feel the meaning of those linkages even though there's nothing in the words or symbols themselves to tell you that. (It's exactly like knowing that go, went, gone are related versions of the same concept despite there being little to no signal in the sounds of the words that they mean the "same" thing.) But even though you can use these relationships fluently in multiplication, division and fraction calculations, it doesn't necessarily follow that you fully understand the "meaning" of multiplication. Most of us get that understanding just from frequent use. If it doesn't come naturally, it's very little trouble for a book or a teacher to give us the final push to understanding if we can handle the numbers and processes fluently.

Find another online maths course or even one for teachers that offers free worksheets. And just do lots and lots and lots of practice. If I were teaching you algebra at the level you're talking about, I'd expect you to do a couple of 8 to 10 question worksheets (among lots of other things) in a one hour session. I'd then expect you to do 20 to 40 graduated difficulty exercises of the same technique for homework before our next session. And then we'd do it all again. I might add in another skill or another level of difficulty if it was going well - but probably not if you're telling me this is giving you grief. Everybody has occasional sticking points and there's no option but to work through them. I'd be more likely to give you additional "brain break" exercises in another topic where you felt more confident, maintaining and building existing skills while this newer skill takes more time to get established.

Your only option is more and more practice. You might like to look for second hand textbooks where you can be sure that different writers will have different approaches to describing concepts and to setting graduated difficulty for exercises.

Just practice.

Originally Posted by yickahey

The concepts we have explored thus far in chemistry haven’t dealt with math greatly and I feel as though I’ve been able to understand the material thoroughly. I don’t know…

I guess at this stage, you don't need much more than addition to check that the two sides of a chemical equation balance. If you go on to study chemistry more seriously, you will find it gets much more mathematical.

I was not too good at maths at school (I like to blame the teachers but ...) and as a result, hated it. When I went back to college and then university after working for a few years, I found it much easier - perhaps because I had been applying it in the meantime (or maybe I had better teachers). As an engineer, I could not do my job without maths.

Thanks for your help! Your explanation of distributive property made a lot of since, I feel like I will do much better in instances where I have to use it.

I’m glad I started this thread because everyone has been so nice and helpful. You’ve inspired me to change my relationship with mathematics. It’s based on acquired skill, not recalling facts. I’ve always treated it as if I learn it once, then I never go back to it. But it’s something I have to work on in order to build upon my understanding. I guess my limitations with math are a result of the way I go about it rather than a cognitive disability. Thanks

thank you for the advice. i shall take it!

Festina lente. Make haste, slowly.

You're bound to run into struggles no matter what path you take. These questions help you to build your arsenal of tools, but do not be disheartened if again you feel it's not working. Take your time, and take enjoyment in your frustrations. It is my experience that frustrations come when we are really learning something. Some people don't pull through the frustration.

Math to me helps model phenomena. I wouldn't have understood some physics problems without the use of calculus to model the situation to an understandable level. First problem that comes to mind is based on the graph, "tell at which points the particle is moving the fastest or slowest," and you're given some equations to work with or numbers on the graph. Using basic principles actually helped me a lot. But I am still not exactly the best when it comes to math, but I can do moderately well by wokring many problems. I found by doing that (working problems) I could understand it conceptually via graphing etc...

Some other problems I found in chemistry (freshman level) were easier to complete given the person knew how to use integral calculus. But I also had problems in mathematics, like you, in terms of conception. But if you work many problems with the steps first you can become more proficient with the problems and it becomes a bit better conceptually. It can be frustrating at first but like most hard things, usually only a few will do it because they try.

To me math is the keys to science and many practical things in life.

It's somewhat interesting when I compare myself to other teacher candidates. The math teachers, often have an inherent love of math and try with varying degrees of success to transfer that love of math to their students. My approach is to integrate it with science, carpentry and practical things in life. I've get certified to teach math, but it's not my first love--any more than that the huge red roll around tool box in my garage.

I struggle with math. I can use basic algebra to rearrange formulas and such, but straight mathematics without practical application really give me a hard time. My hardest classes in college weren't organic chemistry or senior level geology courses, they were the basic intro to algebra and trig and calculus. People think that if you're good at something like chemistry, you must be good at math as well. To be completely honest, you can struggle with math and still be involved in the sciences in a meaningful way.

I am numerically challenged.
I have never been good in working with actual numbers, and as a result for the first few years in school I was absolutely brutal in maths. I hated it, because I never seemed to get anything right, and long division and percentages was just sooooooo boring. That all changed radically when we hit algebra - somehow all those x's and y's really seemed to resonate with me, and I excelled at it ( while still getting basic numbers wrong ). I started to teach myself advanced topics from library textbooks; by the tenth grade I knew how to differentiate and integrate - by my senior year I was self-studying tensors and GR. Not that any of that came easy to me, oh no, but now I had an interest in it, and that made all the difference. The rest is simply practice and perseverance. I would not, however, consider myself an especially gifted mathematician - not even close, in fact. It is simply a tool, a language, to me.
And to this very day I like maths, but hate numbers...talk about paradoxes !!

Understanding calculus has certainly helped me understand scientific concepts better. Once you can train your mind to think mathematically (which isn't as difficult as you might think), your understanding of scientific concepts will increase. It just trains your brain to dissect things logically. Math is pure logic and anyone can understand it. That's the beauty of it. I would definitely recommend learning algebra and calculus. You could also learn statistics, if you want to train your mind to think more counterintuitively. Khanacademy.org is an excellent website that has free video lectures to watch and the narrator describes mathematical concepts clearer than just about anyone I've heard. Don't misunderstand me, though. You'll be able to understand a lot about science without knowing math, but if you want to train your brain to really analyze what you're reading, learning math definitely helps. At least it does for me.

Oh, and to answer the second part of your question, math is purely logical language to me.

I can think about that movie- planet of the apes (modern version). We humans were given the ability to communicate with one another, either by language or by telepathy. But whats the use of the age old centuries year old reasoning minds when our intelligentsia is of no use if we weren't communicating right in other words shelving ourselves from one another!!! Then we could still be looking like stone age without the need for communication.

intelligentsia

(just felt like saying that)