What exactly makes Math hard to some people?

[Thotas]

The most common reason that people suck at math, or at least aren't better at it ...

... and I stress, most -- as has been noted, everyone's different, but as has also been noted, the general lack of ability in the populace is appalling ...

... is that the first thing most people learn about math is that it's hard. The second thing they learn is that it's ugly. Neither is true; although admitedly math isn't easy and does get harder as you go. And most of the excuses I hear are bogus. My friend Bill who "can't do math"? Try watching him play Magic: the Gathering. Artistic types can't do math? Well, when I'm around and those who know me have a math/science/logic question, I'm usually the first place they go. And when they have a need for someone to do a drawing, those same people look to me immediately. Rather than excluding each other, in my case anyway, they inform each other. I use mathematical ideas in my art, and artistic ideas help my appreciation of math.

Unlearn that it's hard, but know that doesn't mean it's easy. In 99% of cases, that will help.

 

[Davek]

Math requires a kind of abstract thinking and some people never seem to learn that "jump" out of the material world into the abstract world of math. They have trouble thinking of numbers as just numbers, and the whole thing seems really pointless and unwieldy to them.

I think this represents the problem quite well.

I remember learning math in school by using very 'rote' like methods. We were never really taught how to even distinguish between material and abstract. We were just told 'this is how it is' and expected to do so.

It wasn't until I started 'rebelling' and thinking outside of the box that I was able to jump over some of the mental blocks I had with math. I learned to come up with my own way of calculating results, and eventually I was able to understand the 'official' methods were really doing the same thing, just more efficiently.

I think that more effort needs to be spent on teaching kids/people how to solve problems in general, not so much on giving them formulae to do so. That will come once they understand how to deal with problems. Sometimes I feel that today's education system is more geared on the final result ie. grades, correct answers, etc. rather than the process used to get there. I feel if the process is taught, eventually the results will follow. Teach them how to solve problems and many problems will get solved. Teach them the solution to one problem and only one problem will get solved.

 

[Umbran]

Math has a way of explaining things in a very definite matter, and getting there it uses a good amount of (what I feel are) assumed facts.

Yes. But you see, you need to begin somewhere. At some point you have to assume that something is true. In mathematics, this is called an axiom. Every formal logical system needs them.

It is entirely possble to choose axioms which lead to maths that don't describe anything in our real world. However, it is easy enough to pick them so that the math does describe what we see. Right now, though, nobody can tell you why those particular axioms are what work for us. They are a given of the Universe. You must simply accept that they are what do the trick.

As an example - at the basis of the number system we use is an axiom which can be stated many different ways, but they all equate to "The empty set exists". There is no way to prove it exists, it must be assumed. The only consolation we can offer is that this assumption leads to the existance fo the computer you type on - not proof that it is true, but reasonably good evidence

I just don't think everything in the universe can be explained off by numbers

Actually, mathematics has proven that. Kurt Godel proved that within any formal logical system with a finite list of axioms, there will exist true statements that cannot be proven within the system. That is equivalent to saying that not everything in the Universe can be explained off by numbers.

Mind you, the fact that this is true does not mean that a great many things in the Universe can be explained of by numbers. Godel's work is not an excuse for intellectual lazyness. The stuff they teach you in trig, geometry and calculus are well within the realm of things that can be proven, no matter how you dislike it

 

[resistor]

One of the biggest problems I see is that people are unable to generalize knowledge. If you know how to solve one problem, you need to be able to use that solution to help your solve a similar problem.

For instance, in my Discrete Math class we learned to solve Chinese Remainder Theorem systems of equations. On the test, the professor asked us to solve system that, instead of having values, had A, B, and C. And half the people, who are all quite intelligent people, freaked out and could not solve it because they could not generalize the solution from what we'd done before to this similar but different problem.

I've seen similar problems in language, another topic generally considered "hard." I have known students who did well in English (even grammar-intensive courses) but could not grasp the concept of a Latin dative (dative = indirect object).

Languages, like math, have to be generalized, and this generalization seems to be something that a lot of people just aren't good at.

 

[Ankh-Morpork Guard]

Yes. But you see, you need to begin somewhere. At some point you have to assume that something is true. In mathematics, this is called an axiom. Every formal logical system needs them.

...and that is the problem with logic! Why can't we all just be crazy and chaotic?

Actually, mathematics has proven that. Kurt Godel proved that within any formal logical system with a finite list of axioms, there will exist true statements that cannot be proven within the system. That is equivalent to saying that not everything in the Universe can be explained off by numbers.

Mind you, the fact that this is true does not mean that a great many things in the Universe can be explained of by numbers. Godel's work is not an excuse for intellectual lazyness. The stuff they teach you in trig, geometry and calculus are well within the realm of things that can be proven, no matter how you dislike it

Curses! That's not fair! Ah well. I can do the important stuff for day to day life, and even though I may not like it, sometimes you just need certain things no matter what. I think I'm just spiteful that I only had one teacher in High School that would at least admit to us that there were far more things going on that 'just because'.

 

[EricNoah]

I'm not bad at math, but I was horrible at taking the timed math tests. Just give me a couple of minutes to think, please! And like many I find subtraction harder than addition.

I think my problems may stem from how I visualize the number line. It's not, shall we say, particularly straight and doesn't lend itself to arithmetic. (See attached). You don't want to know where the negative numbers disappear to. Also this isn't strictly accurate -- I don't see this "head on" -- I'm sort of looking at it at an angle when I'm visualizing numbers.

My dad's numberline visualization is more of a corkscrew with the low numbers in the center.

 

[John Q. Mayhem]

Don't laugh, but I can say without qualification that math has been the single most emotionally painful thing in my life (lucky, I know). I've broken down in tears many times over it, and fairly severely damaged myself in frustration. I don't know what it is about math, because I'm pretty smart; I get borderline genius results on all the intelligence tests I've ever taken, including one administered by a professional psychologist (or psychiatrist, I don't know). I can see that to some people, math is a beautiful and elegant thing, but I just can't see it. I can do low-level problems in my head, and I love proofs, but I just don't get most math. It took me 3 years to finish Algebra 1, and at 17 I still haven't gotten all the way through 2.

 

[Hypersmurf]

I think my problems may stem from how I visualize the number line. It's not, shall we say, particularly straight and doesn't lend itself to arithmetic. (See attached).

...!

-Hyp.

 

[EricNoah]

...!

-Hyp.

Oh it's even worse than that...

In my head the numbers are white and float on an infinite black void. The numbers 1-10 gently slope upwards a bit. I generally look at the numbers at an angle with 1 or 20 right in front of me and numbers 2-10 gently slope upwards to my left.

Also I can rotate my "camera" but only to a limited degree.

Up into the 100s I stop really "seeing" each individual number. My camera "stops" around 100 but I can see big blocks of numbers (each representing a hundred). Then even further in the distance (and turning to the left again) I can see blocks of 1000 ... and then that gets very fuzzy though I can see the spot where a million starts.

Oddly enough, I can then take my camera right to 1 million and see big chunks representing millions and billions. But again if I "look" too close it goes a bit fuzzy.

I know there's gotta be someone else out there who sees numbers in some strange way....

 

[tarchon]

Actually, mathematics has proven that. Kurt Godel proved that within any formal logical system with a finite list of axioms, there will exist true statements that cannot be proven within the system. That is equivalent to saying that not everything in the Universe can be explained off by numbers.

Certain properties have to be present in a formal system for Gödel's Theorem to apply. There are some in which all propositions are decidable.