My Issues with Mathematics

[jason_m]

Hello,

I love mathematics - I enjoy the challenge of solving a difficult problem, performing a difficult computation, etc. However, in a sense I mind math, because I never have a feeling of rock-solid certainty; it is all-to-easy to misplace a decimal, leave out a step, miscarry a digit, etc. And, when doing mathematics, there isn't just one thing that can go wrong, but any number of them... That makes it very hard to check over your answer to make sure that it is correct (because you could still be wrong at any step) - and why I never have that solid feeling of certainty. Proofs are even harder for me for just this reason: how do you know that what you've demonstrated is correct, when you might have left out something out? This is why I'm instead drawn to other fields - like computer science and philosophy. When programming, there is no need to worry about leaving out a comma, because the compiler will catch any and all syntax errors. And, as input is always driven by output, you can almost always catch a run-time error by systematically testing your program. By the same token, one's philosophical abilities are determined by their ability to write. Therefore, in the same vein, one misplaced period or an inessential logic error will not ruin an essay the same way it ruins a mathematical computation. Therefore, I like philosophy for similar reasons. Nonetheless, when you eliminate the 'bookkeeping,' I thoroughly enjoy mathematics - and I can be very good as well. And, also, when you take math and put it purely into words (e.g., in economics), for some reason, I really understand. (This could be the 'crux' of the issue, for reasons I cannot pinpoint...)

Therefore, here is my question: what psychologically would cause this? What could be going on based on modern psychological models that would make it this way for me?

[jason_m]

I was just studying graph theory tonight, and I don't believe it has something to do with my nonverbal mathematical skills - in fact, just the opposite, it would be something verbal. I noticed in doing graph theory that anything that I can simply look at or visualize is incredibly easy, but if you take those images and replace them with words (e.g., theorems, definitions, formulas, etc.), then I can still perform the task, but things become much more slow/sluggish, as if my mind can deal with images in a way it simply can't with words. Perhaps economics is easier for me, because fewer steps are skipped, and so it requires less verbal processing to deal with the information, helping to fill in the verbal gaps that my mind has trouble seeing. (Just a theory...)

[GuavaDrunk]

Maybe you a/ have a mind more suited to applied > pure maths ie: not extremely strong at abstraction and b/ are visual > verbal > numerical.

[Pookie]

I've only ever heard people say they are visual learners or hands on. Never auditory.

[Contra]

I pretty much have the same issue as the OP. Although i also find purely abstract mathematics hard to conceptualize-- and for some reason the conceptualization is important to me. I notice a lot of people who are very good at math don't even worry about understanding it as much as knowing the steps involved. I used to badger my math teachers in high school about why we are doing what we are doing and what each step 'means' I generally found that they usually couldn't answer my questions. They'd just get frustrated.

I also had a stats teacher in college who i did the same thing too. I couldn't seem to understand the material without a lengthy explanation as to what is being quantified and how it might look visually-- sort of putting the stats into philsophical terms, for lack of a better descriptor. She did it flawlessly but I found this method was taking too much of my time even if it worked.

I also find that no matter how much help I get, because the material is taught very mechanistically, I have practically 0 retention for math. No matter how well I understand it at one point, it's like i have amnesia.

My personal answer for this? We just have different brains and different brains/minds find different things cognitively useful. I have never had a pressing question that would have a purely mathematical answer. Because of this I figure i just don't conceptualize it well-- and i certainly won't retain it. Obviously my explanation may not be the same as yours because you enjoy math. so, really, i don't know.

Edit: I'll also add that I feel that uncertainty the OP talks about very acutely when i'm doing math. It's the reason I'd badger my stats teacher. I need to know precisely what I'm trying to measure and how the answer should look for that uncertainty to go away. I mean, how can you know a mistake wasn't made if you don't know what your trying to measure and what a reasonable answer looks like?

Edit2: I've always hated the brain explanation, and I'm still not comfortable with it, because it feels like such a cop-out. I mean, how is abstract math such an issue when i don't struggle in pretty much any other subject? But no, i'm cursed with the material just hitting the windshield of my brain and sliding along the outside.

[jason_m]

Another issue: I love the idea of being a programmer or even actuary, but in the workplace, it seems as if the fun is taken out of the mathematical/logical side. In other words, if the work done is like a computer program, all of the emphasis is on input and output - with almost no focus on the actual processing. This is a big issue for me, because all I essentially bring to the table mathematically is processing power... Ideally, I would do all of my calculations by hand, or write out code with some very intricate logic, and then simply check my answer against the computer/compiler (because I'm also prone to making small computational errors...), but from what I gather, most of the logic is hidden and handled by the computer! As an actuary, I would assume you would essentially feed the information into a program, and it would do all of the calculations for you! Or, as a programmer, you would simply draw out the objects, and then the computer turns them into code. It is definitely about the logic for me, so this is not what I like about mathematics at all.. In any event, I'd love to have some type of tech/actuarial job that is mathematically based, so someone please tell me that I'm not right!

[Jeremy8419]

Try looking into the subtypes of programming.

Problem solving is the start of any programming project, and you have to logically sort out the order processing and structuring of what the programs will be and how they will work. The part where you actually write the program (I.e., knowing how to program) is basically just writing what you did in the previous step down on the computer in a different language. This is why they're called programming languages. Once you're proficient at the language, the chore of programming ceases to be an issue.

Time spent figuring out how to "solve" the equation of turning the input of "I want a program that does..." into the output of "the program did it!" can be large or small, depending on how fast your noggin is. And time is money. People like their equations solved as cheaply as possible.

[jason_m]

Another point: I wonder if it's this way because work is essentially a monetary enterprise. In other words, all of the emphasis (for both employers and employees) is on money. My reasons for going into work are not about money at all, but entirely psychological - about socionics, IQ, learning styles, etc. The workforce has probably neglected the psychological side because of it. Therefore, improving computer programming as a task/job would be entirely about making faster, more cost-efficient programming tools, and not at all about catering to a programmer's psychology. Maybe that's why I don't find those jobs interesting - because they're designed around making money, not about psychological concerns, like what's 'interesting' and what isn't. But that's just my take...

[Jeremy8419]

Another point: I wonder if it's this way because work is essentially a monetary enterprise. In other words, all of the emphasis (for both employers and employees) is on money. My reasons for going into work are not about money at all, but entirely psychological - about socionics, IQ, learning styles, etc. The workforce has probably neglected the psychological side because of it. Therefore, improving computer programming as a task/job would be entirely about making faster, more cost-efficient programming tools, and not at all about catering to a programmer's psychology. Maybe that's why I don't find those jobs psychologically satisfying. But that's just my take...

Well no job caters to employees like that, because that would be the employer working for the employee. The employee's job is to satisfy the customer (the employer), so that the employer can satisfy the external customer, and receive money for it. The employee works by directly creating a product, the employer works by creating a product of efficient producers, and the customer gives them both money, so they can do whatever with it.

No matter what you do in life, you need to supply a product to receive money to exchange for another product you need.

[jason_m]

Another thing about computer programming: I look at programming in school vs. career as follows: imagine you want to become a writer, so just like everyone else, you go to university and study English - because that's usually the route to becoming a working writer. When you get to university, the tests are filled with essentially cut and dry/multiple choice/etc. questions about grammar, spelling, vocabulary, style etc. You might do something like read a passage and describe what it's about, or proofread a text for errors. You might even write an essay, but the topic is clear-cut - there is no room for interpretation. And when you delve deeper, the focus is on essentially linguistics topics - grammar trees, semantics, syntax derivations - that are more complicated, but essentially the same. You love all of this. However, you're worried that real writing is not like this. When you look at the work an author usually produces, there seems to be little focus on grammar, spelling, syntax trees, etc. and a ton of emphasis on theme, plot, creativity, metaphor - none of which was covered in your university classes. Therefore, you're really worried, and not sure you should pursue English as a career.

I have the same issues with computer science. What I learned in university was how to trace code, check for syntax errors, debug programs - and even the deeper theory behind computers - all of which I absolutely loved (and all the work extremely similar in format to the mock English major above). However, I look at the work in industry, and it's not like that. The focus is less on the logic of computing and more on webpage design, systems analysis, network design, software engineering - all very practical topics, in which I am less interested. To me, this difference is essentially due to valuing Ti (relational logic) over Te (practical logic), but I'm not sure.

For the person with the English degree, I realize it might be difficult, but I would strongly suggest not pursuing a career as a writer at all. Instead, that person sounds like they would be an outstanding linguist - whether that means becoming a foreign languages expert, and therefore translating, interpreting etc., where they constantly work with grammar, diction, spelling, syntax, vocabulary, etc. OR pursuing a career in theoretical linguistics, where they can toy with things like grammar trees, semantics, etc. - which they showed some liking towards.

For me, I am like that student, and the problem is that I don't know what the computing equivalent is to foreign languages expert or linguist.

[Hot Scalding Gayser]

Could be a lack of self confidence. Se polr/weak Se. If you double check your answers but you are actually right like every time- then maybe you just need to let it go - but its a good thing you do this because a human being just isn't a calculator. Weakness and emotion will plague even the best of logical thinking types.

Therefore, in the same vein, one misplaced period or an inessential logic error will not ruin an essay the same way it ruins a mathematical computation.

I respectfully disagree- a good philosophy system will strongly take logic into account otherwise you risk treading in the area of fantasy and imagination. You might as well just be some sort of entertainer as opposed to a philosopher. Or, you're just plain wrong- which is even worse. But I think philosophy is bullshit anyway. Honestly, being a philosopher is often times just an excuse to troll people and be an asshole- like k0rpsey proved in that one thread. You can't philosophically argue about much in life to me because its scientifically set in stone.

I really like computer programming too though - its can be like this fun puzzle to get the program to do what you want in your head. What you think is simple is often really complex. The best things in life are both strongly emotional & entertaining and also logical. I love video games with good mechanics, but also with faggy heart and characters I can relate to.

[ouronis]

I agree with you. The practical aspects are immensely boring compared to digging out this nugget of truth that no one's known before, or that at least feels that way. My advice to you is to take what you're doing and go find some place where they need someone like you - where organization sucks, but innovation thrives. That's a kind of place I think a Ti-Ne person does well in. This will lessen the degree of practicality but not eliminate it--best advice I have for that is the usual 'cope with the suck.'

[jason_m]

Maybe you a/ have a mind more suited to applied > pure maths ie: not extremely strong at abstraction and b/ are visual > verbal > numerical.

I've thought about this, and I think you are really onto something... I also think it might have something to do with my skills at maths being more sequential (in comparison with my language skills, which are more abstract/non-sequential). That's one resaon why I believe I am drawn to studying subjects like economics: I find that when studying something mathematical, if steps are skipped or if material is presented out of sequence, then I have a hard time grasping the material... Also, I think that's one reason why I'm not good at abstract mathematics; I can follow almost any proof, but in doing it on my own, I assume you have to be somewhat global, in order to guide how your constructing your answer. You can become easily lost if you're simply doing it one step at a time. With the social sciences and humanities I'm the exact opposite: I just want the overall picture, less any of the detail... But anyway, despite this, you're answer sounds correct as well: the more verbal or visual the subject-matter mathematically, the better I also tend to do...

Jason

[Jeremy8419]

So be a debugger?

[jason_m]

I think this is exactly it: http://thepowerofdyslexia.com/dyscalculia/.

Basic, basic mathematics is sluggish and imprecise; any mathematical skill beyond this is not affected at all - e.g., none of the symptoms here: http://www.aboutdyscalculia.org/symptoms.html.

[Hitta]

The irony is that nothing that a person does in college in terms of math is what a mathematician actually does. Even in applied math the theory matters more than the human calculator. Being able to set up numerical scenarios in order to get the expected result is pretty much the basis of math... not calculating.

[The Reality Denialist]

My issue is usually that is too boxed. While everything should be reduced to a same point but it tries its best to not to show it to you.

Calculus has meaning but not so much rigor. Analysis (= advanced calculus) has very little meaning but it is very rigorous. You need both to understand it more broadly.
Also: linear algebra. First it looks like completely pointless until you encounter vector analysis or differential equations.. or statistics. Courses are too isolated.


Overall I have good understanding of the concepts. It takes a while to get into details...

Which brings to me another issue: I actually created a beautiful universal solution to a problem. Result: 0 points. It worked but the instructor didn't comprehend all my steps. I didn't explained it too well. Wonderful motivation booster... To be honest there were instructors who actually encouraged me for example when I used l'Hospital in totally unexpected place and actually got some thumbs up.

I was once in CS course. They used Java (it kills your brains and your willingness to live with its verbosity). I couldn't handle it and learned Python alongside with Cython (Python and C creole language).

[The Reality Denialist]

I'm not saying that dyscalculia does not exists. I have seen real cases. Sometimes you can actually have huge leaps when you just explain and try together. I have seen people that didn't pass an exam to get very good grades in the next exam. It takes patience from both. I remember one case who couldn't understand numbers bigger than 1 000. It didn't take a long time to get her to understand 1 000 000 and so on.

[Tonatiuh]

I'm not saying that dyscalculia does not exists. I have seen real cases. Sometimes you can actually have huge leaps when you just explain and try together. I have seen people that didn't pass an exam to get very good grades in the next exam. It takes patience from both. I remember one case who couldn't understand numbers bigger than 1 000. It didn't take a long time to get her to understand 1 000 000 and so on.

From your example, I can surmise that you don't really know anything about dyscalculia at all.

Would you in turn answer me this. Why would you pretend to know what you're talking about, or do you really believe that you are correct?

[The Reality Denialist]

How come? I doubt that it is binary like condition.
There are obviously different ways to perceive numbers. For example I don't really like counting using visual method in external images. I might make mistakes in those cases. Still I have no problems understanding numbers.In fact

I said that many times there is some kind of rush getting people through using same methods on everyone and not examining their individual patterns and where to make a work around. There are cases where nothing works.

[chrys]

Math made me happy... well actually not all the time. I was mentally retarded for like most of my life (and still am but have improved in the art of creative bullshit and sloppy but efficient learning ) until high school, I couldn't understand long division at all and still don't know how to do it, failed multiple basic math classes until high school... then the only stuff I knew how to do was shit I basically had to repeat over and over again throughout school anyways, like basic arithmetic, graphing, logic in general... enough to do ok on my SATs apparently But I haven't take a math class since i failed honors pre calc junior year out of complete confusion and disorientation (I caught on to what we were learning way too late for it to do any good ).... so I really can't predict what I'll be able to learn or what I still know. I almost want to learn (pre- level) calculus on my own again just to revisit happy memories of graphing flowers and making squiggly waves. ^^

Though actually I am taking Java classes right now so I may encounter new areas of trouble with mathematical logic.

[Chae]

[Chae]

Past the basics that are necessary to master this world, I never had an incentive. I tried hard to score good grades (the only available practical goal) but without a concrete, rewarding, useful real life application you can't force no Gamma NT to do that abusive nonsense and have fun while doing so




Solve difficult equations? Why?? WHYY! Back then I was already sure that I would not need advanced math in my future job and I never regretted it so I was right about my approach. Most math teachers killed my curiosity for numbers anyway, with their attitude of "Do well or get rekt!", they felt so entitled to force us. That kind of mentality can not be considered teaching anymore, that's control. The atmosphere resembled a prison.

They never even explained the purpose of what they are doing!

Asking them was no good idea either because they had no clue which made me feel like I'm surrounded by a machinery of fools that only do it for the money. The books were just as unemotional as well and I didn't like that, I prefer to be stimulated.

The student is only a reflection of the teacher so what does my rant say about the way they taught math at school? :-)
Long story short I was never passionate about it thanks to my environment, the only thing that saved me was my stubborn ambition to compete, which is a process as sick as the entire educational system. Cooperate > compete.