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Discussion Starter #1 (Edited)
Can Do, But Can't Understand Math

Help! I sort of recently realized something. I can do math and understand what I am supposed to do. For example if somebody says find 4 squared, then I know that means do 4 by 4. If somebody says something like to divide fractions to this you reverse the first one then multiply becuase this reason. The reasoning tends to just go over my head completely, and sometimes I'll get it like multiple the length of the side of a square by 4 to get perimeter becuase it's the same an all 4 sides. Sometimes someone will explain the reasoning to me, and I'll be like oh yeah that makes sense. Then a day later or something I'll just totally forget it, only to be reminded again. Sometimes I will take in instinctive guess like maybe the you multiply the 2 numbers you're supposed to divide the first number by then divide, it will work. Sometimes they turn out to be right other times not so much. This was okay during elementary for the most part, but now that I'm in high school and want to go to university I might have to take harder courses. I was sick a lot when I was younger, now I'm in a more healthy phase. I have chronic health issues, so I ended up missing a lot of chunks of school in elementary. At about 6th grade I moved to a city where they had teachers for kids at the hospital, but my elementary school in my new city didn't really coordinate well with the hospital teachers. For middle school I started being home schooled because of this, and my teacher at the home school place is good about contacting the hospital teachers. I was kind of lazy in elementary and didn't memorize my times tables. I recited them everyday for a while but probably not long enough. This could be part of it. As far as I know I don't having a any learning disabilities or anything like ADHD. Part of it could also be math anxiety, because I currently feel stressed when I have to do math. Maybe I just need to spend more time studying and be more studious about it, and try harder. Any advice? If you need calfirication feel free to ask, I know this is kinda messy, but I just feel stressed about the whole thing. Thanks.


Sorry another thought. Could this be related to being INFP, I don't nessarily know if it is but someone might bring it up so, I want to include this. Maybe no Ti just Te in a lower rank. Even though I'm INFP I do want to be good at math, so please no your strengths like in other places platitudes. They honestly don't my writing skills are okay but nowhere near worthy of particular notice by anyone. My art is probably better that the average person's but that's because I practice, whereas I'm gonna guess most people spend what less than 30 minutes yearly on artsy stuff. And compared to other artists that are my age it's not that great.
 

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i know exactly how you feel. i went through the same thing. (math anxiety, that's the term for it. *nods* ) i'm... honestly not sure if it's a type thing or not. my mom is an infp and seems to be good at math, and she tells me it's because she can easily "visualize it in patterns" but she has never explained what that means or how, and i just don't get it myself. however she has also said that math is not her strong point, not really. i guess i can see it being an ne thing that makes it harder on us, but i'm not sure exactly.

i used to struggle all the time with the order of operations because each math teacher taught it with different rules each year, and rarely did what they teach match up with what was printed in our math books, so that made it way too hard on me. when i confronted any of them with it, they replied that i just needed to do it how they said to and not any other way, "that was last year, this is this year" and stuff like that. basically they implied that it didn't need to be understood, just done. as you can imagine, this did not help AT ALL. i had one teacher do the order of operations two different ways, showing on the marker board how they each came to different answers. she asked the class, "do you see now how this way is correct and this way is not?" and all the students answered in unison, "yes," and i was the only one saying "no." because she didn't PROVE to me which one was right and which one was wrong, all she proved was that they were different. for all i knew they were both wrong.

i hate to make things complicated for you, but i saw a video not too long ago that explained that the order of operations as it is commonly taught in school is wrong (why am i not surprised?), and they gave very simple, easy to understand explanations why. i don't remember any of them, because math, but i understood it at the time i watched it, and it was revolutionary.

(i think this might be it, i can't load it correctly on my computer to verify but just the title and thumbnail look familiar, so hopefully it works:
)

but yeah, i definitely identify with the feeling of that weird "gut instinct" that you know what you're doing but don't really know why or how, as well as the strange roundabout ways of solving problems. it certainly does nothing to clear up any confusion. my suggestion is that you find a resource that is very simplistic in its explanations and then you MILK THAT RESOURCE FOR ALL ITS WORTH. maybe doing a search for something along the lines of "[field of math] for dummies" might help to start with. if you know somebody (say, someone in the family) who is really good at math, do what you can to learn from that person, and hopefully they're good at teaching. if they're not good at teaching, stop trying to learn from them, or else it will just muddy things up for you even further.

personally, using visual examples helps me a lot. charts, diagrams, those little stackable colored plastic cubes they gave us in the first grade to teach us how to add to ten, that sort of thing.

wish i could be better help than all this, though. :p
 

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I absolutely suck at maths. My doctor told me it was because I was born premature. Premature babies are worse at maths...
:/
But yeah, I can be told something and just forget it later.
I can understand when someone shows me an example.
But the formulas and problem solving things NEVER stay in my brain.
 
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What you describe seems totally normal to me. A lot of people can't understand OR do math, so you seem ahead of the curve already. I think you'll be fine in university... unless you have a burning desire to do something that goes really deep into math?

I think in order to really get the WHY of math, you have to be able to directly visualize it. By that I mean, it's easy to visualize in your head why 10 + 5 = 15 or why 2 x 2 = 4. Like you can literally see the numbers adding or multiplying together. But for most people, it's not easy to do the same kind of visualization when it comes to, like... why the exponents come before multiplication and division in the order of operations. You may know this by heart, but as to why... who knows? I imagine people who are actually mathematicians or physicists can actually SEE in their minds why it would be so.

For me, I'm a little bit of both. Sometimes, I can't for the life of me remember how to just DO some basic math operation. But at other times I can actually understand math things at a deep level. But often I can't. But it's never been a problem... I use math in my grad classes but all you have to do is memorize certain operations/ equations you do all the time, it's not a big deal.
 

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Haha, so, when I went to a math tutor for the SAT, he gave me a pre-test to diagnose where I was getting things wrong. When he came out with the results, he said to me something along the lines of, Well, actually, you don't really seem to struggle with any particular area, but I have no idea how you did most of these problems. It's like you do something that's kind of close but technically completely wrong and most of the time you end up close enough to the right answer anyway. So, um, that's basically my personal experience with math. I scored 100 points higher on the SAT after the tutor and I've taken uni-level courses since then and I've learned that I can do just fine if I really crack down, learn step-by-step, and study hard, buuuuut I can also skate by reasonably relying on some wacky N understanding of things. I actually use a fair amount of basic math - addition, subtraction, division, multiplication - in my job currently, and it's not a big deal. I think my super-math-whiz INTP coworker believes I'm a bit batty, but I guess I am, so that's fine. :)

My thoughts for you are these:

(1) A lot of schools and teachers tend to teach the step-by-step how but not the why, so unless you remember the steps you're out of luck when it comes to deriving it yourself. And INFPs aren't great at remembering lots of little logical details. So especially if you have gaps in your foundational learning, it's not necessarily surprising that you're struggling. My guess is that if you sat down and worked on the foundational learning like the times tables, and then worked to learn the major concepts first, before having to apply the small steps, you'd do a lot better. I would suggest looking into working with a teacher or a tutor, yourself.

On that note, I don't think INFP necessarily determines that you're bad at math, but I do think it inclines you to be less interested in the rote steps of math for no greater purpose. For an NF who doesn't care that much about the how of math in the first place, just learning the step-by-step is not a setup for success. I remember thinking math was really quite boring for most of my schooling and it was only when I got to university that I discovered that it's actually conceptually a cool thing. Push to learn the concepts. You may need to find more resources. Google what you're learning... see what it's used for in the real world and what it means. Learn what you're actually using the steps to do. Learn top-down; learn the framework so you can derive the steps by yourself. I mentioned I use math in my career now - and naturally sometimes I screw the steps up. The reason I can catch it and fix it is that I understand what I'm using the math to do. That's what I think will help you. Understand why you're manipulating the data, what question you're essentially trying to answer. Then the steps will fall intuitively into place - and the math itself will be less of a frightening prospect. Remember it's all just tools to help you. There are other ways to solve problems, but math sometimes is metaphorically the shortest distance between two points. It's there for you... school is, too. Try to remember that when you get anxious about it. The point of learning it is to build you up, not drag you down. If it doesn't work for you, you'll find another way. Which brings me to:

(2) I know someone with a learning disorder who just doesn't grasp certain areas of math - seems mostly to impact him with algebra and understanding variables. As far as I can tell from your OP, that doesn't apply to you, but it does exist. Anyway, he scraped through his final math class in uni with a D and has a happy, successful career. Sounds like you get by well enough that you'll be just fine. If you end up struggling at uni most professors will work with you one-on-one and there is typically a disability office you can coordinate with. Generally they want you to succeed and will help you pass if you demonstrate genuine dedication and perseverance in the subject.
 

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If you can make visual or different rationales for the same, you'll understand the pattern and not just the operation.

Q: 5/2 divide by 1/4
Same as: How many times does 1/4 go into 5, divided by 2
1/4 goes into 1 four times, which goes into 5 five times, divided by 2

The notation
4 x 5 / 2
 
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i used to struggle all the time with the order of operations because each math teacher taught it with different rules each year, and rarely did what they teach match up with what was printed in our math books, so that made it way too hard on me. when i confronted any of them with it, they replied that i just needed to do it how they said to and not any other way, "that was last year, this is this year" and stuff like that. basically they implied that it didn't need to be understood, just done. as you can imagine, this did not help AT ALL. i had one teacher do the order of operations two different ways, showing on the marker board how they each came to different answers. she asked the class, "do you see now how this way is correct and this way is not?" and all the students answered in unison, "yes," and i was the only one saying "no." because she didn't PROVE to me which one was right and which one was wrong, all she proved was that they were different. for all i knew they were both wrong.

i hate to make things complicated for you, but i saw a video not too long ago that explained that the order of operations as it is commonly taught in school is wrong (why am i not surprised?), and they gave very simple, easy to understand explanations why. i don't remember any of them, because math, but i understood it at the time i watched it, and it was revolutionary.

(i think this might be it, i can't load it correctly on my computer to verify but just the title and thumbnail look familiar, so hopefully it works:
I remember being taught at some point during my school years, pa-mu-di-a-su but this actually never was an issue because we were also taught to write division with a horizontal line i.e. as a grouping symbol and not as : or / or what have you. It is in principle possible to write all mathematical symbols as grouping symbols, which would have make things easier in that you'd never have to remember what order to do them. Alternatively you can write them with explicit parenthesis every step of the way for the sake of clarity. Many programmers do this with not explicitly mathematical operators especially in programming languages where you have 57 operators with 16 levels of of precedence. Another way is to write them as post or prefix expressions, in which you do away with parenthesis altogether, you can forget about precedence altogether, and do the entire expression from left to right, or right to left, however such expressions have the drawback of becoming unreadable, especially if they are lengthy. There is a myriad of ways of doing it, and there is no "right way" of doing it - it is like language, there are a myriad of languages and none of them are more right over the other, it's just a way of expressing something, which in this case is a mathematical proposition. Math is not a language though but a science, and just like any science it is also expressed in a language, and P-E-MD-AS is just a feature of the most common language used to express math. To understand it is not to understand anything about math, but to understand a language. That might seem like a disappointing fact to you but there is much utility in having a common language, otherwise we would not be able to understand each other.

I'm sorry to say this but your math teachers screwed up your education, and this seems to be a trend that is getting worse by the year. The only remedy to this, if you have not been lucky to have a good teacher is to take the initiative to study these things on your own until you can figure out what it is that you are doing when you are doing math, or find someone who can help you.

As some have already hinted, the key to understanding math is the ability to visualize mathematical problems. To be good at math you need your right brain to cooperate with your left brain; without the former you lose perspective and just mechanically manipulate symbols without knowing what they mean, and without the latter you are not able to pick apart and find the exact solution to your problem, and often, especially in higher math you are forced to be innovative in finding your solution which requires some intuition.
 

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I'm sorry to say this but your math teachers screwed up your education, and this seems to be a trend that is getting worse by the year. The only remedy to this, if you have not been lucky to have a good teacher is to take the initiative to study these things on your own until you can figure out what it is that you are doing when you are doing math, or find someone who can help you.
hoo, yeah, they sure did, and that wasn't the only thing. and yeah, even during middle/ high school i always figured i would have to rip up some books and websites in my pursuit of getting it all done the right way. i have succeeded well enough in some subjects, but math.... ohhhh math. >_<; that is the one subject that wrecked me the hardest at school, and i still struggle disproportionately to most people of my age or education level. *sigh...* i did also have some really good teachers, and i'm thankful for that.
 

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I don't think it has much to do with your type, I mean, from what I understand INFPs have Te as their inferior process, which is a great function to use when trying to understand and work through math. Not to mention, you have all that Ne and Si there to help you with it. Hell, maybe you could even learn to see value systems as graphs, and use your deep value system to see numbers from a perspective not easily seen by other types?

But, regardless of type, you can totally do whatever you want, as long as you are willing to put in the time and effort. I was in a position similar to yours a while back, and wanted to go to university. I caught up in all my math deficiencies and after a few years I transferred from a junior college to uni. I want to tell you about all of my experiences in the positive and the negative, but honestly those experiences and coming to your own conclusions about school is almost what makes it worth it.

Also, the past isn't helpful in gauging your own potential; your history is known, and set in stone, but your potential is what YOU make of it. All you have to do is apply yourself, and continue to work at it.

Besides, unless you're going for a PhD or an engineering degree, you likely won't need to take any math classes above calculus 1, which is just limits and derivatives. Which, if this is the case, having a general idea of the procedures and roughly what they do should be enough. You wouldn't need to do any serious quantitative reasoning until calculus II, or discrete math. I've taken both of those courses and still struggle to remember all of the concepts I learned in them off the top of my head. However, I don't think the purpose is to have everything memorized, but instead to know how to access the right resources for an effective solution when trying to solve a problem. Even though schooling doesn't treat the material that way.

However, if you're really determined to truly understand the math, you can. Honestly, it's just a matter of spending a lot of time with the material, just like anything else. You have to continually try to see the information for what it is. I honestly didn't feel like I understood anything about math until I took discrete math, because it reveals a lot of the deep, fundamental aspects of the math we are taught, but are never shown when we are younger. It makes a lot more sense after seeing it in a new way. I still come to look at this site at times, just to visualize this stuff some more: mathwarehouse.com/algebra/

If there were any tips I could suggest to you would be to compare graphs of functions, side by side and see how they change. Try to identify which parts of an expression have a given effect you see in the graph. One of my favorite books that can show these kinds of diagrams, or explain these concepts better than I can, can be downloaded for free at people.vcu.edu/~rhammack/BookOfProof/

A lot of really interesting things emerge when you look at things geometrically, especially when you manipulate them. Like, take for instance, in trigonometry you're shown that if you place a right triangle in a circle with the hypotenuse extended from the center to the edge of a circle with a radius of one; no matter how little you move the position of the hypotenuse, the triangles shape will constantly be changing (<--calculus!) as the hypotenuse follows the edge of the circle. That same triangle, always has a hypotenuse equal to 1, which is equal to squaring and adding the other two sides, thanks to the Pythagorean theorem. Then, if you unroll, and graph the resulting line of that circle on a regular coordinate grid, you get a wave. upload.wikimedia.org/wikipedia/commons/6/67/2pi-unrolled.gif

It might be a pain in the arse to learn the order of operations, or to know all the basic rules of derivations, but in time you realize it's a lot like spelling a word; each symbol has a place, and means a certain thing.

p.s. booo, they wont let me post links :p
 

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Haha, so, when I went to a math tutor for the SAT, he gave me a pre-test to diagnose where I was getting things wrong. When he came out with the results, he said to me something along the lines of, Well, actually, you don't really seem to struggle with any particular area, but I have no idea how you did most of these problems. It's like you do something that's kind of close but technically completely wrong and most of the time you end up close enough to the right answer anyway. So, um, that's basically my personal experience with math. I scored 100 points higher on the SAT after the tutor and I've taken uni-level courses since then and I've learned that I can do just fine if I really crack down, learn step-by-step, and study hard, buuuuut I can also skate by reasonably relying on some wacky N understanding of things. I actually use a fair amount of basic math - addition, subtraction, division, multiplication - in my job currently, and it's not a big deal. I think my super-math-whiz INTP coworker believes I'm a bit batty, but I guess I am, so that's fine. :)

My thoughts for you are these:

(1) A lot of schools and teachers tend to teach the step-by-step how but not the why, so unless you remember the steps you're out of luck when it comes to deriving it yourself. And INFPs aren't great at remembering lots of little logical details. So especially if you have gaps in your foundational learning, it's not necessarily surprising that you're struggling. My guess is that if you sat down and worked on the foundational learning like the times tables, and then worked to learn the major concepts first, before having to apply the small steps, you'd do a lot better. I would suggest looking into working with a teacher or a tutor, yourself.

On that note, I don't think INFP necessarily determines that you're bad at math, but I do think it inclines you to be less interested in the rote steps of math for no greater purpose. For an NF who doesn't care that much about the how of math in the first place, just learning the step-by-step is not a setup for success. I remember thinking math was really quite boring for most of my schooling and it was only when I got to university that I discovered that it's actually conceptually a cool thing. Push to learn the concepts. You may need to find more resources. Google what you're learning... see what it's used for in the real world and what it means. Learn what you're actually using the steps to do. Learn top-down; learn the framework so you can derive the steps by yourself. I mentioned I use math in my career now - and naturally sometimes I screw the steps up. The reason I can catch it and fix it is that I understand what I'm using the math to do. That's what I think will help you. Understand why you're manipulating the data, what question you're essentially trying to answer. Then the steps will fall intuitively into place - and the math itself will be less of a frightening prospect. Remember it's all just tools to help you. There are other ways to solve problems, but math sometimes is metaphorically the shortest distance between two points. It's there for you... school is, too. Try to remember that when you get anxious about it. The point of learning it is to build you up, not drag you down. If it doesn't work for you, you'll find another way. Which brings me to:

(2) I know someone with a learning disorder who just doesn't grasp certain areas of math - seems mostly to impact him with algebra and understanding variables. As far as I can tell from your OP, that doesn't apply to you, but it does exist. Anyway, he scraped through his final math class in uni with a D and has a happy, successful career. Sounds like you get by well enough that you'll be just fine. If you end up struggling at uni most professors will work with you one-on-one and there is typically a disability office you can coordinate with. Generally they want you to succeed and will help you pass if you demonstrate genuine dedication and perseverance in the subject.
@Mr. Meepers is an INFP mathematician.
We also have several NTs on the forum who prefer humanities.


IIRC there was a statistic somewhere that ISFJs do particularly well in school----which, using my parents as a frame of reference, is true. My ISFJ mother got medals in school, and maths as well; my INFJ dad did not and he ended up becoming a physicist-turned-engineer.

Thus, I would be hesitant to attribute mathematical ability to any particular personality type (as well as interest in humanities subjects to a particular subject either).

Particularly since math education in many countries tends to be very S-oriented, especially Si.
What with the focus on retention of step-by-step processes, which my ISFJ mother is great at.
 

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Trying memorizing equations. That might help.
 

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Discussion Starter #12
@apropos in elementary when I was trying to understand integers, I did come up with this strange value based system for trying to understand how they worked, when subtracting from negative integers: I thought positive is negative for negative, somethings along the lines of good is bad for bad. Looking back it probably wasn't they way I was supposed to understand them, but that was how I understood them at the time. @angelfish I really did want to understand math, even though I was lazy and could have tried harder, I did try to understand at times. Even though I didn't fully memorize my multiplication tables, when there was a new concept being taught I did try to ask about it and figure it out for myself. One time I tried to get my mom to explain something to me, and even though we spent I think a least an hour on it I just could not understand and broke down in tears, whilst my mom got frustrated with me. Something I've noticed is that I will be introduced to a math concept, but it will only be years later that I understand it. I don't know if this is a sign of being stupid or dumber than the average person, but yeah it happens. I might only realize in Gr. 9 what a math teacher meant when she said something in Gr. 5. Sorry I didn't respond sooner but stuff happened and I wasn't sure what to say exactly. Thanks for the responses, I really appreciate that you guys really took the time for that.
 

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@angelfish I really did want to understand math, even though I was lazy and could have tried harder, I did try to understand at times. Even though I didn't fully memorize my multiplication tables, when there was a new concept being taught I did try to ask about it and figure it out for myself. One time I tried to get my mom to explain something to me, and even though we spent I think a least an hour on it I just could not understand and broke down in tears, whilst my mom got frustrated with me. Something I've noticed is that I will be introduced to a math concept, but it will only be years later that I understand it. I don't know if this is a sign of being stupid or dumber than the average person, but yeah it happens. I might only realize in Gr. 9 what a math teacher meant when she said something in Gr. 5. Sorry I didn't respond sooner but stuff happened and I wasn't sure what to say exactly. Thanks for the responses, I really appreciate that you guys really took the time for that.
No problem. It doesn't sound like you're stupid - but it may be that you do have a particular difficulty when it comes to math. We all have our weaknesses... I have a hard time with idealizing people and am bad at controlling my emotions. Those aren't graded in school so I guess I get off the hook there, but sure shows up in other areas of my life. Anyway, I was reading a bit and it looks like one study reported about 6% of school-age children having significant difficulty with math, even though math difficulty is neither as well-known or addressed as difficulty with reading. Perhaps you could try working with a tutor in your area... I would look for someone who has worked with LDs before - not because you necessarily have an LD, but because I believe they would tend to be much better equipped many different methods of teaching/tutoring and may hit on some that work well for you. Regardless of what you do - good luck!
 

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Math is based upon axioms, if you understand some axioms everything builds up layer upon layer pretty naturally.

Also, if you have problems to understand a branch of math try studying another one: isn't rare that that the same concept is used with slightly different definitions in more branches and maybe you'll understand it if in a particular context and that will make everything else far more clear.

Also, visualizing is good as a start line but has its limitations so your understanding of math has to be so abstract that even imagination becomes obsolete: can you imagine a square with negative area? Can you imagine a space with infinite dimensions? In maths those things does exist.
 

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Discussion Starter #15
Can I skate by in high school math, by just using formulas and only partially understanding proofs? I can do formulas pretty well. Sometimes I feel like I understand math and then suddenly don't then I do again. I want to ask my math teacher for help as he has offered, but he is often busy. I don't know if he has time to do anything too extensive with me, also I'm pretty shy.
 
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