# NT's and math



## teddy564339 (Jun 23, 2010)

Sorry if this has already been asked...I searched and couldn't find any threads about it.


As a high school math teacher, even though I've never (and don't know if I ever will) used type to truly change how I teach, I still find myself wondering about how it affects people. For example, learning about the S/N difference I think made me think that how different people can find certain things easier or more difficult to understand.


So I'm very curious how the different NT types view this. Now, I'm starting to come to the belief that type may not have a strong influence in how much one likes math or understands it. Even if it is a factor, there are certainly plenty of other ones, including environmental exposure to it at different ages. Because I've known people who I've suspected are NT's that were brilliant at math, and others who seem to hate it with a passion.


It's interesting because it seems like there are things about math that would appeal to an NT and things that would not.

On one hand, math in itself is very abstract and theoretical. Even though it can be used for all kinds of practical purposes, in itself that's not what it is. It's almost like science, but about less concrete concepts. This would seem like it would appeal to an NT, who would be better than an S at picturing these concepts. NT's also would appear to be the best out of the temperaments at piecing together all kinds of connections mentally without having to take it one step at a time... they could see a theorem, property or proof and immediately see how it could be applied in a lot of different situations.

On the other hand, a lot the way math is presented in high school is very S in nature, or at least very SJ. This is partly because high school (at least in the US, but probably in a lot of countries) is set up in a very SJ manner in general, and if the majority of the population truly is SJ, then that would partly explain why. 

But with math in particular, I think this is the case. In high school, it's very procedural, sequential, concrete and detailed. There is a lot of information, and getting the "right answer" is what's emphasized the most.

But I think the thing is that it seems like it's so rare for someone to truly understand math and be brilliant at it, and it almost seems like those people would be NT's. 

So the whole thing is weird to me...I guess I just don't understand what would allow one NT to understand math really well, and what would cause another one to have total trouble with it. Because I see math as being a huge balance of S and N...it's very abstract, theoretical and conceptual, but at the same time it has practical applications, has details that are important, and has a lot of algorithmic procedures.

It almost feels like anything else with S's and N's...that N's come up with the theories and concepts, and S's take care of the details of how to put them in place. But at the same time, don't NT's need to understand those details too, so they can show them to S's?

That's why I'm kind of curious and confused about an NT's take on math. Like I said, I don't know how much of it is type related at all, or if there's a difference in how each of the four NT types view it. Hence, why I'm making this thread.







Like I said, I'm not asking for advice about how to teach math to NT's, since that's really getting into a very blurry realm in regards to my job. But I'm still kind of curious to hear about different NT's experiences with math.


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## Deus Absconditus (Feb 27, 2011)

I've thought about this (well learning in all subjects in general), and understand why you could be confused. From my point of view I think the reason some NT's enjoy math and others don't is how they are being taught. As an INTP once we understand the concept we want to immediately move on to the next thing we do not like to stay on the same subject if we fully understand it's concept. As a teacher I understand you have to teach in a way where the majority of your class can understand what they're doing, so you may repeat yourself in multiple different ways to show the class more then one way of figuring something out. If an INTP already understands it though then it may just annoy them and they want to move on to the next problem to figure it out. They do not like to be kept at a pace for everyone else to learn.

So with all that being said some NTs (such as INTPs, not as a whole but most INTPs I think) may hate the subject because they're going at a pace to slow for them and instead of going ahead they may get distracted with a different subject they like and go more in depth with that subject. Other NTs may enjoy it because its purely theoretical and abstract so they find the interests in going more in depth with the math and trying to create new problems from what they have learned and understood, and even going ahead of the class just to teach themselves more because they want to learn at their own specific pace which is usually much quicker then non-NTs.


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## topgun31 (Nov 23, 2010)

ENTJ. Here's my take.

Growing up, I was very, very good at math. For algebra II in high school, I would finish my homework a month ahead, fall asleep in class, and still pull off with the highest grade...BUT I thought it was pretty boring, so math never sparked my interest past the minimum. That all changed when I took physics in college. I thought that I would hate it. Call me crazy, but physics ended up being one of my favorite subjects. I finally understood why all the math that I learned was important. It gave MEANING to the mundane details of math. 

You hit the nail on the head with the SJ/NT difference. The best way to teach an NT is to connect with the bigger picture, the 'why?' behind the mundane details...and reinforce that point constantly. Appeal to their love for theories and the big picture. Give math a PURPOSE.


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## goodgracesbadinfluence (Feb 28, 2011)

A lot of people I associate with at my college do not like the way math is taught. I know you said you teach high school, but I still think there is a difference. 

I had trouble with math in middle school because I never understood why we had to do something... even something so simple and basic as adding/subtracting/whatever the same thing on both sides. When I got into high school, I just accepted that's what you did, so I moved on. But it wasn't until I got into college and started taking higher math courses (I'm a mathematics major) that I realised you do it so you don't change the problem. 

A lot of emphasis is placed on doing something because "that's just the way it is" and this description doesn't tend to satisfy me and probably doesn't satisfy a lot of other NTs. I can really only speak for INTPs though, because that's what I am. And a lot of emphasis is placed on showing all your work. Sometimes to me, writing every single tiny step is boring and redundant because I already know what I'm supposed to do... for example, I have no need to write out that 8*4=32; I can do that in my head. I also tend to be able to remember certain problems and refer back to them and notice the pattern and I can come up with an answer instantly and in good confidence that way, but I can't necessarily explain why I got that answer, because once I have the answer, the steps are meaningless to me. 

The opposite is also true... if you skip a step that I really need, I get confused (obviously) and then I try to figure it out on my own. I employ multiple techniques until I can find the answer you got... which may/may not be the right one. I think most NTs would attempt to figure the problem out on their own first before asking for help. 

I think NTs tend to be good at math because we are more pattern-oriented, system-oriented, and have no problem with theoretical things. But I wouldn't call myself brilliant at math because a lot of math teachers (and I'm not saying you do this) are so accustomed to the material that they don't understand how someone could have trouble with it, which makes a lot of people reluctant to ask for help. And chances are, if you're an NT and you struggle with math, you don't struggle with all aspects of it. When something comes up that I don't understand, mentally I'm like, "Ugh, why can't I do this?" And it's never completely over my head, either. I can always grasp at the material, and I usually understand it when I watch someone else do it, but when it's time for me to do it myself, I get kind of lost. 

Another thing I might add (I know this is getting long, and I'm not even really sure if I'm helping you at all) is that I am terrible at practical math. Don't give me word problems, don't ask me how many miles you can travel in 4 minutes if you're going 130mph, don't ever ask me anything practical. But if you want the derivative of something, yeah, go ahead, ask, it's fun and infinitely easier.


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## TheWaffle (Aug 4, 2010)

I've always been fairly good at math and, occasionally, even find myself enjoying it. But at school, it's unbearably boring. My geometry teacher now is about sixty years old and doesn't teach very well at all. She rushes through the slide shows for the lesson and is generally unhelpful. I end up teaching myself all the math.

I also skip steps or not show work for problems and lose points. >_>


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## Mr.Xl Vii (Jan 19, 2011)

As an NT that was good at math, but sort of hated it I can begin to answer your question. As a subject goes, I find math very interesting and it was my best subject all though school, but I hated doing it. Mainly because math class was more about how much homework you did, and about showing every conceivable step, that it became tedious and annoying. I was lucky that I got a lot of NT math teachers and on NF math teacher so they knew where I was coming from with my issues.

More times than not, I was bored. I found it incredibly repetitive, and just for the challenge, I would learn the topic in class and not look over the notes ever again and "wing it" on the tests. Most of my teachers realized that I knew what I was talking about, and that I liked the challenge of solving difficult questions, but it was the structure in itself that annoyed me.

I have an NT friend that doesn't like math at all either, but it's not because he doesn't understand mathematical concepts he's just not the type that enjoys it. He's more the "let's ponder the big picture" type. He doesn't really care about learning the intricacies involved. Personally, the only math levels I enjoyed were the higher levels. Algebra II was fun only because it was easy, but I enjoyed Pre-Cal and Calculus. The only thing that annoyed me about both was the amount work you have to show.

You were right when you said the way math is taught is entirely SJ. Some of the NT types can handle that. I know plenty INTJ and ENTJ types that loved math class for that reason. I being an ENTP enjoyed learning mathematical concepts, but hated implementing them over and over and over again. And the friend I mentioned above was an INTP that hated it in its entirety. I'm not sure if this is prevalent amongst all of each type, but I wouldn't be surprised if it were the case. 

When I had other NT teachers they usually would be able to explain the concepts to me in a way that kept me interested, but not every math teacher is an NT so I can easily see how it could bore NTs. Even if the teacher is an NT, I find myself doodling for most of class, talking to my neighbor, or sleeping while I waited for the other students to catch up. School was incredibly boring for me in general, and even topics I found interesting, stopped being interesting very quick because of that.

There's a large possibility that those NTs don't necessarily find math boring, but they're just bored with school in general. That's not to say all NTs are smarter or that other types are necessarily slower, but my NT friends usually picked up new concepts a bit quicker. The other kids usually did better on the tests because they took the time to study and all that, so it balanced out.


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## Scruffy (Aug 17, 2009)

Math always cramped my style, I was never really _bad _at it; math was just a chasm of loneliness & suffering, carried on the backs of elder sloths and misfits. Math was best for me when I was shown "why do I care" (topgun's point about bigger picture). The tedium of the details are not worth the reward of completing the problem. 

I didn't like following the steps, I'd often try awkward work arounds (some successful, some failure) just to keep myself entertained. My problem forever with math: I don't like how it makes me blank out, if I'm sitting there doing a chain of problems my mind becomes too focused, and does not wander. I lose my imagination.

I love math for what it is, and for what it stands for, just don't make me do it. Showing me the reasoning and why it matters is the only way I'll learn/care/do it. I always enjoyed math quirks as well, on a basic level things like 111x111 ends up with some sort of 123 pattern.


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## Tragic (Jan 31, 2011)

When learning maths there are many, many ways to understand even the simplest of problems.
For an extremely simple silly example:
a(b+c)=ab + ac

1) Try it with actual numbers, it works!
2) Look at a rectangle, one side of length a, one side of length (b+c), and you see geometrically why it's true.
3) It's an axiom/ it's a definition. 
4) It's a theorem, derived from more elementary axioms.

If one person understands a concept one way, and another person understands it another way then one will be "bad" at using it to solve certain problems, and one will be "good". The way people are storing and understanding concepts in their head can make such a difference. From conversations with people I've had about the subject I think this is the main reason some people are good and some people are bad at maths. They can both 'understand' but only from a certain point of view that may not be the most beneficial one for the problem at hand.


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## teddy564339 (Jun 23, 2010)

It's hard for me to respond too much without making a huge, uber long post. There are so many things for me to rant about, many of which aren't necessarily related to type...from the frustrating limitations of the system and my expectations/pressures from my superiors as a teacher to the difficulty of dealing with a huge group of diverse students, not only in them getting along, but all of them learning. It's a tough job for anyone of any type, and I've known teachers of different temperaments that all face a lot of the same challenges.

This can even be shown in this thread, where there are these two different mentalities from two NT's.



topgun31 said:


> You hit the nail on the head with the SJ/NT difference. The best way to teach an NT is to connect with the bigger picture, the 'why?' behind the mundane details...and reinforce that point constantly. Appeal to their love for theories and the big picture. Give math a PURPOSE.





goodgracesbadinfluence said:


> Another thing I might add (I know this is getting long, and I'm not even really sure if I'm helping you at all) is that I am terrible at practical math. Don't give me word problems, don't ask me how many miles you can travel in 4 minutes if you're going 130mph, don't ever ask me anything practical. But if you want the derivative of something, yeah, go ahead, ask, it's fun and infinitely easier.



So I could go on for pages and pages and pages here...but I'll try to just stick to some main points. 

I think what bothers me a lot is that when I was teaching a class called Discrete Math, I overall loved it. To me, almost everything in the class was naturally interesting. It was much easier to come up with activities and ideas that kept the interest of a lot of my students...they could see the purpose in pretty much everything we did, from election theory, graph theory to probability. I also taught mostly seniors who were pretty mature, and I felt no pressure to "get them ready" for college or a standardized test.

But I then got transferred to a school I don't like as much and I'm stuck teaching Geometry and Algebra 2. While I like the math, I'm not passionate about it in the same way I was. I've gotten kind of personally selfish in the aspect that what I go for the most is getting most of my students to pass the standardized test...not only because the students need to pass it to pass the class, but also because my principals judge me the most based on that, and keeping my job, preferably with decent classes, is my biggest priority.

So I end up teaching in a pretty SJ manner, because that's easiest for most of my students to understand. Most of my students still like me, and most are just thankful to have a teacher that they can understand. But they also don't like the math much. For a lot of them, that doesn't matter, they just deal with it. But I know a few have a problem...particularly one student who I think might be an ENTP. Now, in all fairness, this student struggles a lot in all of his classes and looks like he's going to have trouble graduating. But I can tell that he's very N-like in the aspect that he's always looking at the big picture and the look future of a problem instead of taking it one step at a time and focusing on the details. I think he'll be ok in the end, but along the way it's tough because in order to pass this test, the details will be important...and he needs it to graduate. But it's kind of frustrating. 

He (and a lot of students) are a lot of times asking for the bigger purpose in the math. And with Discrete, it was so easy to point that out. But it's so much tougher with the Algebra. And even though I know the best thing to do would be doing a lot of research and looking into it a whole lot more, but due to my own exhaustion, laziness, and uncertainty about the future of my situation, I haven't and don't. Maybe it's selfish, but it's all I can do to just survive.

Anyway, I'm starting to rant and vent a little, but that's what kind of inspired me to make this thread today. 





Michaeldh0589 said:


> I've thought about this (well learning in all subjects in general), and understand why you could be confused. From my point of view I think the reason some NT's enjoy math and others don't is how they are being taught. As an INTP once we understand the concept we want to immediately move on to the next thing we do not like to stay on the same subject if we fully understand it's concept. As a teacher I understand you have to teach in a way where the majority of your class can understand what they're doing, so you may repeat yourself in multiple different ways to show the class more then one way of figuring something out. If an INTP already understands it though then it may just annoy them and they want to move on to the next problem to figure it out. They do not like to be kept at a pace for everyone else to learn.
> 
> So with all that being said some NTs (such as INTPs, not as a whole but most INTPs I think) may hate the subject because they're going at a pace to slow for them and instead of going ahead they may get distracted with a different subject they like and go more in depth with that subject. Other NTs may enjoy it because its purely theoretical and abstract so they find the interests in going more in depth with the math and trying to create new problems from what they have learned and understood, and even going ahead of the class just to teach themselves more because they want to learn at their own specific pace which is usually much quicker then non-NTs.


Yeah, and that's what's so tough about teaching...because so much of my time, energy and attention goes to all students, particularly those that are struggling. The good thing is that I always get along with the independent students pretty well. The only thing that's frustrating is when we're going through things as a whole class and the brighter students are jumping ahead so much that it starts confusing most of the others, and I have to backtrack and slow down. 



goodgracesbadinfluence said:


> A lot of emphasis is placed on doing something because "that's just the way it is" and this description doesn't tend to satisfy me and probably doesn't satisfy a lot of other NTs. I can really only speak for INTPs though, because that's what I am. And a lot of emphasis is placed on showing all your work. Sometimes to me, writing every single tiny step is boring and redundant because I already know what I'm supposed to do... for example, I have no need to write out that 8*4=32; I can do that in my head. I also tend to be able to remember certain problems and refer back to them and notice the pattern and I can come up with an answer instantly and in good confidence that way, but I can't necessarily explain why I got that answer, because once I have the answer, the steps are meaningless to me.


Yeah, this is kind of the same thing...I always like going back and explaining concepts when students ask, but then those explanations end up confusing a lot more of the "basic" thinking students, and it gets frustrating. A lot of times I wish I could split my classes into pieces and teach them one at a time.




goodgracesbadinfluence said:


> I think NTs tend to be good at math because we are more pattern-oriented, system-oriented, and have no problem with theoretical things. But I wouldn't call myself brilliant at math because a lot of math teachers (and I'm not saying you do this) are so accustomed to the material that they don't understand how someone could have trouble with it, which makes a lot of people reluctant to ask for help. And chances are, if you're an NT and you struggle with math, you don't struggle with all aspects of it. When something comes up that I don't understand, mentally I'm like, "Ugh, why can't I do this?" And it's never completely over my head, either. I can always grasp at the material, and I usually understand it when I watch someone else do it, but when it's time for me to do it myself, I get kind of lost.


Yeah, that's one thing that overall I think I'm really good at. This is where being a feeler helps, especially with Fe...I'm overall very patient and am willing to take my time with students explaining things and going back through it. In general I make my students really comfortable about asking for help. Usually the only students who fail me are ones that don't really try or the ones who had a whole lot of trouble in all of their other math classes. I don't think I'm a great teacher, but in general my students do well and many tell me I'm better than a number of teachers they've had.






Anyway, I know I turned this personal...I try not to, but sometimes I can't help it....silly F, I know. But I really appreciate all of the responses, I've found them quite interesting.


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## teddy564339 (Jun 23, 2010)

Scruffy said:


> I love math for what it is, and for what it stands for, just don't make me do it. Showing me the reasoning and why it matters is the only way I'll learn/care/do it. I always enjoyed math quirks as well, on a basic level things like 111x111 ends up with some sort of 123 pattern.


Yeah, I like stuff like that too. I have a lot of little number tricks and logic puzzle things that I show my students when we have extra time. You may have seen stuff like this before, but they usually like this one:

*a) Pick a number between 1 and 9 (including 1 or 9).*
*
*
*b) Multiply your number by 2.*
*
*
*c) Add 5 to the number you created in part b.*
*
*
*d) Multiply the number you created in part c by 50.*
*
*
*e) If you haven't had your birthday yet this year, add 1760 to the number you created in part d. If you've had your birthday, add 1761 to that number.*
*
*
*f) Subtract the year you were born (ex: 1990) from the number you created in part e.*
*
*
*You should come up with a three digit number. The first digit is the number you picked in part a and the last two digits should be your age.*


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## clawsthatcatch (Feb 1, 2011)

Math isn't my strong suit. It's too detail-oriented for me.


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## Tragic (Jan 31, 2011)

I never enjoyed maths for its applications. I always liked the "Ooooh pretty!!" feeling when seeing something nice and enlightening. Around 16-17 the things that made me get really in to the subject were the little niceties, like the gamma function or irrationality of root 2. Also the non-obvious theorems like binomial/factor/symmetric polynomial/taylor. Not solving any problem, but just seeing a deeper connection and exploring.


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## Protagoras (Sep 12, 2010)

I think this is really interesting, because I have had a love-hate attitude towards math ever since my first year of high school (I'm in my last year now). On the one hand there are all these interesting theories that help explain reality and in which I'm really interested, but the manner in which it's taught is mind-numbingly boring and repetitive. I always joke about how teaching people math as it's taught in high school is the best way to indoctrinate people for political purposes, because it's based around repeating the same rules and exercises over and over again until the students just take it for granted without thinking for themselves. The strange thing is that I don't have any difficulty in understanding the mathematical aspects of physics or economics. During my last student review my economics teacher and math teacher found themselves talking about a completely different student while discussing me: my economics teacher thought I was one of the more intelligent students through being able to grasp even the most abstract economical theories, while my math teacher thought I was one of the demotivated and thick-headed students. I think this is mostly due to the nature of mathematical education in high schools: it's for SJs. An INTP like me gets demotivated by all the repetition and lack of theoretical continuity in the lessons. During most math lessons I find myself completely disinterested, which makes me prone to rationalizing my unwillingness to make homework and learn for tests... which in turn leads to me scoring horrible notes at the tests...


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## absentminded (Dec 3, 2010)

Math is awesome. I think the problem that a lot of NT's have with math (I hate to regurgitate what everyone said already) is how it's taught.

Math is the language of logic, e.g. set theory lies at the root of huge swaths of philosophy. A focus on why it works and what it's good for would greatly improve NT's relationship with it. Most math teachers, in my experience, focus on memorizing what the quadratic formula is and how you solve it. I wanted to know why the formula worked and they didn't know or weren't interested in showing me, so I had to teach myself. The college approach is much nicer: concepts and not blind formulas/solutions. YES!!!! 

Sweeten the deal by talking about general cubic and quartic solutions. Those are fun.


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## B-Con (Dec 24, 2010)

I majored in math. I love it.

The higher the level of math, the more abstract you get. I spent a year learning Abstract Algebra, and there was only like one application given to us every other week. Eventually, you study logic and structures just for the sake of doing so, application is only an added benefit (that, if you're a professor or grad student, may help you get funding).

I think that math may start being taught in an SJ style, but by the time you're in 3rd or 4th year of university work, it's largely NP in style.

Thinking of all the students beside me who did well, I think they were all NTPs or NTJs, with just a couple exceptions. (Interestingly, those couple exceptions didn't even seem to like the major.)

I would agree that math is inherently an NT-oriented topic. Direct application may not be so, but as you move away from "math as a life tool" to "math as an existence", you see it's NT nature. You really have to interpret the meaning and build deep understanding of the material to truly get it. It's not uncommon for you to study a subject and then get a test with a completely different problem you've never seen before. If you don't understand the material beyond your own experiences with it, you are probably stuck at that point.


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## hoom (Jan 22, 2011)

I've always rather enjoyed math... I find that my classes draw on and until this year all of my classmates and teachers have been fairly incompetent... but I always enjoy getting that little "Ok class, take a look at this. Now, if we see the area..." and then immediately figuring out the conclusion and most of the steps needed to reach it. Last year I sat in the back of the room on my laptop programming (being the only student allowed to do so) because my teacher recognized that I didn't have to do shit to do well - he was a good guy.

This year I've probably got an INTX teacher and it's one of the classes for the most advanced math students in the school, so everything is a bit better. We still go over steps to the point of tedium and spend way too long on things we shouldn't have to (as a collective now), but at least we're actually led to think things through for ourselves.

They really do need to make a required 'problem solving' class for all high schools, math where the teacher says "using any prior knowledge and the fact that blah blah blah is blah, find out how to determine blah." and just let us loose to work on that. I suppose it would be essentially a discrete mathematics course... here's point A and point B, figure out how to connect the dots. Could even just give them point A and tell them to find something cool. Would be great to have a test where we were just told to figure something out. I think that the 'S' brains could use a little problem solving experience.


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## phina saurus rex (Mar 4, 2011)

What an absolutely awesome idea that would make math so much more fun especially in my school. the only advanced math you get is moving up a level but then your just with the stupid kids from the next grade up.

i love the times when my teachers just let me work/sleep and all they give us is an idea and a set of numbers.


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## teddy564339 (Jun 23, 2010)

hoom said:


> They really do need to make a required 'problem solving' class for all high schools, math where the teacher says "using any prior knowledge and the fact that blah blah blah is blah, find out how to determine blah." and just let us loose to work on that. I suppose it would be essentially a discrete mathematics course... here's point A and point B, figure out how to connect the dots. Could even just give them point A and tell them to find something cool. Would be great to have a test where we were just told to figure something out. I think that the 'S' brains could use a little problem solving experience.


In theory, I agree with you. My INFP teacher friend (he teaches English) and I talk about stuff like this all of the time.

The problem is that the vast majority of students we get just don't know how to think. I think it boils down to their elementary school and middle school backgrounds. At the middle school that feeds into my high school, every single kid is passed through...no matter what they know or what they've done. 

And, with all of the NCLB limitations on funding, high schools are penalized for dropout rates and low graduation rates. So as a result, the whole system bends over backwards to try to get everyone to pass, and in the end everything gets dumbed down extremely. It creates a big mess. 


This, however, is what I believe is a fantastic essay about math. It's lengthy, but I've always loved reading it.

http://www.maa.org/devlin/LockhartsLament.pdf


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## luemb (Dec 21, 2010)

I am an engineering student and I really enjoy math. I tend to solve problems quickly in my head and then work them out on paper. Most of the time I am right, but occasionally I miss an important detail which means I have to work through the entire problem again. 

I had the wonderful opportunity to take an enriched math course in 10th grade. Although there were a lot of S's in the class, my teacher allowed for enough time for me to work ahead a little bit in his class. For example, he would set out a problem on the board, and then give us, or me at least, enough time to think it through and try and come up with a way to solve it. Then he would show us how to solve it. He knew I was a very bright student and challenged me to learn the material. 
The only marks I lost in that class were from mixing up my numbers on my paper. Oh, and once I used a wrong formula. 

After that the math classes were boring. The material was obvious, and the answers were spoon-fed to me. And we never went into detail. I love detail. I love knowing everything about the subject. When some function is just glossed over I get confused. I can normally work off the assumption that what the teacher told us is right, but I don't understand or remember it as well as if I was shown all the details into how something works. 

Calculus at the end of high school was alright because it was something new, and it was easy to visualize. In my multiple intelligences, I'm a visual/spacial learner first, then a logical/mathematical. I think the multiple intelligences has as much to do with how we learn as our personality types. 

In university calc moves a lot quicker, and all the details are presented. I really enjoy it, although I sometimes need to sit down and combine all the details that I've learned in order to make a bigger picture out of it. 

For me in general:
Arithmetic was memory work, although understanding the basic principles was a big help. 
Algebra made a lot more sense once I could visualize it on a graph, and understood how it worked. I also needed to know why each of the steps to solving the equations worked. 
Other equations of lines also made more sense once I could visualize them. Understanding the connections, for example between logs and exponentials, was also helpful. 

If I'm lost in thought I can mindlessly write down information from the blackboard and not understand what I'm writing. I have to concentrate on what the teacher is saying and analyse it as we go along. If the class is slow-moving, I've already analyzed it before the teacher finishes writing, and then I go off on another tangent and miss several of the next points, even if they are written down on my page.


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## goodgracesbadinfluence (Feb 28, 2011)

B-Con said:


> I majored in math. I love it.
> 
> The higher the level of math, the more abstract you get. I spent a year learning Abstract Algebra, and there was only like one application given to us every other week.


I am SO excited about taking Abstract Algebra.


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## hoom (Jan 22, 2011)

teddy564339 said:


> *Stuff*
> 
> http://www.maa.org/devlin/LockhartsLament.pdf


@teddy564339, definitely an interesting read. Personally, I think that that particular viewpoint is a bit extremist, a lot of the things that we learn in the current system are quite useful and I'll probably retain them, I *do* however think that many of my classmates will not ever see the worth, and thus forget much of it. To that end and as a continuation of my previous statement, I'm much more interested in creating a _parallel_ mathematics curriculum, one that does focus on teaching the elements as described in this article. A certain level of competency with techniques is a must, and to that end I must disagree with Lockheart, but there's no reason why the current system couldn't be condensed and have some of the fat trimmed out so we can introduce mathematics as an art as well. If I ever become a teacher, and I may, I will try to make an elective called 'The Art of Mathematics' which will function like this... if it went well, I'd add additional levels... that or let the credit be repeated with a new curriculum and focus of study each year.


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## teddy564339 (Jun 23, 2010)

hoom said:


> @teddy564339, definitely an interesting read. Personally, I think that that particular viewpoint is a bit extremist, a lot of the things that we learn in the current system are quite useful and I'll probably retain them, I *do* however think that many of my classmates will not ever see the worth, and thus forget much of it. To that end and as a continuation of my previous statement, I'm much more interested in creating a _parallel_ mathematics curriculum, one that does focus on teaching the elements as described in this article. A certain level of competency with techniques is a must, and to that end I must disagree with Lockheart, but there's no reason why the current system couldn't be condensed and have some of the fat trimmed out so we can introduce mathematics as an art as well. If I ever become a teacher, and I may, I will try to make an elective called 'The Art of Mathematics' which will function like this... if it went well, I'd add additional levels... that or let the credit be repeated with a new curriculum and focus of study each year.


I agree that it is extreme. On the other hand, I feel like he wrote it that way on purpose, just to stand out and make his point. And he does talk about "the pendulum" not being pushed too far in one direction...he does argue for balance in math education. His problem is that there is a total absence of creativity and thinking going on in our current system.

I'm in my fifth year of teaching and my perspective on it has changed a lot since before I started teaching. Maybe it's just the particular state that I live in, but I'm starting to think it's the entire US. There are just so many basic things that I thought most students did and I've realized that most of them don't. I could go on and on about this, but I don't want this to turn into a rant. It's just frustrating that how so many students don't know how to think, or how to study, or even how to take notes. And a large part of the problem is that this is what they're taught throughout elementary and middle school...they're just taught to follow procedures. A lot of times they can't even do arithmetic without a calculator. Some of my Geometry and Algebra 2 students don't know how to add or subtract negative numbers without a calculator, let alone do fractions.

Of course, I don't teach honors classes for the most part, so I don't know how many NT students I actually end up teaching anyway. Most of my students will end up going to community college. Not that there's anything wrong with that...it's just that these are the types that usually don't enjoy learning just for the sake of learning.


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## hoom (Jan 22, 2011)

teddy564339 said:


> *stuff*


Yeah, it probably also helps that I come from a district that is known for being particularly strong - one that never actually has to worry about state mandated tests or anything like that...


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## teddy564339 (Jun 23, 2010)

hoom said:


> Yeah, it probably also helps that I come from a district that is known for being particularly strong - one that never actually has to worry about state mandated tests or anything like that...


Yeah, that makes a huge difference. My district is obsessed with test scores. That's pretty much all our principals care about, and that's the focus of all kinds of meetings that we have.


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## cam3llia (Mar 5, 2011)

The strange thing was that I understood most/if not all of the concepts quite well in Math. However, when I did the test; I lost a lot of marks (mostly due to carelessness). It was to the point where the marks were so bad, it made me question my own intellect.


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## B-Con (Dec 24, 2010)

goodgracesbadinfluence said:


> I am SO excited about taking Abstract Algebra.


What textbook are you using?


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## voxic (Mar 10, 2011)

goodgracesbadinfluence said:


> A lot of emphasis is placed on doing something because "that's just the way it is" and this description doesn't tend to satisfy me and probably doesn't satisfy a lot of other NTs. And a lot of emphasis is placed on showing all your work.The opposite is also true... if you skip a step that I really need, I get confused. I think most NTs would attempt to figure the problem out on their own first before asking for help. I can always grasp at the material, and I usually understand it when I watch someone else do it, but when it's time for me to do it myself, I get kind of lost.
> 
> Another thing I might add (I know this is getting long, and I'm not even really sure if I'm helping you at all) is that I am terrible at practical math. Don't give me word problems, don't ask me how many miles you can travel in 4 minutes if you're going 130mph, don't ever ask me anything practical. But if you want the derivative of something, yeah, go ahead, ask, it's fun and infinitely easier.


agreed, except that for me it's the other way, I love word problems but hate derivatives and the such. I used to be ace maths in the lower grades when they still had word problems. In college, when it became all numbers, I flunked every single exam. It was boring to me, and there didn't seemed to be any point in doing it, we were forever just repeating and applying some formula. However, I loved physics, I could imagine the whole scenario in 3d and such, and I was brilliant at it, I really wanted to take physics, but because I didn't turn up for the higher maths major exam(really didn't felt like it, i guess this is common for INTPs?), I could only choose humanities in college...



> There's a large possibility that those NTs don't necessarily find math boring, but they're just bored with school in general. That's not to say all NTs are smarter or that other types are necessarily slower, but my NT friends usually picked up new concepts a bit quicker.


yeap...I do pick up new concepts quicker, but school is really boring so I never bothered.

looking at all the responses, I guess I would have loved maths at the higher levels, but the way math was taught in middle and high school made me hate it and sort of dashed all my chances of taking it in the higher levels...
I do realize that I tend to do better for math questions that are "different" from the practice questions, and require you to really understand and grasp the concepts and apply it in a way that is not common in the practice questions given during assignments. For the questions that are similar to practice questions, I find them boring and most of the time don't really bother to attempt them.



> Yeah, that makes a huge difference. My district is obsessed with test scores. That's pretty much all our principals care about, and that's the focus of all kinds of meetings that we have.


where I study, test scores are all that matters...
which is why I hate school.

sorry for a long post! but as you said, ranting...


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## Tragic (Jan 31, 2011)

teddy564339 said:


> This, however, is what I believe is a fantastic essay about math. It's lengthy, but I've always loved reading it.
> 
> http://www.maa.org/devlin/LockhartsLament.pdf


I'm at page five, it's very well written and also true...

"The first thing to understand is that mathematics is an art. The difference between math and the other arts such as music and painting, is that our current society does not recognise it as such"​

"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs it is because they are made with ideas."​
Reading it made me think. In my teens when faced with these repetitive "memorise the rule!" type problems for homework I'd program my PC to solve the problems for me. Then I'd input a, b & c etc... and my PC would give me the answer that I'd write down...


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## goodgracesbadinfluence (Feb 28, 2011)

B-Con said:


> What textbook are you using?


I'm not taking it yet... it's a couple semesters down the road. I'm just excited about it.


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## Tragic (Jan 31, 2011)

goodgracesbadinfluence said:


> I'm just excited about it.


I hope it's fun!! I love Cayley-Hamilton theorem, I hope you cover that. Not sure what exactly Abstract Algebra is, in the US. We have different names for things here.


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## Siggy (May 25, 2009)

Sorry I'm late, just chiming in here. I think the bottom line for me was we never could get creative about it. Solving problems, well yea, but what for? Rote learning has its benefits, but it seems as if that was all we did.


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## bigtex1989 (Feb 7, 2011)

The way lower level math is taught (lower-level undergrad and below) is practice problems until your hand cramps. Although this teaches you how to solve particular problems, it is extremely unhelpful in the long run. I am very good at math, and majoring in physics with a minor in math.

I view math as a physical representation of what is around me. I have an innate desire to understand the world, so I learned math. Not until I got into 3000 level math and physics courses did it all start tying together. I view math as a powerful language, able to describe everything conceivable. Most homework is boring and unrealistic. It serves no purpose at all. If you are in a career field that deals in heavy math, and you need the transitive property, and you can't prove it yourself, get out. 

Math is the least SJ thing I can think of. You have set rules, sure. Within those rules there is so much wiggle room of which to take advantage. Real math takes extreme creativity surpassing even the greatest poets. 

School itself is rigid. Subjects are to be explored and connected. The delineation between class periods is a huge problem in my opinion. You have "English" then "History" even though most books are written as a political commentary, which ties in with the history you're learning. Terrible terrible system. The subjects form a web. The typical NT is the spider that moves seamlessly through this. The SJ is a machete that cuts it to ribbons


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## B-Con (Dec 24, 2010)

Tragic said:


> I hope it's fun!! I love Cayley-Hamilton theorem, I hope you cover that. Not sure what exactly Abstract Algebra is, in the US. We have different names for things here.


It covers groups, fields, and the natural fallouts from those subjects (ie, rings).



Tragic said:


> I'm at page five, it's very well written and also true...
> 
> "The first thing to understand is that mathematics is an art. The difference between math and the other arts such as music and painting, is that our current society does not recognise it as such"​
> 
> ...


I've always taken issue with this. I realize that I can't speak with the authority of an accomplished mathematician, but I take exception to this. I think that one's view of math as a pure art or not is related to their view of math and Platoism, eg, is math invented/expressed or is it discovered?

I vote for the later, and hence I do not consider it an art. I acknowledge that it can look like an art and act like an art, but I view that as art describing math, not math being an art.


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## PeevesOfCourse (Apr 15, 2010)

I used to become bored with rote math problems. When it hit algebra I started to like it, and got A's, then petered out when I hit calculus like a brick wall. Terrible at trig and geometry when I was younger. For some reason I think I could do it better now.


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## aerosmithgirl (May 25, 2010)

I am terrible at math. It just doesn't work with my brain. I'm much more suited to the fine nuances of language and music. I can add and multiply large numbers in my head with relative accuracy, but any form of algebra leaves me feeling incompetent and stupid. I understand the theoretical and abstract concepts of math, but if you ask me to solve a problem you'll be disappointed.


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## RogueWave (Mar 16, 2011)

I'm not great at math, nor am I terrible at it. I do hate it however. I specifically hated math classes (both high school and college) because you're doing math for the sake of doing math. I don't like doing calculations for the sake of doing calculations. Now take a math intensive science, like physics, and my attitude changes. You're then using algebra and trig to illustrate and understand phenomena. The calculations aren't self serving. 

I do feel the need to mention I LOVED geometry in high school. Everyone else hated it, but for some reason I just *got it*. I can only think that its because geometry is very abstract and concept based. There are no calculations to make careless errors with, and I make plenty of those in algebra and calc. Once you understand the rules and theorems of geometry, it's all logic. Especially proofs. I owned proofs.


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## PeevesOfCourse (Apr 15, 2010)

bigtex1989 said:


> The way lower level math is taught (lower-level undergrad and below) is practice problems until your hand cramps. Although this teaches you how to solve particular problems, it is extremely unhelpful in the long run. I am very good at math, and majoring in physics with a minor in math.
> 
> I view math as a physical representation of what is around me. I have an innate desire to understand the world, so I learned math. Not until I got into 3000 level math and physics courses did it all start tying together. I view math as a powerful language, able to describe everything conceivable. Most homework is boring and unrealistic. It serves no purpose at all. If you are in a career field that deals in heavy math, and you need the transitive property, and you can't prove it yourself, get out.
> 
> ...


Math is a language that describes physical processes. If you look at it that way, like a language...it becomes a lot more interesting. There is math to describe the trajectory of a baseball, etc.,, just like words would...


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## rappf (Feb 14, 2010)

INTP. Slept through Algebra II, stayed fully awake through Calculus (most days).

I really, really love learning mathematical syntax and theorems, but the moment books break out the practical applications...

Swear to god, it makes me want to curl up in a ball—in the dark—and suck my thumb until it STOPS.

Decimals are so... I hate decimals and scientific notation and rounding and money problems and, and... Anything that takes the neat little _representations_ of irrational numbers (like e, pi, certain radicals, etc.) and converts them to these messy piles of AHHH in order to meet empirical standards...

_x ≈ 0.00064546!#%#$ ... sq. in._ *<-- See that? That drives me CRAZY!*

I mean, I can still DO it, but ahh...


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## teddy564339 (Jun 23, 2010)

I think the funny thing about all of this is how the majority of posters have discussed taking college level math classes, or at least calculus. This is a very different demographic of person than the students that I was thinking about when I created the thread. It's even possible that the ones I'm thinking about are not NT's, but rather NF's (or maybe SP's, but I doubt it). I say that because these students are probably going to go to community college and may never even see calculus. That's not to say that this doesn't happen to NT's...but it certainly shows the difference between their experiences and the ones of many of the posters in this thread.

It points to the fact that type and temperament are only part of the whole picture and that there are other factors that play into this as well. This can definitely be seen in the wide array of responses in this thread, even though there are some common themes among the posts as well.










B-Con said:


> I've always taken issue with this. I realize that I can't speak with the authority of an accomplished mathematician, but I take exception to this. I think that one's view of math as a pure art or not is related to their view of math and Platoism, eg, is math invented/expressed or is it discovered?
> 
> I vote for the later, and hence I do not consider it an art. I acknowledge that it can look like an art and act like an art, but I view that as art describing math, not math being an art.


I am also not a mathematician, so I can't speak about the topic with great wisdom, only my own opinion.

I agree with you that math is discovered moreso than it is created, but I also don't think that this has to be a choice. I think math can be both an art and a science. Because it's so abstract, there is a lot more wiggle room in it than there is in "other sciences", and one has the ability to create different applications and aspects of it when studying it. But, like you said, its principles are going to be the same throughout, so these ideas are discovered like a science as well.


The thing is though...unless you wen through and read the whole essay, the part that Tragic quoted was only one small piece of it...despite the wording, I don't think that was really his main point. His point was that the blunt sharing of information and repetitive drilling is what high school math has become, and that the artistic side of it has been completely removed. He even talks about balance...he's not saying the the practice and repetition has no place in school, just that it shouldn't be the *only* part of math that's focused on or done. He's basically arguing the same thing that a lot of posters in this thread have mentioned.


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## jbking (Jun 4, 2010)

I have a Double Honor's Bachelor of Mathematics with majors in Computer Science and Combinatorics & Optimization from the University of Waterloo. I also finished with a Pure Math minor just to state how much Math I was taught growing up. In the early grades playing with Math puzzles was fun for me and part of me could handle the mechanical aspect of churning out answer after answer as long as I got some kind of payoff for doing well. In high school and beyond Math took a major left turn into way more abstraction though thankfully still staying close enough to linear for me to still be OK studying it. I remember quite well how after my initial Math courses there seemed to be very few numbers in what I was taught and more about various theorems, variables and knowing what tricks to use in answering questions. I tend to enjoy immersion in some subjects and logic is my best learning style so Math is a bit of a natural thing for me. Spelling was another subject I excelled though this got removed in the junior high era so it wasn't like I could university courses about it. However, foreign languages are close enough that I did take a few of those. I still enjoy brushing off the odd Math skill here and there even though I graduated back in '97 with that degree.


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## PAdude (Mar 18, 2011)

I was always literally the best in my class at math in elementary school when it was all rapid fire problem solving, however since Pre-Algebra I've struggled a lot because I just don't care. I'm actually really good at figuring out a lot of algebraic concepts on my own even with no knowledge on the proper way to do it but I was a lazy ass student who paid no attention in class and I never had enough time on the tests to employ my own methods fully on every question.


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## Letol (Oct 4, 2010)

Math, oh math... Well, let's see. I never really had a problem with math up until middle school. In 8th grade, I failed Algebra I Part 2. I didn't go to summer school, and the next year I took Algebra II and passed. In fact, I actually never retook Algebra I Part 2. I continued to take math classes all the way up until Junior year making it to Trig/Pre-Calc, passing every single one. Come time that I went to college, I tested into an elementary algebra class. I've got to be honest, I'm confused by the whole thing myself, but whatever.

Oh, and I saw it mentioned somewhere, so I thought I'd say that I go to a community college. It's not necessarily that I didn't get into any other colleges, though. It's actually because my mom works there, so I got a tuition waver. 2 years of free college working towards a transfer degree? Hell yeah!


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## error (Feb 10, 2011)

I've always been weak in this subject. I can even screw up basic arithmetic, I can look at two numbers add them together and be off by one in the solution. I took Algebra I my sophomore year in high school... and failed it three times, never passed those classes. Did well enough in Basic Science and Biology, managed to somehow pass Chemistry. Failed Physics, failed it hard. I don't know what technicality they pulled that got me my diploma but I never felt I earned that.

Yeah, I pretty much can't do math and I hate it.


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## Apocalypse kid (Mar 20, 2011)

i am good at math but hate it. i got a really good teacher and he helps me learn better then my old teachers but i still dont really like math.my passion is science and discovering new things math everything is figured out and there is only one correct answer.


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## Vox Impopuli (Sep 18, 2010)

I usually score among the highest in math in my school, yet I severely dislike it. (I am a possible ENTP)
It takes a lot of effort to motivate myself into solving something I see no use for, and I am tend to make silly mistakes like forgetting to carry and in quick multiplication. I really enjoy learning new things in math class though- its having to attend to minor technicalities while applying it that kills me.


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