Why Do Some People Struggle with Math?

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In summary: At this age, I think it is interesting that you struggle with basic equations and terms such as "math genius" and "math genius", because it sounds like you have some empathy for people who understand these concepts and people. I think it is also interesting that you find physics fascinating, especially considering that you don't seem to have any trouble with the math. I think that you might benefit from some supplemental materials, such as Khan Academy videos, to help you with the math.
  • #1
Blop
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Background: I live in the U.S. and I am in 7th grade, 13 years old. I have mild ADHD
I don't really hate math, per se, but I can't help thinking that I'm unfit to do anything related to mathematics. I enjoy geometry and abstract scientific problems, but struggle in areas such as basic equations and terms. Everything just seems like it flies over my head, and despite people praising me as a good thinker and philosopher, I feel deep envy for people who understand math and people who can be in high-level classes, because I find physics fascinating (even though it takes mathematical prowess). I always panic when confronted with math homework, and my mind goes blank.
I feel like I need motivation to do better.
 
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  • #2
Can you give an example of what you find hard and maybe one which you find easy?
Is solving ##\frac{2}{21}x-\frac{7}{15}=\frac{43}{35}## hard and "All triangles in a half circle with the diameter being the longest side have a right angle at the perimeter." easy?
 
  • #3
fresh_42 said:
Can you give an example of what you find hard and maybe one which you find easy?
Is solving ##\frac{2}{21}x-\frac{7}{15}=\frac{43}{35}## hard and "All triangles in a half circle with the diameter being the longest side have a right angle at the perimeter." easy?
I think both are pretty easy, but the latter is a bit confusing.
 
  • #4
Blop said:
I think both are pretty easy, but the latter is a bit confusing.
Well, let me look up the correct wording ...
"If A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle."

Anyway, what is an example of something you find hard or boring? And why? I'm not quite sure what you're confronted with at your age in the US.
 
  • #5
fresh_42 said:
Well, let me look up the correct wording ...
"If A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle."

Anyway, what is an example of something you find hard or boring? And why? I'm not quite sure what you're confronted with at your age in the US.
Well, that makes sense.
I can't really put my finger on what exactly intimidates me (since it seems irrational anyways), so I'll just have to list off some of the things that we learn in advanced math 7.
Pythagorean theorem
Area of circles and cylinders
Pre-algebra
Irrational and whole numbers, integers
graphing (histograms specifically)
 
  • #6
And what is it? To memorize the formulas or their applications? And what makes histograms difficult? C'mon if you tell me, I might know some tricks which might or might not help you. But don't expect me to know, what makes a wooden fence difficult on which someone scratched some numbers (histogram).
 
  • #7
Your self-description reminds me of myself at your age. Each of those traits that you have listed are good and I hope you mainain them as I have (ADHD was my bane while growing up, but it has been attenuated since).

When I was your age, I hated math because the math that we were doing was truly boring. I also frequently asked my teachers "when am I going to use this in the real world". That question should have sent them into fascinating tangents in which they would tell me the actual mind-blowing concepts and capabilities that math enables us to have.

However, I didn't get the pleasure of experiencing such a speech until my first year at a private school. I remember 7th grade math, specifically, for being my worst year with math that I would ever experience. I found the content very dull. I was not incapable of the math at all, in fact, it didn't challenge me at all. However, I could absolutely not bring myself to caring about it or putting in the effort to actually do it.

I told my 7th grade math teacher that she was teaching the wrong content to us and that I was going to be an engineer some day despite the class. She told me, in her own words, that I was most likely not going to become an engineer. I started crying right there in the hallway (we were speaking in the hall outside of class while it was in session). Not the kind of crying that people do when they want attention. This was emotion that I could not suppress, and it overwhelmed me and forced me to cry. I'll never forget that blow, coming from a math teacher I was absolutely crushed in every way that a 13 year old could be crushed. It was my first time experiencing a self-doubt so severe that it affronted my most major goal in life. I was scared for my future regarding whether or not I would fulfill what I thought to by my only purpose in life (engineering).

I'm an engineer today. Its quite likely that she owns, or has owned, a machine that I have made tangible intellectual contributions to in my career.
 
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  • #8
Blop said:
Background: I live in the U.S. and I am in 7th grade, 13 years old. I have mild ADHD
I don't really hate math, per se, but I can't help thinking that I'm unfit to do anything related to mathematics. I enjoy geometry and abstract scientific problems, but struggle in areas such as basic equations and terms. Everything just seems like it flies over my head, and despite people praising me as a good thinker and philosopher, I feel deep envy for people who understand math and people who can be in high-level classes, because I find physics fascinating (even though it takes mathematical prowess). I always panic when confronted with math homework, and my mind goes blank.
I feel like I need motivation to do better.

When I was a student, no one had ever heard of ADHD, or it's brother ADD. I struggled my whole life trying to understand why so many people, who clearly, were no smarter than I was, did so much much better in school. When I was in my 40's, I went to see a "head-doc", because of depression. He informed that while he was not prepared to make a formal diagnosis, after only one meeting, that he was pretty sure I was ADD. A couple more sessions, and he made the diagnosis formal.

Here's what I can tell about how to cope, looking back at over 5 decades of living with ADD, but not knowing it, for the first 40+:

  • 1. Nobody is an expert at everything. Holding yourself up to others to make blanket comparisons is unfair to yourself, even if you do not have ADHD.
  • 2. Everybody has the potential to be an expert at something, even those with ADHD. Find something that you are good at, and enjoy, and pursue it with utmost vigor. Make it yours - Own it!
  • 3. Make incremental long-term goals for yourself - 6 month, 1 year, 2 year, 5 year, 10 year, "eventually". Reassess those goals a couple of times a year. Be REALISTIC, but also be optimistic. Think about step-by-step mini-goals to make each big goal achievable.
  • 4. Surround yourself with good people. I will leave the definition of "good people" up to you, since it will be different for everyone, but some examples of "not good people" would be those who abuse substances, animals or people. In general (not always) criminals would also be on my "not good people" list - but I have known some exceptions, so use your best judgement, and when in doubt, make the decision that is most likely to benefit you. Consult someone to help you decide, if you need to. (See #5, below.)
  • 5. Find a mentor. (One you can see and shake hands with.) A family member, professor, or if you attend a church, perhaps someone there. (While this forum doesn't always have good things to say about dogma, I think there is not much argument, when I say that there are some really good people who attend services at the their local church or temple every week.) Learn how to ask for help to find your way - do not expect a "hand-out".
  • 6a. Don't give up on school. No matter how hard it gets, do you level best, everyday. It is a fact that most of what you learn in school, you will forget, or never use - but when you get older, and look back at it, you will most likely be amazed at which portions you actually needed (but didn't think you would), vs which portions you thought you would need (but didn't). That is true for all subjects, not just Math and Science. Be a sponge - soak up knowledge wherever, and whenever you can, most especially outside of formal educational settings, where folks like you and I seem to learn easier.
  • 6b. ...and then there's the extension of that... If you have the means and the opportunity, go to college, even if it's a lesser community college - employers are often more interested in the fact that you went, and finished, than they are with what subject you majored in. (At least as far as the first couple of years of schooling...) Don't discount the possibility of a trade school - there are a lot of people with ADHD who are successful in the trades, according to my Doctor, myself included.
  • 6c. Never stop learning. One of the reasons I frequent this forum is to expand my knowledge. I also read science journals, and when I realize that my knowledge on some subject is limited, I google it, to see what there is to learn. Do I use that knowledge?...not very often, but being a lifetime learner is one way to level the playing field, for people like us. Most people just don't try to learn anything new, after they complete their formal education, and that gives us a chance to catch up! I consider them to be the Hares, and me to be a Tortoise - you have no doubt heard of that story?
  • 7. Never be afraid to fail. Look up the Home Run Stats for any heavy hitter in Baseball, and you will most likely discover that they also lead the league in strike-outs. The only people who never fail are the ones who never try. (They also never succeed...) Most of the valuable lessons I have learned in life were the direct result of falling flat on my face. Sometimes the lessons were humiliating, or downright painful, but the point is, I learned. Every failure is an opportunity to take a step back, and reassess your direction. (see #3 above) When it happens (and I promise you that it will...) get up, dust yourself off, laugh at the situation, and get back to work - this is a life habit that will benefit you all your days.
  • 8. No matter how busy life gets, take some time out for you. Go fishing, kite flying, hunting, run a marathon, build model ships, restore an old car, read a book...whatever you enjoy, spend a little time doing it, on a regular basis. You will be amazed at how much better you feel after a couple of hours of "me time", in a life full of pressure and deadlines.
  • 9. Find someone special to share your life with. (no hurry, you're young...) Having that special someone to look forward to seeing at the end of the day can make life worth living!
  • 10. Finally, get in the habit of forgiving yourself for your shortcomings. Acknowledge them, certainly, but give yourself a break. After all, nobody is an expert at everything...which takes us back to #1...
GOOD LUCK!
 
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  • #9
RogueOne said:
When I was your age, I hated math because the math that we were doing was truly boring.
I think this is a key point. You need to get to using math to solve real and fun problems in order to help your motivation.

You may also want to do some reading about physics that helps to motivate you to want to learn more about real world problems. I think this book would be at the right level to be entertaining and educational and motivating for you: :smile:

https://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Dstripbooks&field-keywords=thinking+physics&tag=pfamazon01-20

51YBVGVV19L._AC_US327_QL65_.jpg
 
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  • #10
watch the movie Gifted, and then you'll know why
 
  • #11
Blop, do not worry one bit. Your concern is enough to tell me that you've got a good head on your shoulders. At your age, I was the same way. I always kind of wanted to be good at math, but it didn't come "as a gift," not that I was bad...just a little below average at the time.

I don't think I started to appreciate mathematics until calculus in high school. I remember algebra 2 was the big hurdle for a lot of people making the LIFE decision whether to "hate" or "love" math forever. You will probably struggle, but once you beat algebra 2, the rest comes easier. (I had to drop honors Algebra 2 to go to regular because I was doing poorly. After that transition I was the best in my class for the rest of the year. That really boosted my confidence and I went back to honors maths the next year.) Trigonometry didn't interest me enough, so it had it's difficult moments too. But you'll get through it.

Math takes time to get good at, and don't let yourself fall into the category of people who claim they "can't do math". ANYONE can learn math. ANYONE. Period. Math is equivalent to a language. It takes a long while to master, but it comes to those who force themselves to get through it. Math is easier than all your other subjects in many senses...I'll let you discover why on your own...for now just chug through it.

The stuff you are learning now isn't meant to be picked up immediately [It didn't for me at least]. It takes time...Years. I didn't "master" all that algebra 1&2/trigonometry UNTIL taking calc 1 in COLLEGE (after previously taking calculus in high school)...Now I'm taking calc 3 and differential equations. Not to toot my own horn, but I've earned the highest grade in BOTH: my calc 1 and 2 classes in college, and have been the one people come to for help (calc 1: 100% /calc 2: 98%). I feel damn proud of this because I honestly feel that I fully understand the material (I'm truly not trying to brag, I'm trying to bring you confidence, because I was the same way as you)

The fact that you already show appreciation towards math tells me you will excel in it later. Just trust your gut, and if your gut is wanting you to like/be good at math. It will happen. I'd bet on it. Just give it time and work at it.

The best thing I could offer to you is this: try as best as you can to appreciate the beauty/simplicity of mathematics. And if you are not already, try to read on a daily/weekly basis. Getting into the habbit of reading is the best thing I ever did, and I got into it right around your age. It has endless benefits that you can look up on your own time. It might be tough at first, but eventually you will like it. "Never reading is just as bad as never going outside"

Sorry this reply was so long. Your post just struck something inside of me.

"Nothing in this world is worth having or worth doing unless it means effort, pain, difficulty... I have never in my life envied a human being who led an easy life. I have envied a great many people who led diffcult lives and led them well"

Best of luck,
Chris
 
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  • #12
You hate math because you are parroting it. Philosophy is easy to grasp. It is also very engaging and stimulates your brain to think on its own. In order to become good at math, you must find a way to similarly engage your imagination and get inspired to think beyond your textbook problems.

This is something that teachers are supposed to help with. Unfortunately you will rarely meet teachers who can make higher math seem interesting.

Few warnings: Do not ignore your textbook practices. You cannot think beyond textbook if your basic skills are not solid. Also, math will never become as entertaining and engaging as physics or philosophy.
 
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  • #13
Can you give concrete examples of problems from textbook and explain.

Try abstracting stuff from everyday world into math problems by going more and more universally applicaple cases.
 
  • #14
spero14159 said:
Also, math will never become as entertaining and engaging as physics or philosophy.

Maybe sometimes it can, though. Speaking as a former, seemingly life-long math-phobe, I can say that we are capable of surprising discoveries about our interests & capabilities at any age, whether young (e.g. teens) or relatively old (e.g. late middle age). This experience isn't unique to me. I have been very struck by some of the personal accounts I have read on this forum, including a couple in this thread.
 
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  • #15
An acquaintance of mine has Attention deficit. He started treatment a few weeks before entering a university program and starting his first precalculus course. After the first lecture, he remarked to me, "You know, math makes sense if you can pay attention."
 
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  • #16
Hendrik Boom said:
"You know, math makes sense if you can pay attention."

In, fact, I can say from personal experience, that "most" things do.

We had words/names for people that couldn't pay attention, before we labeled it ADHD/ADD. Silly-Nilly, Wiggle-Wort, daydreamer, wandering mind, undisciplined, stupid, mule-headed, stubborn, dim...and many, many more. I was on the receiving end of them, more than I could ever hope to count.

It was the teachers that knew how to reach through the ADD fog I lived in, and shine some light on the subject at hand that I remember and appreciate the most. Believe it or not, my high school Physics Teacher, who gave me a D+, will always be my favorite. That man just knew how to reach me, and while I could not remember formulas to do well on his tests, I learned an awful lot from him. His lessons on vectors improved my pool game, too. :wink:
 
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  • #17
spero14159 said:
Also, math will never become as entertaining and engaging as physics or philosophy.

Have to disagree here. I find math to be much more profound than philosophy due to its rigour, and more entertaining than physics due to it's lack of real-world constraints.

I wish somebody had told me those things much, much earlier though.

-Dave K
 
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  • #18
dkotschessaa said:
Have to disagree here. I find math to be much more profound than philosophy due to its rigour, and more entertaining than physics due to it's lack of real-world constraints.

I wish somebody had told me those things much, much earlier though.

-Dave K
I too prefer hard sciences when it comes to discussions and debates, but I rarely catch myself subconsciously thinking about math the way I think about biology, physics and other much more grounded subjects. This happens because physics, biology etc have lots of real world context cues, and our brain functions using temporal contexts.

How do you bypass this hurdle? Do you practice thinking in math?
 
  • #19
spero14159 said:
I too prefer hard sciences when it comes to discussions and debates, but I rarely catch myself subconsciously thinking about math the way I think about biology, physics and other much more grounded subjects. This happens because physics, biology etc have lots of real world context cues, and our brain functions using temporal contexts.

How do you bypass this hurdle? Do you practice thinking in math?

I think I'm just a weirdo. :D For me it's not a hurdle because I have always found abstraction more interesting than concreteness, and I think this predisposition is what dictates which way people tend to go. In philosophy terms I would be characterized as something like a platonist. I love the perfection that exists in the purely platonic mathematical world. I also love the lack of limitation. Physicists have to choose the subset of mathematics which conforms to the real world, but a mathematician has only to be logically rigorous and then there is no limit.

Obviously I love physics and all that, and lately have been doing more statistics as well. But I've been approaching it from more of an abstract pattern-searching kind of approach then somebody who was interested in applied math from the start.

Oh, and one tremendously liberating thing for me was to realize that there were so many types of math, that it was OK that I didn't really like them all. A grad student pointed that out to me when I was still an undergrad. I found myself as a math major being kind of miserable in calculus, and he said "that's ok. There's other kinds of math." He was right! I can do/teach/understand calculus of course, but it's just not my favorite subject. I like graph theory, algebraic topology and more "discrete" math, and it turns out professors have similar prepositions.

-Dave K
 
  • #20
dkotschessaa said:
I think I'm just a weirdo. :D For me it's not a hurdle because I have always found abstraction more interesting than concreteness, and I think this predisposition is what dictates which way people tend to go. In philosophy terms I would be characterized as something like a platonist. I love the perfection that exists in the purely platonic mathematical world. I also love the lack of limitation. Physicists have to choose the subset of mathematics which conforms to the real world, but a mathematician has only to be logically rigorous and then there is no limit.

Obviously I love physics and all that, and lately have been doing more statistics as well. But I've been approaching it from more of an abstract pattern-searching kind of approach then somebody who was interested in applied math from the start.

Oh, and one tremendously liberating thing for me was to realize that there were so many types of math, that it was OK that I didn't really like them all. A grad student pointed that out to me when I was still an undergrad. I found myself as a math major being kind of miserable in calculus, and he said "that's ok. There's other kinds of math." He was right! I can do/teach/understand calculus of course, but it's just not my favorite subject. I like graph theory, algebraic topology and more "discrete" math, and it turns out professors have similar prepositions.

-Dave K
I can sympathies with you regarding your viewpoint on calculus :-)

Unfortunately calculus carries a lot of weight in exams and that affected me in a negative way. I have always been fascinated by calculus though. Differentiation is easy, but integration is like a puzzle. I am slowly getting back at it.
 
  • #21
spero14159 said:
I rarely catch myself subconsciously thinking about math the way I think about biology, physics and other much more grounded subjects. This happens because physics, biology etc have lots of real world context cues, and our brain functions using temporal contexts.
What about composers/musicians, abstract painters/sculptors, & others interested in abstract qualities? To put it more generally, what you see as cues, whether you think these based on "brain functions" or some other rationale, would likely be meaningless to persons with different interests than yours; and vice versa.

Dangerous to generalize too freely from only our own experience.
 
  • #22
Haha! You share a very similar relationship with math as I do. It's probably a sickness, but it's not the end of the world. We do differ a bit; I can genuinely say that on some level I absolutely despise numbers and math. For me it was likely both nature and nurture as I can remember early on in primary school thinking about how math (the longest curriculum period) seemed to drag on forever. Also, I found the "mad minute" tests to be exasperatingly frustrating; the brain would simply lock up under the temporal pressure. All these bad memories formed a mental callous that completely turned me off to the subject as a whole.

I like to claim that's why I got into a line of work where a lot of numbers are more or less made-up so you don't have to take them so seriously. "Nominal" is a nice panacea if you're an individual who's too busy for numerical accuracy.

Seriously though, there is a large body of research out there relating how individual human brains handle broad concepts such as math, language, reading, ect. One common line of research connects mathematical ability with many other pattern-based natural aptitudes such as music, as well as people above toddler age picking up a foreign language. In light of these indications it might not be surprising that I never felt a passion for language class, which struck me as dull memorization, as well as music which, although I enjoy with an indescribable immensity, I have flat-out no aptitude for.

Finally, to foster a promise of a light at the end of the tunnel, let me tell you that as for my experience in formal education, what I found is that the further I went in math the more easily I found myself wrapping my mind around it. The tedium of algebra gave way to the beautiful and wonderful ways that higher maths and calculus can describe the touchy-feely world around us, and I was finally able to make an uneasy peace with numbers. It probably helped that I now had the tools to stick absurd values like infinity into equations... and get a result! Does it get any cooler?

If you're into history at all I would reccomend doing some background reading in Archimedes. One boggles at the stories of such a unique mind, it could change the way you view mathematics.
 
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  • #23
krater said:
I would reccomend doing some background reading in Archimedes.
EUREKA!
 
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  • #24
krater said:
...
Wow! - 5 years a member (to the day, I might add), and you only have 63 posts. You sir (madam?), are a consummate lurker, if ever there were one! :oldsurprised:
 
  • #25
Blank_Stare said:
Wow! - 5 years a member (to the day, I might add), and you only have 63 posts. You sir, are a consummate lurker, if ever there were one! :oldsurprised:

I prefer to think of it as laziness... I'm usually too exhausted to contend with most of the intellectual bruisers around here. Sadly the larger balance of my stamina lies in the physical and not mental realm. I always fought with math but pretty much wrote every research paper in about ten hours the day before it was due after leaving the library that afternoon with a stack of books. I consider that an act of adrenaline and not intellectualism. Think of it like the way guys are geniuses in combat.
 
  • #26
Seventeen-year-old high schooler here. I don't have ADHD and I can't say math has ever been hard for me, but I found it boring until I encountered a degree of abstraction. That happened this year, when I took a calculus course. Once I started reading proofs, I was hooked. I'd loved solving logic puzzles and performing the associated mental gymnastics since I was nine, but I never found that intellectual stimulation in math until I reached a certain level. You say you enjoy philosophy, so perhaps it's the same for you? Try pondering the order and beauty of the systems in your textbook, or, if you're feeling adventurous, read a layman's guide to Euler's identity. Maybe you just need to discover how exciting mathematics can be.
 
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  • #27
Hello Blop - welcome.

I am 50, there was no diagnosis of ADD or ADHD when I was in school, in fact due to this and a long diagnosed lazy eye - I was LD ( learning disabled - classified) until 9th grade. Today I have come to understand what I am good at and what I am poor at, and what things help:

I am better at logical connections and relationships - than facts(memory). For example I tested into College Calc 1 knowing 3 trig things T=S/C S(0)=0 and cos is the opposite. from that I would figure out everything else. I also seem to really hone in on anomalies - when things are out of place, for a while I was in field service, and this actually made me a very good troubleshooter.

As for the memory thing, look at what that does to your basic math classes. If you have trouble memorizing you can not get those 50 problem math sheets done in time. Then you get bad grades, then guidance does not think you are good at math.. etc.

I had a problem with blurting out things in conversation or in classes, or meetings. Now I keep a notebook so I can "let the thoughts out" and not interrupt others, or say things that I have not really thought about.

Try to figure out HOW you learn best - every way you interact with information and concepts is a possible path to memory. I am an AWFUL audible learner (listening), so, there is that notebook again. I try to at least jot down important things, I may never need to look at the notes again, but the Act of writing, AND then the ACT of reading / looking at the notes when I make them, takes something you only heard, and turnes it into 3 ways to interact with the material.

Look for WHEN during the day you are better at different things. You may find you study best just before dinner, but after dinner - forget about it.

Exercise ( proven to help ADD and Depression) - in 9th grade I joined swim team - so within 6 months I went from LD to honor roll.

I do believe the ADD issue DOES get better as you get older. I do not know if the severity diminishes, or you just find ways to cope. You have gotten a lot of advice here - and I believe you can see many of the people have faced similar issues. I have a good friend - brilliant man, pHD BioChemist, a Research Fellow for a Pharma co. and he feels the same way - especially about the concepts and relationships - can't remember where he put his keys. ( One time I left my wallet in the freezer - it can be frustrating)

My last point, I believe ADD/ADHD exists, I have it my son has it, but a lot of people just see it as a cop-out, or a marketing ploy by pharma to sell pills. It gets a bad reputation for a number of reasons, medicine may help or it may be necessary to function.
 
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  • #28
If math were just the grade-school procedures for performing the basic arithmetic operations, it would be one of the most tedious subjects around.

But there's another, very different mathematics, and that's what excites mathematicians: Math as the study of pattern. Pretty well the earliest-studied patterns were geometry, number, and music.
 
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  • #29
UsableThought said:
What about composers/musicians, abstract painters/sculptors, & others interested in abstract qualities? To put it more generally, what you see as cues, whether you think these based on "brain functions" or some other rationale, would likely be meaningless to persons with different interests than yours; and vice versa.

Dangerous to generalize too freely from only our own experience.

I was a musician (classical and jazz guitarist) for years before I went back to school for math. So yeah, possibly there is a certain thing about abstraction here.
 
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  • #30
dkotschessaa said:
I was a musician (classical and jazz guitarist) for years before I went back to school for math. So yeah, possibly there is a certain thing about abstraction here.

Nice. Definitely some patterns there.
 
  • #31
Hendrik Boom said:
If math were just the grade-school procedures for performing the basic arithmetic operations, it would be one of the most tedious subjects around.

But there's another, very different mathematics, and that's what excites mathematicians: Math as the study of pattern. Pretty well the earliest-studied patterns were geometry, number, and music.

Which is why I wish we would teach number theory and graph theory or some related topics from the start. Just turn the whole thing into a game. Forget about relating it to the "real world." The ability to do arithmetic is actually not a useful real world skill. The ability to recognize the underlying patterns behind things (like arithmetic operations) and to reason is a very useful ability in many aspects of life.

-Dave K
 
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  • #32
dkotschessaa said:
I was a musician (classical and jazz guitarist) for years before I went back to school for math. So yeah, possibly there is a certain thing about abstraction here.
Many mathematicians are musicians, as well. An interesting contribution can be found in the books of G. Mazzola:
 
  • #33
dkotschessaa said:
Just turn the whole thing into a game. Forget about relating it to the "real world." The ability to do arithmetic is actually not a useful real world skill. The ability to recognize the underlying patterns behind things (like arithmetic operations) and to reason is a very useful ability in many aspects of life.

This is exactly the position taken by the guy who wrote A Mathematician's Lament, an essay and later a book by Paul Lockhart, a math teacher at St. Ann's School, a K-12 school in Brooklyn Heights, NY. I assume most here know of at least the essay, given that it was publicized back in 2008 by Keith Devlin in his MMA column. The essay is here as a PDF and the book is available on Amazon and elsewhere. Book & essay attack traditional teaching along the lines given by @dkotschessaa, and suggest play as a far more suitable approach, e.g. treating math more like art class than history or science. He also has a more recent book Measurement, which is a self-teaching guide for adolescents or older; the reader is invited to "play" with math via geometric patterns such as symmetry, rotation, etc. I started that book but found it a bit daunting, plus it doesn't meet my current goals (re-learning high school algebra) so I put it aside.

In response to a couple of comments saying that learning mere calculation (as we are supposed to in grade school & secondary school) will never be anything but tedious - I disagree; I think it depends on your circumstances and attitude. If you are re-teaching yourself high school algebra, as I am for example, you can go at your own pace; and you can concentrate on those things you find interesting. This is similar to what I've read about the concept of "flow" as espoused by psychologist Mihaly Csikszentmihalyi: almost activity can support an enjoyable state of flow so long as the person doing it able to take charge of how they do it, can set their own goals & receive immediate feedback, and engage in it as if it were a game.

I will add that in my case, my ability to guide my own learning is probably much greater as an adult than it was when I was very young; and although I no longer have the full measure of wonder that everyone misses from childhood, I can understand certain difficult subjects better now than I could then. Also, I have been heavily influenced by a MOOC I took early on, Keith Devlin's Introduction to Mathematical Thinking, that taught predicate logic and simple proofs; quite a few of the proofs involved number theory. So now when I do my simple algebra problems in Gelfand and Shen, or Brown et al, I often go beyond the problem as stated and do a proof; and also look for interesting patterns. It's actually good that I've been so bad at math most of my life, because now even high school algebra is rich territory for me!
 
  • #34
If you're relearning algebra, look for patterns in the formulas.
 
  • #35
Hendrik Boom said:
If you're relearning algebra, look for patterns in the formulas.
Someone said that already . . . oops, it was me:
UsableThought said:
So now when I do my simple algebra problems in Gelfand and Shen, or Brown et al, I often go beyond the problem as stated and do a proof; and also look for interesting patterns.
 
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