8 ms·

Are all brains good at math?

35 points by dnetesn 4y ago

carapace 4y ago
I'm firmly of the opinion that kids are naturally born geniuses, and that our [lack of] child-rearing and educational systems traumatizes them into dullards before they get a chance to grow into their full potential. Clearly, it's possible to do much better than the status quo, E.g.: "Squeak Etoys, Children & Learning", Alan Kay > The projects developed in Squeak use a different and simpler kind of incremental mathematics that allows very young children to understand some of the key ideas in calculus. We have found that more than 90% of 5th graders not only understand “Galilean gravity” but are able to derive the mathematical “formulas” (actually 2nd order differential equations) using this alternative mathematics, and author a simulation that matches up very well with the experimental data. http://www.vpri.org/pdf/rn2005001_learning.pdf http://www.vpri.org/pdf/rn2005001_learning.pdf Or László Polgár > László Polgár (born 11 May 1946) is a Hungarian chess teacher and educational psychologist. He is the father of the famous Polgár sisters: Zsuzsa, Zsófia, and Judit, whom he raised to be chess prodigies, with Judit and Zsuzsa becoming the best and second-best female chess players in the world, respectively. https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3_Polg%C3%A1r https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3_Polg%C3%A1r
- jayant_kaushik 4y ago
  Just read the wiki. What a great inspiration Mr. Polgar. I have quiet a few nephew and nieces (all below 10) and that allows me to see the pattern. I see that we need to create a list of skills that a kid should know by a certain age and teach them- it sky rockets their level of confidence and they are able to achieve more faster in any sphere of life. Specialising in a few areas sounds good and till now I have thought about making my kids specialise in astronomy as I think by the time they turn 20, we would have landed on Mars and lots of ISS and talented people would be required to run them / go there. The second option is - AI ( but don’t know if we attain AGI, would the world need any talent in this space) So yes, I think about fatherhood even though I’m not there yet. Talking about education system, it’s we the people who have created it to outsource the job of rearing the kid to the schools. So they can learn the skills demanded by the world to survive. We do that to focus on our career, dreams, or just to chill. And schools are doing a terrible job world over. In
- ellyagg 4y ago
  Probably true. My daughter finished 2nd grade behind in math and with a deep dread of it. I had been too busy to realize what was happening. So I bought the California Common Core books for 3rd grade to understand the requirements. In our 10 minute car rides to and from camp every day, I was able to teach her all of it, without books or writing anything down. The way they teach this in schools is just so far from optimial it's heartbreaking. To give one concrete example, a huge part of 3rd grade here is memorizing the times and divide tables. After some quick experiments, it was obvious that all she'd need to do was learn to count each number series, which is MUCH easier than memorizing flashcards, and can be done anywhere. Once you can count the number series, times and divide problems fall out naturally with practically no memorization needed. The second big thing this year is word problems for those math facts. These word problems are so easy if you give the child the vocabulary and concepts to break them down in into their key parts. Instead, schools just leave it up to the courage and interest of the student to keep hitting their heads against the wall. We're on to 4th grade math now and she's a week into 4th grade. I'm keen to check the Alan Kay link. :)
  - boppo1 4y ago
    >learn to count each number series, which is MUCH easier than memorizing flashcards, and can be done anywhere. Once you can count the number series, times and divide problems fall out naturally Can you describe this process a little more clearly?
    - ciphol 4y ago
      I'm guessing - instead of memorizing "7*9=63" (and numerous other products), you memorize that the multiples of 9 are "9,18,27,36,45,54,63..." and the 7th one in that list is the one you want?
      - hinkley 4y ago
        And pick whichever one comes to mind easier. I am generally very good at taking tests but that was learned behavior. My origin story was a conversation about timed math tests with multiplication tables, and I was hit with the twin observations that you don’t have to do the answers in order, and if you can’t recall 7x9 but you can recall 9x7 it’s the same answer. All of a sudden I wanted to know what other tricks there were and boy did I look for all of them.
- tpmx 4y ago
  Are dogs also naturally born geniuses and its our lack of pup-rearing and educational systems that traumatizes them into dullards before they get a chance to grow into their full potential?
  - oblak 4y ago
    Unlikely, though dogs can appear stupid due to being dogs, hence having different drives in life. This may apply to anything besides dogs.
    - deleted 4y ago
      [deleted]
- stephendause 4y ago
  > I'm firmly of the opinion that kids are naturally born geniuses Do you mean that, relative to kids' intelligence today, everyone could do a lot better but not necessarily equally better? Or do you mean that everyone is born with roughly the same ability and that only some people succeed due to our child-rearing and educational systems?
  - carapace 4y ago
    Both. I don't actually know, of course, and there are obviously people who are born idiots, or savants, or both, eh? But generally speaking, yes, every more-or-less normal child could do a lot better. Could they all do equally better? Is everyone born with roughly the same ability? I believe so for two reasons: First, the ability to learn new abilities is the defining characteristic of being a human being. Humans are universal learners in the same way that Turing Machines are universal machines. So yeah, it seems to me that any human should be able to learn to do anything any other human can do (modulus raw physical parameters, of course. But even there there's a lot of flexibility.) Second, I believe that the spark of genius is a metaphysical or spiritual thing that is universally available to all people, you just have to learn how to "tap into it". Since genius is not intrinsic to the individual (no more than gravity or the Sun) we all have equal access to it, although not all of us realize it or make use of it in our daily lives.
- annyeonghada 4y ago
  >I'm firmly of the opinion that kids are naturally born geniuses Well, your opinion goes against the basics of genetics and reality. >and that our [lack of] child-rearing and educational systems traumatizes them into dullards before they get a chance to grow into their full potential. Incredible how that only some people get to be traumatized and others do perfectly fine. >László Polgár What is never mentioned in László Polgár's story is that he made the sister choose the activity they already enjoyed and were good at (natural talent, in other words), and by doing that he completely invalidates the results he would have liked to obtain: I bet that if he were to force the sister to study Physics or Chemistry or Literature or whatever he would have not achieved the same "extraordinary" results.
blackbear_ 4y ago
Is any of this specific to math, though? Or is it just that math "proficiency" is easier to measure?
mrkramer 4y ago
No, at least mine is not.
erdos4d 4y ago
Oh hell no. There is no other subject I am aware of that has the skill variance math does. Some people you cannot teach, others you cannot catch.
tpmx 4y ago
No.
- samatman 4y ago
  Succinct. I'll add that it's cruel to pretend that all are.
Raidion 4y ago
I would assume (like everything else) most people fall on a Bell curve, where there is higher level math that's inaccessible to most people, but the math for daily use is (almost by definition) pretty useful. I definietly think there are better ways to approach math, some like the theoretical perspective, some prefer the engineering approach "I need to solve this problem, and these are some tools to help us do so. I'm not "good" at math (and I could dig out old college transcripts to prove it), but I do have a math minor because I really enjoyed the experimental engineering/physics/comp sci stuff, but found math classes on their own really boring. I feel a lot of people would benefit a more holistic approach to math, starting with algebra/geometry. It's just a mess of graphs and equations, and I struggled to find a reason to care, though I was fortunate to have a brain (and the cultural conditioning) that made those abstract "puzzles" interesting. I got a B in Linear Algebra, and I still can't describe why you'd need that in the real world, while calculus/diff eq/discrete math were clearly tied to physics/thermodynamcis/computer science problems I knew. To bastardize a famous quote: If you wish to build mathematicians, do not divide the men into teams and send them to the forest to graph equations. Instead, teach them to long for the vast and endless understanding of a problem that they find interesting.
- sigstoat 4y ago
  > I got a B in Linear Algebra, and I still can't describe why you'd need that in the real world seems odd in a world full of 3D graphics and machine learning, which are built on heaping piles of linear algebra.
  - eindiran 4y ago
    I think this is one of the big advantages of a broad undergraduate education in math; the math that I use frequently looks very different from the math used by people in <insert other field>. I have essentially never used any calc/analysis/topology/geometry/number theory/etc stuff in the real world, but graph theory, stats, linear algebra, etc have come up a LOT. Which stands at odds with a lot of my college friends who need a completely different set of tools in their current work.
- ivansavz 4y ago
pigtailgirl 4y ago
https://wikipedia.org/wiki/Dyscalculia https://wikipedia.org/wiki/Dyscalculia -- from the article: Of course, some kids do have clinical learning disabilities that are not caused by anxiety, cultural myths, or poor teaching. Developmental dyscalculia, a clinical term for someone who has a math-related learning disability, affects about 3 to 7 percent of the population. This is the lesser-known analog of dyslexia, a learning disability related to reading, and the two conditions often occur together. --
knaik94 4y ago
I recognize the purpose of learning fundamentals but I think we do a great disservice to students learning mathematics by not emphasizing the power of computers and calculators in modern arithmetic. Many people with math anxiety see mathematical skills to be the same as mental arithmetic skills. Textbooks still focus things like von Neumann's ability ability to multiply large digit numbers in his head as a proxy for his math proficiency. While impressive, the technologies built on top of von Neumann's work make that kind of skill obsolete. I firmly believe that all brains are good at math but not everyone has had a teacher who will spend the time to teach the cognitive tools required for it. If we stop teaching calculators as "cheating" then a lot more students will be able to focus on the understanding the underlying concepts and will feel less scared about approaching new mathematical problems.
- buscoquadnary 4y ago
  I'd argue that not all brains are good at math but that they can be trained to be good at math. That's the problem we treat math like it is some innate talent, it's not it just requires certain ways and forms of thinking. Example: I was decent at math in HS, I didn't do very well because I didn't like doing the homework and quite frankly most people good at math aren't going to end up being public school teachers, so the explanations were always lacking. Well I went on learning programming on my own got a job as an SWE, then a couple of years later ran into a situation where I had to learn some new math. It was world's easier this time, because of my work with programming it all jelled immediately and suddenly clicked it all became very logical. I don't believe I suddenly became better at math, but rather I had developed certain thought patterns and ways of thinking that could be applied to mathematics.
  - syzar 4y ago
    Not everyone can learn calculus or even basic algebra. A person with a severe intellectual disability isn’t going to be able to learn these subjects. Between severely intellectually disabled and Einstein is a boundary between those who can and those who can’t. I don’t know where the boundary is but it exists.
abdulhaq 4y ago
Some people will learn maths much faster than others. A person of IQ 140 will learn calculus in much less time than someone with an IQ of 70. Even if everyone had infinite time I think we would all hit a limit, and that limit would span a very large range of ability. Hence the answer is no, not all brains are 'good' at math.
- yboris 4y ago
  It seems you're answering a narrow question focusing on "all". At this point, you may as well argue "there are people in persistent vegetative state, so 'no, not all brains are good at math'". This doesn't seem like a charitable interpretation of what the focus is on. If we are looking at the 95% of the population, excluding the obvious examples, your argument might not apply very much. I think the claim is also contingent on what is meant by math (how far do you need to go to be proclaimed "good" at it) - and I doubt calculus is a requirement. For your argument to work, you'd need to confront whether in fact at least 95% of the general population would be capable of understanding enough math for (and here we can differ on what "good" is, but I'd say something like) general understanding of algebra and its application towards regular life activities (e.g. understanding percents, exponential growth, loan interest payments, solving for an unknown, etc).
  - abdulhaq 4y ago
    Yes it comes down to 'good' meaning having achieved a certain level, or 'good' implying the existence of a significant spread in ability across e.g a central 95% of people. I've chosen the second meaning, and do believe the spread remains significant.
  - zmgsabst 4y ago
    At my university, almost all of the math majors and a fair number of engineering students graduated high school with calculus credits. I think the person is making a fair distinction that most brains are okay at math — and some at each end of the bell curve are good or bad at math. - - - - - A few asides: - really understanding exponential growth requires derivatives/rates of change - we do a bad job at conveying math subjects in education; you can teach kids the basics of abstract algebra and calculus if you tie the ideas to familiar concepts - we should definitely rework the curriculum in light of computers
bitwize 4y ago
My dog divides the food in her dish cleanly in half, eating one half now and saving the other half for later. I read somewhere that dogs can count up to about four, so taking half of something is within their bailiwick. I suspect that brains, human and otherwise, are better at math than we usually give them credit for.
RcouF1uZ4gsC 4y ago
I think an analogy to writing is helpful. Universal literacy is a very recent phenomenon. In the past, only a few elites in society could read and write. However, now the expectation is that everyone should be able to read and write and in developed countries there is above 90% literacy rates. Just like with math, there is a continuum of skills. Not everyone will be able to write like Hemingway or Faulkner or Proust. But, we can and should expect a certain level of competency from everyone. Same with math. If being good at math is being like Ramanujan or Noether, then I suck at math. However, there are a lot of stuff I know about math and can use it to solve a lot of problems. Once we make a certain level of mathematical competence expected and gear our educational system to achieve that, this question becomes moot. Yes, some brains are better at math than others. Some brains are better at writing than others. Some bodies are better at running than others. But we shouldn't let that stop us from having everyone achieve competence. My kid will never be Usain Bolt, but I will do my best to make sure he can walk and run and jump.
butUhmErm 4y ago
I’ve been thinking about this a lot lately; human languages are only 5,000 years old. Humanoid spatial reasoning, intuiting “enough heat, food, water” is a set of fundamental problems we evolved to survive. I’d say it’s more than just “all brains” and say “all bodies”. Maybe our brains gave us the ability to generate syntax to capture meaning but our bodies play a role in letting us know when we are “cold” as a response to external measure. A body is a gradient of spatial points, matter interacting with fields; not just the brain. Rigid physical models of the past must give way to updated awareness, an idea many have understood throughout time. People missing 80% of their brain have gone on to live full lives, graduate from higher education, succeed in a career. The brain is not the center of our awareness, merely a component.
jongjong 4y ago
I think it's mostly about how it's taught. As much as I like math, I really don't like math education. It's one of those subjects which is simple to understand conceptually but the terminology used to explain math is both overcomplicated and inadequate. The way people typically use English is too ambiguous to describe something which requires as much precision as math... And people who are good at math aren't particularly good at communication. Also, mathematicians like to keep inventing new words instead of reusing existing words; reading math articles on Wikipedia often requires a LOT of clicking through definitions to make sense of really simple concepts. Ironically though, when it comes to symbols, mathematicians love to reuse the same symbol for different things (depending on the specific field).
sinenomine 4y ago
There is an interesting, relatively novel body of research studying electrophysiological and genetic correlates of mathematical talent. And among it one can find preliminary evidence showing that even after controlling for general intelligence, there are are some nontrivial differences between individuals with mathematical talent and controls: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4052339/pdf/fnhum-08-00430.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4052339/pdf/fnh... https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3000871 https://journals.plos.org/plosbiology/article?id=10.1371/jou... Looks like mathematical aptitude really takes a different architecture of the brain.
exolymph 4y ago
Betteridge's law strikes again! Anyone who's done math tutoring knows that the answer is no.
- oblak 4y ago
  It doesn't take tutoring to realize that not all people can be good at thing. South Park had a nice episode about Kyle getting good basketball
avnigo 4y ago
Here's a fascinating related Numberphile video with Professor Brian Butterworth on the way our brains see numbers: https://www.youtube.com/watch?v=D1sPBCxlDQQ https://www.youtube.com/watch?v=D1sPBCxlDQQ
mjreacher 4y ago
One thing I think would be interesting to research is how different people are good in different areas of math. There's lots of anecdotal evidence[0] of people saying they tend to be good at either more algebraic subjects (say group theory or algebraic number theory) or more analytical ones (PDEs or measure theory) likewise I would extend this to also include geometric/topological subjects. In general especially as once gets into more advanced mathematics the abstraction level gets much higher quite quickly so it would interesting to know if there is any connection between brain structures and ability to grasp abstract mathematics. As an example I know a physicist who can tell you everything about general relativity and has a solid grasp of differential geometry but one time I was trying to teach him some mathematical logic and he just couldn't grok it no matter how many hours we spent on it. Likewise subjects that use category theory heavily (homological algebra/algebraic geometry for example) are known to be difficult to understand even for professional mathematicians in other areas. [0]: https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-pr...
neosat 4y ago
Rather than generalizing ability to "Math" as a whole, I think it might be more meaningful to state that individuals may differ in the type of problem solving their brain is better at (or at least they enjoy more and thus with effort get better at it). Enjoying and being good at abstract mathematical concepts of sets and number theory might be different than being good at geometrical manipulations or calculus. Some capabilities required for certain types of math problems might cluster closer with problem solving capabilities in other domains (e.g. chemistry or computer science or even writing) than they do other capabilities in math.

35 points by dnetesn 4y ago

I'm firmly of the opinion that kids are naturally born geniuses, and that our [lack of] child-rearing and educational systems traumatizes them into dullards before they get a chance to grow into their full potential. Clearly, it's possible to do much better than the status quo, E.g.: "Squeak Etoys, Children & Learning", Alan Kay > The projects developed in Squeak use a different and simpler kind of incremental mathematics that allows very young children to understand some of the key ideas in calculus. We have found that more than 90% of 5th graders not only understand “Galilean gravity” but are able to derive the mathematical “formulas” (actually 2nd order differential equations) using this alternative mathematics, and author a simulation that matches up very well with the experimental data. http://www.vpri.org/pdf/rn2005001_learning.pdf http://www.vpri.org/pdf/rn2005001_learning.pdf Or László Polgár > László Polgár (born 11 May 1946) is a Hungarian chess teacher and educational psychologist. He is the father of the famous Polgár sisters: Zsuzsa, Zsófia, and Judit, whom he raised to be chess prodigies, with Judit and Zsuzsa becoming the best and second-best female chess players in the world, respectively. https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3_Polg%C3%A1r https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3_Polg%C3%A1r

jayant_kaushik 4y ago
Just read the wiki. What a great inspiration Mr. Polgar. I have quiet a few nephew and nieces (all below 10) and that allows me to see the pattern. I see that we need to create a list of skills that a kid should know by a certain age and teach them- it sky rockets their level of confidence and they are able to achieve more faster in any sphere of life. Specialising in a few areas sounds good and till now I have thought about making my kids specialise in astronomy as I think by the time they turn 20, we would have landed on Mars and lots of ISS and talented people would be required to run them / go there. The second option is - AI ( but don’t know if we attain AGI, would the world need any talent in this space) So yes, I think about fatherhood even though I’m not there yet. Talking about education system, it’s we the people who have created it to outsource the job of rearing the kid to the schools. So they can learn the skills demanded by the world to survive. We do that to focus on our career, dreams, or just to chill. And schools are doing a terrible job world over. In
ellyagg 4y ago
Probably true. My daughter finished 2nd grade behind in math and with a deep dread of it. I had been too busy to realize what was happening. So I bought the California Common Core books for 3rd grade to understand the requirements. In our 10 minute car rides to and from camp every day, I was able to teach her all of it, without books or writing anything down. The way they teach this in schools is just so far from optimial it's heartbreaking. To give one concrete example, a huge part of 3rd grade here is memorizing the times and divide tables. After some quick experiments, it was obvious that all she'd need to do was learn to count each number series, which is MUCH easier than memorizing flashcards, and can be done anywhere. Once you can count the number series, times and divide problems fall out naturally with practically no memorization needed. The second big thing this year is word problems for those math facts. These word problems are so easy if you give the child the vocabulary and concepts to break them down in into their key parts. Instead, schools just leave it up to the courage and interest of the student to keep hitting their heads against the wall. We're on to 4th grade math now and she's a week into 4th grade. I'm keen to check the Alan Kay link. :)
- boppo1 4y ago
  >learn to count each number series, which is MUCH easier than memorizing flashcards, and can be done anywhere. Once you can count the number series, times and divide problems fall out naturally Can you describe this process a little more clearly?
  - ciphol 4y ago
    I'm guessing - instead of memorizing "7*9=63" (and numerous other products), you memorize that the multiples of 9 are "9,18,27,36,45,54,63..." and the 7th one in that list is the one you want?
    - hinkley 4y ago
      And pick whichever one comes to mind easier. I am generally very good at taking tests but that was learned behavior. My origin story was a conversation about timed math tests with multiplication tables, and I was hit with the twin observations that you don’t have to do the answers in order, and if you can’t recall 7x9 but you can recall 9x7 it’s the same answer. All of a sudden I wanted to know what other tricks there were and boy did I look for all of them.
tpmx 4y ago
Are dogs also naturally born geniuses and its our lack of pup-rearing and educational systems that traumatizes them into dullards before they get a chance to grow into their full potential?
- oblak 4y ago
  Unlikely, though dogs can appear stupid due to being dogs, hence having different drives in life. This may apply to anything besides dogs.
  - deleted 4y ago
    [deleted]
stephendause 4y ago
> I'm firmly of the opinion that kids are naturally born geniuses Do you mean that, relative to kids' intelligence today, everyone could do a lot better but not necessarily equally better? Or do you mean that everyone is born with roughly the same ability and that only some people succeed due to our child-rearing and educational systems?
- carapace 4y ago
  Both. I don't actually know, of course, and there are obviously people who are born idiots, or savants, or both, eh? But generally speaking, yes, every more-or-less normal child could do a lot better. Could they all do equally better? Is everyone born with roughly the same ability? I believe so for two reasons: First, the ability to learn new abilities is the defining characteristic of being a human being. Humans are universal learners in the same way that Turing Machines are universal machines. So yeah, it seems to me that any human should be able to learn to do anything any other human can do (modulus raw physical parameters, of course. But even there there's a lot of flexibility.) Second, I believe that the spark of genius is a metaphysical or spiritual thing that is universally available to all people, you just have to learn how to "tap into it". Since genius is not intrinsic to the individual (no more than gravity or the Sun) we all have equal access to it, although not all of us realize it or make use of it in our daily lives.
annyeonghada 4y ago
>I'm firmly of the opinion that kids are naturally born geniuses Well, your opinion goes against the basics of genetics and reality. >and that our [lack of] child-rearing and educational systems traumatizes them into dullards before they get a chance to grow into their full potential. Incredible how that only some people get to be traumatized and others do perfectly fine. >László Polgár What is never mentioned in László Polgár's story is that he made the sister choose the activity they already enjoyed and were good at (natural talent, in other words), and by doing that he completely invalidates the results he would have liked to obtain: I bet that if he were to force the sister to study Physics or Chemistry or Literature or whatever he would have not achieved the same "extraordinary" results.

blackbear_ 4y ago

Is any of this specific to math, though? Or is it just that math "proficiency" is easier to measure?

mrkramer 4y ago

No, at least mine is not.

erdos4d 4y ago

Oh hell no. There is no other subject I am aware of that has the skill variance math does. Some people you cannot teach, others you cannot catch.

tpmx 4y ago

No.

samatman 4y ago
Succinct. I'll add that it's cruel to pretend that all are.

Raidion 4y ago

I would assume (like everything else) most people fall on a Bell curve, where there is higher level math that's inaccessible to most people, but the math for daily use is (almost by definition) pretty useful. I definietly think there are better ways to approach math, some like the theoretical perspective, some prefer the engineering approach "I need to solve this problem, and these are some tools to help us do so. I'm not "good" at math (and I could dig out old college transcripts to prove it), but I do have a math minor because I really enjoyed the experimental engineering/physics/comp sci stuff, but found math classes on their own really boring. I feel a lot of people would benefit a more holistic approach to math, starting with algebra/geometry. It's just a mess of graphs and equations, and I struggled to find a reason to care, though I was fortunate to have a brain (and the cultural conditioning) that made those abstract "puzzles" interesting. I got a B in Linear Algebra, and I still can't describe why you'd need that in the real world, while calculus/diff eq/discrete math were clearly tied to physics/thermodynamcis/computer science problems I knew. To bastardize a famous quote: If you wish to build mathematicians, do not divide the men into teams and send them to the forest to graph equations. Instead, teach them to long for the vast and endless understanding of a problem that they find interesting.

sigstoat 4y ago
> I got a B in Linear Algebra, and I still can't describe why you'd need that in the real world seems odd in a world full of 3D graphics and machine learning, which are built on heaping piles of linear algebra.
- eindiran 4y ago
  I think this is one of the big advantages of a broad undergraduate education in math; the math that I use frequently looks very different from the math used by people in <insert other field>. I have essentially never used any calc/analysis/topology/geometry/number theory/etc stuff in the real world, but graph theory, stats, linear algebra, etc have come up a LOT. Which stands at odds with a lot of my college friends who need a completely different set of tools in their current work.
ivansavz 4y ago

pigtailgirl 4y ago

https://wikipedia.org/wiki/Dyscalculia https://wikipedia.org/wiki/Dyscalculia -- from the article: Of course, some kids do have clinical learning disabilities that are not caused by anxiety, cultural myths, or poor teaching. Developmental dyscalculia, a clinical term for someone who has a math-related learning disability, affects about 3 to 7 percent of the population. This is the lesser-known analog of dyslexia, a learning disability related to reading, and the two conditions often occur together. --

knaik94 4y ago

I recognize the purpose of learning fundamentals but I think we do a great disservice to students learning mathematics by not emphasizing the power of computers and calculators in modern arithmetic. Many people with math anxiety see mathematical skills to be the same as mental arithmetic skills. Textbooks still focus things like von Neumann's ability ability to multiply large digit numbers in his head as a proxy for his math proficiency. While impressive, the technologies built on top of von Neumann's work make that kind of skill obsolete. I firmly believe that all brains are good at math but not everyone has had a teacher who will spend the time to teach the cognitive tools required for it. If we stop teaching calculators as "cheating" then a lot more students will be able to focus on the understanding the underlying concepts and will feel less scared about approaching new mathematical problems.

buscoquadnary 4y ago
I'd argue that not all brains are good at math but that they can be trained to be good at math. That's the problem we treat math like it is some innate talent, it's not it just requires certain ways and forms of thinking. Example: I was decent at math in HS, I didn't do very well because I didn't like doing the homework and quite frankly most people good at math aren't going to end up being public school teachers, so the explanations were always lacking. Well I went on learning programming on my own got a job as an SWE, then a couple of years later ran into a situation where I had to learn some new math. It was world's easier this time, because of my work with programming it all jelled immediately and suddenly clicked it all became very logical. I don't believe I suddenly became better at math, but rather I had developed certain thought patterns and ways of thinking that could be applied to mathematics.
- syzar 4y ago
  Not everyone can learn calculus or even basic algebra. A person with a severe intellectual disability isn’t going to be able to learn these subjects. Between severely intellectually disabled and Einstein is a boundary between those who can and those who can’t. I don’t know where the boundary is but it exists.

abdulhaq 4y ago

Some people will learn maths much faster than others. A person of IQ 140 will learn calculus in much less time than someone with an IQ of 70. Even if everyone had infinite time I think we would all hit a limit, and that limit would span a very large range of ability. Hence the answer is no, not all brains are 'good' at math.

yboris 4y ago
It seems you're answering a narrow question focusing on "all". At this point, you may as well argue "there are people in persistent vegetative state, so 'no, not all brains are good at math'". This doesn't seem like a charitable interpretation of what the focus is on. If we are looking at the 95% of the population, excluding the obvious examples, your argument might not apply very much. I think the claim is also contingent on what is meant by math (how far do you need to go to be proclaimed "good" at it) - and I doubt calculus is a requirement. For your argument to work, you'd need to confront whether in fact at least 95% of the general population would be capable of understanding enough math for (and here we can differ on what "good" is, but I'd say something like) general understanding of algebra and its application towards regular life activities (e.g. understanding percents, exponential growth, loan interest payments, solving for an unknown, etc).
- abdulhaq 4y ago
  Yes it comes down to 'good' meaning having achieved a certain level, or 'good' implying the existence of a significant spread in ability across e.g a central 95% of people. I've chosen the second meaning, and do believe the spread remains significant.
- zmgsabst 4y ago
  At my university, almost all of the math majors and a fair number of engineering students graduated high school with calculus credits. I think the person is making a fair distinction that most brains are okay at math — and some at each end of the bell curve are good or bad at math. - - - - - A few asides: - really understanding exponential growth requires derivatives/rates of change - we do a bad job at conveying math subjects in education; you can teach kids the basics of abstract algebra and calculus if you tie the ideas to familiar concepts - we should definitely rework the curriculum in light of computers

bitwize 4y ago

My dog divides the food in her dish cleanly in half, eating one half now and saving the other half for later. I read somewhere that dogs can count up to about four, so taking half of something is within their bailiwick. I suspect that brains, human and otherwise, are better at math than we usually give them credit for.

RcouF1uZ4gsC 4y ago

I think an analogy to writing is helpful. Universal literacy is a very recent phenomenon. In the past, only a few elites in society could read and write. However, now the expectation is that everyone should be able to read and write and in developed countries there is above 90% literacy rates. Just like with math, there is a continuum of skills. Not everyone will be able to write like Hemingway or Faulkner or Proust. But, we can and should expect a certain level of competency from everyone. Same with math. If being good at math is being like Ramanujan or Noether, then I suck at math. However, there are a lot of stuff I know about math and can use it to solve a lot of problems. Once we make a certain level of mathematical competence expected and gear our educational system to achieve that, this question becomes moot. Yes, some brains are better at math than others. Some brains are better at writing than others. Some bodies are better at running than others. But we shouldn't let that stop us from having everyone achieve competence. My kid will never be Usain Bolt, but I will do my best to make sure he can walk and run and jump.

butUhmErm 4y ago

I’ve been thinking about this a lot lately; human languages are only 5,000 years old. Humanoid spatial reasoning, intuiting “enough heat, food, water” is a set of fundamental problems we evolved to survive. I’d say it’s more than just “all brains” and say “all bodies”. Maybe our brains gave us the ability to generate syntax to capture meaning but our bodies play a role in letting us know when we are “cold” as a response to external measure. A body is a gradient of spatial points, matter interacting with fields; not just the brain. Rigid physical models of the past must give way to updated awareness, an idea many have understood throughout time. People missing 80% of their brain have gone on to live full lives, graduate from higher education, succeed in a career. The brain is not the center of our awareness, merely a component.

jongjong 4y ago

I think it's mostly about how it's taught. As much as I like math, I really don't like math education. It's one of those subjects which is simple to understand conceptually but the terminology used to explain math is both overcomplicated and inadequate. The way people typically use English is too ambiguous to describe something which requires as much precision as math... And people who are good at math aren't particularly good at communication. Also, mathematicians like to keep inventing new words instead of reusing existing words; reading math articles on Wikipedia often requires a LOT of clicking through definitions to make sense of really simple concepts. Ironically though, when it comes to symbols, mathematicians love to reuse the same symbol for different things (depending on the specific field).

sinenomine 4y ago

There is an interesting, relatively novel body of research studying electrophysiological and genetic correlates of mathematical talent. And among it one can find preliminary evidence showing that even after controlling for general intelligence, there are are some nontrivial differences between individuals with mathematical talent and controls: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4052339/pdf/fnhum-08-00430.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4052339/pdf/fnh... https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3000871 https://journals.plos.org/plosbiology/article?id=10.1371/jou... Looks like mathematical aptitude really takes a different architecture of the brain.

exolymph 4y ago

Betteridge's law strikes again! Anyone who's done math tutoring knows that the answer is no.

oblak 4y ago
It doesn't take tutoring to realize that not all people can be good at thing. South Park had a nice episode about Kyle getting good basketball

avnigo 4y ago

Here's a fascinating related Numberphile video with Professor Brian Butterworth on the way our brains see numbers: https://www.youtube.com/watch?v=D1sPBCxlDQQ https://www.youtube.com/watch?v=D1sPBCxlDQQ

mjreacher 4y ago

One thing I think would be interesting to research is how different people are good in different areas of math. There's lots of anecdotal evidence[0] of people saying they tend to be good at either more algebraic subjects (say group theory or algebraic number theory) or more analytical ones (PDEs or measure theory) likewise I would extend this to also include geometric/topological subjects. In general especially as once gets into more advanced mathematics the abstraction level gets much higher quite quickly so it would interesting to know if there is any connection between brain structures and ability to grasp abstract mathematics. As an example I know a physicist who can tell you everything about general relativity and has a solid grasp of differential geometry but one time I was trying to teach him some mathematical logic and he just couldn't grok it no matter how many hours we spent on it. Likewise subjects that use category theory heavily (homological algebra/algebraic geometry for example) are known to be difficult to understand even for professional mathematicians in other areas. [0]: https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html https://bentilly.blogspot.com/2010/08/analysis-vs-algebra-pr...

neosat 4y ago

Rather than generalizing ability to "Math" as a whole, I think it might be more meaningful to state that individuals may differ in the type of problem solving their brain is better at (or at least they enjoy more and thus with effort get better at it). Enjoying and being good at abstract mathematical concepts of sets and number theory might be different than being good at geometrical manipulations or calculus. Some capabilities required for certain types of math problems might cluster closer with problem solving capabilities in other domains (e.g. chemistry or computer science or even writing) than they do other capabilities in math.