Where Does Mathematical Ability Come From?

Why is it that some of us will study math textbooks for hours and barely grasp what is going on, while other people will grasp these same concepts while only skimming the textbook? To what extent are you born with mathematical ability? How much does your environment affect the development of your mathematical ability?

And most importantly, what exactly is mathematical ability?

I have a friend whose dad owns a construction business, and they built their own house together. As a result, my friend is naturally inclined to build and fix all sorts of things whether they are mechanical, electrical, or structural. It seems this natural inclination has translated into an insane ability to grasp and understand mathematical concepts almost instantly. I had several math classes with him, and he rarely did his homework and was mostly indifferent about how he did in school... yet he got an A in every math class he took. But again I wonder, is there really a correlation, or is it just a coincidence?

I have another friend who also has a tremendous ability to build and fix all sorts of things; he is a self-taught electrical engineer, computer scientist, and botanist, among other things. However, he had a complete and utter disregard for his schoolwork, and never got an A in a math class. In fact, he struggled with math in school even more than I did. Is it possible he has mathematical ability, but it failed to show in school because of how much he despised schoolwork?

My parents insisted I had tremendous mathematical ability and pushed me and pushed me to excel in math. They put me in a supplemental school for several years so I could learn more advanced mathematical concepts when I was younger, and get ahead of everyone at school. I never had much trouble with math as a result, but I never thought it was because I was good at math. However, due to excessive pushing, by high school I hated doing math, and this inhibited my ability to learn new mathematical concepts. I struggled through several years of high school and college math, despising every minute of it, always only doing the minimum amount of work required to get a decent grade.

After middle school I never got an A in an advanced math class, and I wonder, is it because I don't have the mathematical ability, or because of the utter lack of desire to do anything math related?

The only way I can answer the above questions is by finding what mathematical ability is, and where it comes from. So what exactly is mathematical ability?

Based on my experiences I believe it consists of several major factors.
1) Internal motivation to figure out problems
2) Desire to know how things work
3) The ability to think logically
4) The ability to focus on one thing for extended periods of time

Where does mathematical ability come from?
1) Natural talent- Some people are simply born with a superior grasp of logic and mathematics. I can't explain why except maybe through genetics.
2) Parental influence- If parents guide their kids in the right way they can maximize their kids' mathematical ability.
3) Education- Math classes build up one's mathematical ability by training kids how to think logically.
4) Motivation- The desire to be good at math and logic can go a long ways.
5) Environment- People that are less social have less distractions and may find it easier to find their internal motivation, and are better able to focus on one thing for extended periods of time.

Where does it come from? The instinct to survive. Simple mathematics is ingrained in our brain from birth.

Monkeys Do Math Like Humans

To see how far back more advanced capabilities such as addition might go, researchers at Duke University in Durham, N.C., focused on somewhat distant relatives of humans—rhesus monkeys. While the ancestors of chimpanzees—humanity's closest living relatives—diverged from us about 6 million years ago, humans and rhesus monkeys parted ways roughly 25 million years ago. In comparison, the age of dinosaurs only ended roughly 65 million years ago.

The scientists tested two monkeys and 14 college students on a math task where they had to add two sets of dots together. They were each shown one set of dots on a computer touchscreen for a half-second, and then another set a half-second later. They were then shown two separate clusters of dots at the same time, one of which was the correct sum of the first two sets. The monkeys were rewarded with Kool-Aid for choosing the right answers.

"When I first began training the monkeys on the addition task, I thought I would have to wait for many weeks before they understood the task," said researcher Jessica Cantlon, a cognitive neuroscientist at Duke. "We started the monkeys out on an easy version of the addition task, and the plan was to increase the difficulty of the problems gradually over time."

However, when Cantlon looked at the data from the first sessions, "it turned out that the monkeys were already performing the easy problems very well, and so I had to scramble to program the more difficult version of the task," she recalled.

Why they do it

Cantlon and her colleagues suggest math could help monkeys and other animals choose larger amounts of food or gauge the size of a rival group.

"Although we can never travel back in time to know exactly why or how this arithmetic ability evolved in humans, social battles might have something to do with it," she said. "Finding the perfect spot in the forest to stop and forage might also have something to do with it."

The researchers now want to learn more about what this primitive math system in monkeys is capable of "and whether it is the evolutionary basis of human mathematical thinking," Cantlon said. "We are also interested in whether this primitive mathematical system forms the basis of mathematical development in human children."

www.livescience.com...

Like Monkeys, Babies Know Math

In the study, seven-month-old babies were presented with the voices of two or three women saying "look." The infants could choose between looking at a video image of two or women saying the word or an image of three women saying it. The babies spent significantly more time looking at the image that matched the number of women talking.

"We conclude that the babies are showing an internal representation of 'two-ness' or 'three-ness' that is separate from sensory modalities and, thus, reflects an abstract internal process," said Elizabeth Brannon of Duke University.

www.livescience.com...

Pigeons Are Brilliant in Math

Pigeons have just tied with non-human primates in terms of math competence.

- Pigeons can not only discriminate quantities, they can also learn abstract mathematical concepts.

Pigeons may be ubiquitous, but they're also brainy, according to a new study that found these birds are on par with primates when it comes to numerical competence.

The study, published in the latest issue of the journal Science, discovered that pigeons can discriminate against different amounts of number-like objects, order pairs, and learn abstract mathematical rules. Aside from humans, only rhesus monkeys have exhibited equivalent skills.

news.discovery.com...

Now, I've never been good at math, as soon as it got complicated. I studied and tried but it never stuck. Other than geometry..... I don't know why, but then again I didn't go to the best of schools as a child. I guess that's why I ventured to the more creative side of life. I'm a designer, but then again a lot of that has to do with geometry, in a creative way.

But I think math definitely has to do something with brain structure or function. Those savants that are math geniuses or people that become math geniuses after a brain injury seem to be proof of that.

reply to post by WaterBottle


Thank you very much for your post. I realize I have a lot of questions about this and not a lot of answers, so thank you for your answers they were very helpful.

You have provided overwhelming evidence that we are born with mathematical ability, and that is it an instinct to survive. So now I ask, how does this mathematical ability manifest itself? Obviously if someone is extremely good at math, they have mathematical ability. But what about other things like logical reasoning, learning a new language, common sense, and an ability to build and fix anything. Does mathematical ability cause these things, or are they just correlated?

And can you have repressed mathematical ability?

What you described is exactly the way it worked for me. I got straight A's in math without trying. When i got my first tricycle i took it apart to see how it worked. My first watch, took it apart and put it back together, it worked. Our new color TV? I took it apart to see how it worked. My parents bought me a 1000 piece robot that you had to build. It was full of gears and wound up to work. I simply have to know how everything works and i have always been that way. Math, algebra, geometry, trigonometry, binary, have always been easy pretty much. When i went to school we were not allowed to use calculators either. I know i was born that way because as soon as i was able to use my hands i was taking things apart. So, I would have to assume it is not learned, you either have it or you don't.
Everyone has something that they excel at though.

I was a math-o-phobe until I learned to program, when using math was required to get my answer. The way particulalry advanced math is taught precludes that because it's taught as a pure theory rather than something that can be used to solve problems. I now know there's nothing "wrong" with me in terms of being able to understand math. It's just that I wasn't interested enough to pay enough attention when they zapped algebra on me in 8th grade.

But there's a larger issue here. If we play catch and I throw the ball to you, you can catch it. That's pure trignometry. Not only can you do it, so can your dog. Indeed, he may be better at it than you. The point is that our bodies perform perfect mathematical functions all the time. We don't use formulas. Just a little eye-hand coordination and we're there. It's just that this does not always translate well to "intellectual" study.

reply to post by schuyler


I'm not buying that hand-eye coordination is directly correlated to mathematical ability. I have a friend who is very good at math but can barely keep his balance while playing basketball. He frequently mishandles passes, shoots airballs, and misses the ball completely when going up for a rebound.

An interesting correlation I've noticed is great musicians I've known have all been good at math. I don't know if this stems from mathematical talent though, I think it has just as much to do with the ability to focus for long periods of time, and high levels of self motivation and initiative.

Musical ability has been tied to mathmatical ability, but there is a twist I believe. People who play by ear. Chris Isaak is one artist who can't read a lick of music. My son is the same way. He writes amazing music, but struggled with math in school. He read at age four, and is extremely gifted with language and writing, but struggles with math the way it is taught. I think some people see math differently.

Originally posted by Wang Tang
reply to post by schuyler

 

I'm not buying that hand-eye coordination is directly correlated to mathematical ability. I have a friend who is very good at math but can barely keep his balance while playing basketball. He frequently mishandles passes, shoots airballs, and misses the ball completely when going up for a rebound.

Not really the point. I'm not saying there is a correlation between abilities. I'm saying that your body performs mathematical functions all the time yet many people cannot, for whatever reason, do the mathematical formulas. In other words, there's a disconnect between the two, not a correlation. Your friend may be uncoordinated, be he still plays basketball. He doesn't have to be a star and coordination problems, for that matter, may have a completely different cause.

The point is that we've got mathematical functions physically. We perform trigonometric functions without needing any formulas. Your friend does catch the ball once in awhile, right? Well, his body computed a trig function to do so. He walks, and that requires multiple mathematical calculations per second to stay balanced and upright. When you catch a ball I throw to you, just once, reach out and grab it, you just computed a number of formulas analyzing speed and trajectory plus the movements of your own body, arm, and hand to get them to the place where the ball was going to be to intercept and catch it. It's not a trivial process. Try to figure it out on paper sometime.

The interesting aspect here is that we've actually got math down in many ways, yet so many of us can't seem to "put it on paper," as it were. I maintain there are a couple of reasons for that. One is the way we typically teach advanced math. Frankly, it's boring. Unless you find the process intellectually gratifying, there's little purpose to it. My personal experience was that once I had a real purpose and goal in mind, those regression equations became a lot more interesting. Combine a dull approach to teaching math with a little intellectual laziness, and voila! You have someone who "just can't do math."

But the larger question here is, What is knowledge? If you can DO something, but not express it in abstract terms, does that pertain to your ability and knowledge to DO it, or is it simply a matter of your inability to express it?

How to maximize mathematical ability:

Be exposed to it, and use it at an early age. Using my builder-fixer friend who is not good at math as an example, he has a tremendous aptitude for dealing with physical systems, but not with abstract equations. This is because he was exposed to the physical systems before he was exposed to the abstract mathematical concepts. As a result, he does not do well in school but excels with practical application. But the confusing thing is, can we call his ability "mathematical ability" then? Because he is not actually good at math, just the practical application of it. When you say "mathematical ability" I think of the ability to manipulate and understand abstract mathematical concepts in one's mind, and then apply it. My friend here does not seem to have that ability... so I would argue he has a "practical mind" and not a "mathematical mind."

Me, on the other hand, am neither. I had minimal exposure to physical systems, and forced exposure to math, and now am not too good at either. If I put my mind to it I can understand most physical systems and mathematical concepts, but it is only through tremendous effort; it does not seem to come naturally.

On the other hand, reading, writing, learning new languages, and thinking comes naturally to me. However, I don't know if I developed a creative aptitude as an escape from the terror doing math for hours on end, or if I really am a more creative person.

I don't see myself as naturally creative, however. I see myself as more of a mixture of a mathematical and creative mind... I'd like to call it an "analytic" or "philosophical" mind.

Now that I've thrown all these terms out there, "mathematical mind," "creative mind," "analytic mind," and "philosophical mind," I wonder if these are all separate talents or if they are all somehow interconnected...

Anyways, getting back to the main point of this post, how to maximize mathematical ability. Exposure, but non-forced exposure. Someone who is mathematically gifted has to find it on his own. He may not find it through math class in school... he may struggle in math class even with tremendous mathematical ability. But he may find it through music, logic, engineering, among other things.

This is the reason why I am a philosophy major. I was not born better at reading and writing than I was at math. Up until high school everyone knew me as the guy who was good at math, while I actually enjoyed reading and writing more, even though I was not as good at it. I tried harder in those subjects, and through initiative and self motivation I like to think I've developed a decent analytic and philosophical mind. And I firmly believe I was only able to do this because no one EVER told me to go do my English homework, or go read a book, or go write, or go get into advanced english class. I did that all on my own, so now I can take pride in what I've done.

reply to post by schuyler


I'm not sure what the purpose of mentioning physical mathematical functions. I just don't see how it relates to our mathematical ability. After all, there is math constantly going on in nature, with the planets orbitting around the sun and the tides of the ocean, but that doesn't mean nature has mathematical ability.

So I see you are saying the laws of nature are in mathematics... or... mathematics are in the laws of nature. Either way, being able to discover these mathematical laws while sitting in a math class seems to only be one manifestation of mathematical ability.