The biggest reason why some people are better at math/science than others

Interesting thread. I have spent a lifetime as a practicing mathematician/ statistician. I have a two observations/thoughts:

  1. I think being good in math is a function (no pun intended) of three things:
    • Desire/Attitude/Belief
    • Education/experience/exposure/repletion
    • You have to see a benefit or reward

(I think this is true for any skill – piano, tennis, singing, swimming, woodworking, welding etc)

If you have no desire to do math or no belief in yourself to do math or have a bad attitude – you are NEVER going to be good at math. Parents, friends and society in general send strong signals about what you can/can’t should/shouldn’t do.

It was not cool to be good at math when I was growing up in the 70’s and 80’s. TV/movies mostly had cops, lawyers and dr’s. The first mathematician character I can remember was on “A Different World" in the early 90’s. Today, math is more mainstream (Numb3rs, big bang theory, etc).

Math builds on itself – the more “tricks” you see the more math you can do. Being exposed to lots of problems and techniques for solving problems goes a long way to being good.

I’m not sure “natural ability” plays much of a role. I think people use this as an excuse to not engage (ie "I have no natural ability to do math - so that’s why I’m bad at math)

Growing up I was encouraged to do math and exposed to it. It was “normal”. My grandmother was a “computer” (not the electronic one we have today). She could add a column or 25, 8 digit numbers as fast as she could read them (about 10 seconds). It was a highly desirable skill when she was growing up. My mother was an actuary and my dad was a CPA. (I know I was adopted because I have a personality).

The rewards for being good at math are considerable. It has been my experience that all other things being equal – a person with significant math skills makes considerably more than a person without (at least on average). I had to find a job in the depths of three recessions (82, 91, 01) and had no problem.

  1. When people ask me “what can you do with a math degree (other than teach)?”. I respond It’s a lot shorter conversation to give you a list of what you can’t do with a math degree because math is everywhere (like it or not). Every career/job category has a mathematical end. For example:
    Insurance (actuary)
    Medicine (boiostatistics, epidemiology, …)
    Oil exploration (geophysics, reservoir engineering…)
    Logging (how to cut a log to get the most value out of it)
    Flying (scheduling planes/crews)
    Sanitation services (shortest path through a town to collect all the garbage)
    Acting (predicting the success of movies, animation)

I have never been stumped. But I will admit there may not be a lot of mathematicians scheduling sanitation workers.

Be good at math, combine it with something else that the world wants and you will have a long and successful career.

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I have always loved math. I credit my fifth grade teacher and my parents, particularly my dad, for the love, too. I am, like you, asked what you can do with a math degree and I respond similarly – almost anything, but I also outline a few high paying jobs, too. Engineering, computer science, statisticians, medical professionals, legal professionals, actuaries, cpa’s, architects, physicists, oil and gas people and pretty much every technical profession these days. That’s why STEM is so very important in our educational system.

Now for another question: What are your favorite math books?

Mine are almost anything by Amazon.com: Douglas R. Hofstadter: Books, Biography, Blog, Audiobooks, Kindle
I own many of them but my absolute favorite is Godel, Escher, Bach: Amazon.com

Mathematical puzzles are escpecially fun to me, too. Of course, I love computer science and algorithms, too. All require considerable math skills.

I, too, have had a very rewarding and successful career using math skills, especially in programming.
The best job in the world is one you love so much you’d do it for free but you’re paid very well for doing it. Most of my jobs have been just like that.

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Well, there are people who have dyscalcula (I think that’s the right word). I am better at math than my brother, in the school system of the '60’s and 70’s.

I remember chatting in the Student Union snack bar with a guy who just couldn’t grasp how calculus worked. I realized that I didn’t really understand thoroughly myself. But – the “baby” example (acceleration, speed, distance) worked so perfectly that I just accepted that it worked and worked the problems.

To some degree, I think y’all are looking at the world from your (our) rarified perspective. We’re all smart and trained, and we don’t mingle much with people that aren’t either smart or trained. I’ve worked enough jobs with folks from the other end of the bell curve to tell you that there are huge numbers out there who are not smart, and probably couldn’t be trained to this stuff either. But that gets into a crazy conversation about how we need to “fix” public education. Unfortunately, we’d also need to dump a bunch of money into that system.

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Which thinking leads to debates about that. Really, it needs motivated populous, not money. But money is what we know how to push around, so it’s what we tend to think in terms of. John Stossel had some interesting stuff out there where he does his research stories on School Choice. Here’s one. How to Save Failing Schools - YouTube

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I would be inclined to say is that what the school system needs is motivated and competent teachers, counselors, and other staff. Money is an enormous help in keeping people motivated.

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And to uphold my end of the bargain…
The school system DOES need those items you mention, but more importantly, support from the families/communities the schools serve. Money has been thrown at education hand over fist for decades, and the results continue to slide. Mercenaries can only be so motivated, and even when they give 110% to get the greater monetary reward, can only overcome so much friction. People who are fully in the fray, and committed to the cause, will achieve much higher results. To loosely paraphrase Simon Sinek, people will work for your money if you give them a job, but if they believe what you believe, they’ll work with blood, sweat, and tears. I know some of those teachers, but they can’t overcome the friction of the non-scholastic portion of their students’ lives in many (most, I think) cases, and no amount of money will make that happen; they can’t work any harder.

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BTW, agree wholly on the first point quoted, and wish i felt like i belong in the “We” noted in the second… I think we often believe a thing we find easy, we think others just aren’t trying hard enough, didn’t use the right book, didn’t practice enough… sometimes it really IS about natural talent. We seem to see that about sports (e.g. I will never match LeBron James on the basketball court, no matter how much motivation I have, coaching I get, or practice I put in), but seem blind to it in other aspects, like painting, reading, riting or maths.

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That’s a good point. If the parents aren’t committed to their child’s success, then teaching said children can be a bit bleak.

I’m not sure that all that much money has been thrown at the school system. Teachers aren’t well paid on any scale, especially if you look at it from an hourly perspective. Maybe tons of money has been thrown that way, but it didn’t go the right direction.

Anyway – I have Tons of Thoughts about education, but inadequate info about how the system “works” currently. It seems to be broken, but I don’t exactly know how to fix it. My assumption is that the public school system started from a flawed model, and nobody has gone back to the beginning to fix it.

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Too much politics in it now… try watching (or reading) Stossel"s stuff on the topic. You may disagree on some of his assertions and conclusions, but he usually quotes sources and throws around some figures you can double check…

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In my experience teaching adults who underperform in mathematics, the issue with algebra usually doesn’t set in until you move from linear equations to quadratic equations, general polynomials and complex numbers. I’ve found this to be true for most children as well; however, most of euclidean geometry thinks in highly linear terms.

You have points. Two points form a line and three points form a plane. You can use reasoning about lines to arrive at ideas about triangles (which can also created with three points) in a much simpler and easier to follow way since it corresponds to visual intuition and you can literally draw your proofs with a ruler and a pencil (as the ancient greeks did).

Once you have angles and triangles down, you go to circles and you show how you can use triangles to reason about circles (essentially what trigonometry is about). You can do all of this visually without going into a cartesian coordinate system.

Once you have circles, triangles, lines and planes down, it’s possible to go back to algebra and blast through a lot of it by understanding the relationships between the algebraic equations and geometry. This was actually why cartesian coordinate systems were popularized in western europe. People wanted to do analytic geometry in a coordinate system to greatly expand their capabilities; however, sometimes the synthetic approach is just better for reasoning since you can get lost in the algebra, as almost every algebra student in america can tell us.

If I could change the way algebra is taught, I would actually start with algebra that stays linear (and potentially include a segment on the quadratic equation) and then I would move immediately into geometry and trigonometry. More general polynomials and complex numbers can come afterwards, since the vast majority of our intuition about complex numbers and polynomials is incredibly geometric.

As far as concept maps go, I am a very, very big fan. I use them all of the time. Everyone should learn how to use them; they are provably more efficient if done correctly. If you treat mathematical transformations as mathematical objects in themselves (as you should), then the conceptual mapping method fits nicely when it comes to analyzing a given central concept we are focusing on. Practicing math problems is still a necessity even with conceptual maps, but having a deeper conceptual framework to practice with enhances your problem-solving. I do not find this to be in contradiction with the idea of comprehension in the WPM test, since that merely means that the number of iterations in constructing your concept map are fewer and each iteration is faster. I see concept maps as an extension of what I describe rather than a replacement.

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If people are smart enough to comprehend shapes and chords between sections of a curve, they are smart enough to comprehend university calculus. Dyscalculia does make things much trickier, but this is a relatively rare disorder and I don’t think we’ve applied enough resources to studying it in order to draw conclusions about whether there are fundamental limitations on the learning ability of those who have it. It could just be that there is a different way of thinking about the same concepts that appeals to them.

I agree that emphasizing geometry would help ease students into algebra a bit better. I think there are generally two kinds of people; those with a underlying talent for geometry, and those with an underlying talent for algebra. The first is more common than the second. I fall in the first category, and was drawing mechanical devices long before I knew what a square root was, and most other people I have tutored have fallen into that group. Only a few have fallen into the second group, with a stronger understanding of the abstract than the physical.

Then you have the smaller percentages of the population who have no talent for either due to medical conditions, and those who have an innate talent for mathematics itself (Euler for example).

I think one way to help this education problem would be to introduce the tools of drafting (compass, straightedge, ect) into art while kids are very young. Don’t require their use to pass, but simply put the tools in their hands to build familiarity and intuition. At the very least kids will show up to high school with the ability to draw a circle properly.

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There was not a child in my (public)K-5 who didn’t have and use these tools (granted they were the crappy kind you give kids that age)… are you telling me kids today do NOT use them as a matter of course?

No compass anywhere on these lists:

Are they considered to be prohibited weapons today?

No rulers or protractors either.

Perhaps schools are directing students to use a drawing program on their tablets or computers? That may make learning CAD easier in the future, but does little to help gaining an understanding of how geometry applies in real life.

When I was in school, rulers and protractors were provided by the school; however, they are only strictly necessary when we need to draw something with the correct proportions. You can draw an acute angle that looks like anything between 0 and 90 degrees and just say “theta is 45 degrees”. Obviously, this means that those who like to learn by drawing or doing are at a disadvantage.

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Interesting.
Perusing local school supply lists reminds me how miserable parents trying to work with schools can be.
Lewisville ISD is a very large district, and has this hub for their lists: School Supply Lists / School Supply Lists
Spot checking, elementary school lists do NOT generally specify any of these items, but Castle Hills 5th grade does specify a ruler.


(It also specifies 36 pencils, and I know one fifth-grader who would have found himself in a bucketload of trouble if he went through 36 pencils in a single school year! That’s 1 pencil each week! I don’t think I went through 36 pencils in my scholastic career unless you count art stuff, and those are separated out…)
Back from the digression…
9th grade Hebron does specify protractor and compass, but no ruler…

This time the student is allowed to simply supply writing instruments, rather than a specific number of them…
It surprises me that isn’t specified much earlier in a student’s career (the protractor and compass, not the unspecified # of writing tools).

No idea what Griffin MS in The Colony specifies, as they supply all of it, except for whatever the teacher specifies on the first day of class, that isn’t included in the “all inclusive backpack”…oh, and bring your school-issued iPAD…Except, y’know, if this is your child’s actual first day at that school, why would it have an iPAD… How I do not envy parents and trying to work all this stuff out! Good luck to all you educators out there, and the parents and children. May ye all land on positive common ground despite all the meddling and confusion!
Now, where DID I put my slate & slate pencil…

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I cannot recall exactly when, but my first exposure to a compass was well before 9th grade.

Kids are probably not taught what this is either:

I’ll never forget being taught how to bisect an angle; that was pure magic. Users of drawing programs do not need to know this.

Hand a kid a length of string and scissors; ask that the string be cut into two identical pieces. How many will know what to do? The definitive response is to double the string on itself and make the cut at the obvious spot. Some may ask for a ruler and a calculator…

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Sorry power series… The reference from Gauss method… in reference from summing all the number 1 to 100…
https://www.google.com/amp/s/www.wikihow.com/Add-Consecutive-Integers-from-1-to-100%3Famp=1

Actually, the biggest reason I read slow is my lips can only move that fact… the same goes for reading music… my fingers can only move that fast… as for math… They told me 1 + 1 = 2… and I asked… WHY? Turns out I was a lot smarter than they thought. Same with calculus… they told me how to find the derivative… I wanted to know why it worked and spend a few hours and invoking the binomial theorem (Which I also questioned) to find out why. I mean… if you JUST want the answer, you’ve got it heads and shoulders above me… if “Why” is important to you… welcome! I would never say someone is “BETTER”… I’d say, “DIFFERENT”.

If I am understanding you correctly, you are saying that we should explain “why” certain facts are true in mathematics when teaching these facts. At a certain level of sophistication, I agree that this is vital; however, below that level of sophistication, teaching people how to give proofs before giving them mathematical intuition is generally a recipe for disaster. Even at the highest levels of sophistication, building intuition and exploring simple examples for a long time usually precedes any formal attempt to prove a proposition.

The simplest proof for 1 + 1 = 2 that I’ve ever seen comes from the Peano axioms and that would require you to explain the concept of set algebras, recursion, recursive definitions and induction to a child. You would literally have to teach algebra before teaching arithmetic, which I could only see as unworkable since arithmetic is necessary for checking your own work in algebra. What we could do instead of giving children formal proofs is to instead use visual proofs, which work quite well. You can show almost all of the properties of arithmetic and algebra with a collection of stones.

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