How To Become a Math Person, Vol. 1

MathnetAn article on Quartz makes the argument that we should not think of math ability as innate and ourselves as either “math people” or not.

This 2007 National Institutes of Health Public Access twin study, using relatively transparent methods, estimates that genes account for somewhere in the range from 32% to 45% of mathematical skill at age 10. That leaves 55% to 68% of mathematical skill to be accounted for by other things—including differences in individual effort. (Other estimates of the percentage of variation of mathematical skill in kids due to genes range all the way from 19% to 90%.)

How do we fix the problem? How do we act as though we have faith (in ourselves) so that faith will be given to us? It’s easy:

spend time doing math in the kinds of ways people who love math spend time doing math. Think of math like reading. Not everyone loves reading. But all kids are encouraged to spend time reading, not just for school assignments, but on their own. Just so, not everyone loves math, but everyone should be encouraged to spend time doing math on their own, not just for school assignments. If a kid has a bad experience with trying to learn to read in school, or is bored with the particular books the teacher assigned, few parents would say “Well, maybe you just aren’t a reader.”

Others have made this argument before. The woman who just won a Fields Medal, Maryam Mirzakhani, did not initially conceive of herself as a math person; like so many of us, she wanted to be a writer. She was only inspired to start studying STEM late in high school.

Is there hope, then, for a person like me? I have some decent bona fides: once upon a time, I liked math and science, went to computer camp, learned how to code. In school, I was a decent B or B+ student in Honors levels math classes through high school, but I had no confidence, none, and gave up as soon as I was allowed. Math felt vicious and alien. One year, early on, some test score bumped up me to Super Honors Math, and I was so scared by not understanding what was going on, and even more scared that I would be branded “stupid” if I acknowledged that I needed help, that I avoided homework completely and spent class time alternately in the Nurse’s Office with stress headaches and with the Guidance Counselor, a kind lady who gave up trying to ask me why I was there and just let me hang out. My terror became a self-fulfilling prophecy: I failed mostly from being too scared to try, and yet all I retained was the lesson that math = failure.

Innumeracy has real repercussions, still. I get flustered sometimes when faced with simple arithmetic, lest I botch a calculation that should be obvious. Part of the reason I’m shy about budgets, banking, and finance in general is that it involves numbers and so makes me feel like an outsider. Ridiculous, I know. Almost pathological. Maybe it’s too late for me to make a dent in any of this but I’m kind of inspired by this article, and by Maryam Mirzakhani, and I would like to try. I’m tired of being a Barbie-ish stereotype sighing, “Math class is tough!” And I assume that Step 1 is assuming that becoming a math person — or at least thinking of myself as someone who could become a math person — is possible.

I’m going to do some more research on what the experts recommend, talk to some “math people” about how they think they got to be that way, and report back. Have you overcome a sense that you yourself are not a math person? What worked for you?

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28 Comments / Post A Comment

Theestablishment (#7,469)

I’m not sure if I’m broaching into ‘new math’ territory but I was never a math person in school. I felt way too detached from the formulas they were trying to cram down my throat for no apparent reason.

I didn’t really start to ‘get’ math until grad school. The big difference from prior experiences was that the grad courses used math only as it was needed to illustrate or solve a practical problem. Basically, it became really clear to me that math was a tool/language that helped us to better understand the world in general. Once I figured that out, it was much easier to understand/remember calculations, formulas, and concepts.

Basically, I agree with the general concept of the above. Stop teaching math for math’s sake and start teaching math as a way to communicate and to solve practical and tangible problems.

@Theestablishment That actually would have gotten through to me as a student I think. I am pretty sure every kid who is struggling in math has exasperatedly asked “why do I have to learn this anyway?” Maybe it’s telling that I always did better at word problems than equations.

garli (#4,150)

@Punk-assBookJockey You could say that about any subject. Why do you have to read books you don’t care about? Why do you have to run laps in gym class? Why do you have to take an art class when you don’t care about how to make art?

@garli Sure that’s true. I guess for me though teachers/my parents had satisfactory (to me) answers about other subjects that I questioned, or I didn’t question them because they didn’t take as much effort for me. I never had a strong math teacher in secondary school so I never got those explanations for math, and it was challenging for me. In any subject, it’s hard to learn when the motivation isn’t there. I’m sure there are teachers who explain it in a way that’s motivating but I just didn’t have one.

Elsajeni (#1,763)

@Punk-assBookJockey Yeah, I think in other subjects there’s often a clearer connection between the specific work you’re doing (“Read The Scarlet Letter and write a paper explaining its themes”) and the general skills you’re practicing (reading for comprehension, academic writing), so you get less “UGH but when am I ever going to USE this, I’m not going to be a PROFESSIONAL SCARLET LETTER ANALYST when I grow up” — everyone understands that The Scarlet Letter is just what you’re practicing those skills on. But with math, that connection often isn’t made explicit, so students focus more on the specific thing they’re learning — “When am I ever going to use the quadratic formula? Who cares!” — than on the general skills of mathematical reasoning, data analysis, problem solving, etc.

garli (#4,150)

@Elsajeni That is hilarious to me because I was 100% in camp “I’m not going to be a PROFESSIONAL SCARLET LETTER ANALYST”. I loved reading but I hated how slow high school classes chewed through things.

I also might have picked a major in college at least partly based on fewest expected papers assigned.

annecara (#1,914)

I have such a weird relationship with math. On one hand, I always struggled with it, to the point of having to repeat pre-algebra in 8th grade…which ended up working in my favor when I started high school, because I had an extra-solid foundation for regular algebra and ended up getting straight A’s in all math except geometry (geometry sucks). And then I went to an Ivy League school and took Music Theory for my math credit because there was no way I was even going to bother trying to compete with all the engineers.

garli (#4,150)

I am a math person but I 100% believe that 99.99% of the world can be math people if they chose to be.

I’ve been tutoring my friends since I was 11 and have pretty much tutored kids from 1st grade through basic calc, including kids with a variety of learning disabilities. It’s really all just confidence, staying calm and following rules.

There have only been 2 people I couldn’t help and one of them showed up to every tutoring session drunk.

taylorqlee (#7,534)

@garli Absolutely this. As a fellow math person who has both explained to “non-mathy” friends very complex mathematical concepts, and seen them get it and asking some really interesting questions to boot, makes me feel like the whole “non-mathy” person thing is some variety of a confidence and exposure issue.

spex (#1,159)

@garli Confidence and exposure for sure. The public radio program To The Best of our Knowledge just did an episode about math literacy, & a journalist they interviewed made the great point that most people are exposed to and using language constantly, basically from birth. Even people who aren’t into language/literature academically still engage with it every day. So it’s not surprising if it’s more comfortable and comes more naturally!

fletchasketch (#6,453)

Math in the real world is very different than school math. I work as a statistician, and everyone knows that everyone else makes stupid mistakes that can wildly alter results. Some of those mistakes you will catch yourself, and the rest of the time you ask someone you work with to check your work – knowing that they will find something in your approach they disagree with, and sometimes they will find something that makes you start over from scratch. In school you are supposed to see all of your own mistakes, and people who see mistakes as personal failures get scared off by that. You also don’t typically see how other people approach the same problem (besides the teacher), which perpetuates the cycle of not being able to see your own mistakes.

Also, non-math people claiming that math is impossible is.so.annoying. 1)because it is the most common thing math people hear when they talk about their work, and 2) because it would be extremely difficult (approaching impossible) for me to my job if I hadn’t spent years studying how to math.

OllyOlly (#669)

I am not sure that I have overcome it, but I at least am at a place where I can question my idea that I am not a math person. I often try to reply in my mind what led me so far away from considering engineering for college, it is a huge regret for me at the moment. I did very well in my two years of AP Calc, and was even asked to take on a year of independent study so that I would reach Diff EQ by the end of HS…but I told myself I wasn’t a ‘math person,’ I couldn’t come up with answers without being taught the methods, unlike a select few in my class. I figured I would never succeed in an engineering program, I felt like a general good student, but not a math person.

Which is why this particularly hits me! Nothing wrong with needing to be taught the methods in school, that is how most everything works. (I am a woman FWIW)

Penelope Pine (#2,808)

Just popping in to say that coding skills =/= math skills, and to be good at one you do not have to be good at the other. But learning one will help you become more comfortable and confident with the other.

Remember that in The Social Network, Mark Zuckerberg asked his math nerd roommate for help with the “hot or not” ranking algorithm.

Theestablishment (#7,469)

@Penelope Pine no doubt. Another misconception is that you have to be a math person to be successful in finance or accounting. Absolutely not the case (with exceptions for the really technical modelers in investment banking).

Aconite (#6,401)

@Theestablishment Yes! This is true. I was resolutely NOT a maths person all the way through school, and gave it up as soon as humanly possible. This meant I also gave up sciences, which I loved, because in my brain I had an all-or-nothing, arts vs sciences thing going on and couldn’t conceive of doing both. Anyway then I did English at university and now I’ve been an analyst at an investment fund for a few years. I do maths some days and research every day. I couldn’t be a quant for an investment bank, for sure, but my level of “comfortable with numbers” (rather than “maths genius”) is just fine for a lot of roles in the financial sector.

Yes to all of this. I feel this way in both directions actually. I never felt like I was a math person and I wonder where this came from. And yet I felt like I didn’t have the talent for art or music either, because I had to work at it. I was good at reading and writing, I was always a good student, but if I had to work hard at it I got frustrated and gave up. I have heard recently an idea that kids who are told they are good at some things that come easy to them don’t realize that they can also be good at things they have to work for and I think that resonates.

EmilyAnomaly (#4,238)

@Punk-assBookJockey THIS. I did not have to work at school much until high school, and then it was hard when I started hitting roadblocks like Calculus because I actually needed to put effort into learning and I didn’t know how to do that. I gave up trying, barely passed the class and didn’t test high enough on the AP Calc exam to get any college credit. I wish teachers/my parents had told me that it was okay to struggle with something.

dotcommie (#662)

I never thought I was a math person, despite taking BC calc my junior year and getting a 5 on the exam. I’ve been taking a lot of stats and econ in grad school and to my surprise, I’m doing well, really love it, and want to pursue it more in my career. I think part of it is that I’m just smarter and more confident than I was in high school. Also, I work full time, so math homework seems like a fun diversion compared to my job. It’s like a logic puzzle. The stakes are also lower, since it’s no longer “if you fail this class you will never get into college or get a good job!!!1!”

maxwelljd (#7,340)

Ester (and all others) you might want to check out the wonderful series Steven Strogatz did for the New York Times in 2010. I’ll let him describe it (from the first part of the series):

“I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.”

http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html

Elsajeni (#1,763)

I have always been a math person, in the sense that whatever math I was supposed to be doing in school always came easily to me; I was not a math person in the sense of liking math until high school, partly because I did well enough in math to be singled out by teachers, including a couple of total jerk teachers who would use my test score to shame kids (boys) who scored lower. I was eventually converted to liking math by a really, really great teacher in high school.

Riaana (#2,520)

I think an important point to remember here is that “being a math person” does not depend on how closely your brain resembles a calculator. Working with numbers is my job, but anything past the six times table is just too much. We can outsource any and all calculations now! In my mind, being a “math person” now is knowing what numbers to use to answer the question you have (and so many questions can be answered with numbers!), and how to understand the numbers you’ve calculated.

honey cowl (#1,510)

I have a lot of feelings about math from which I shall spare the comments section of this article. To boil it down: I used to hate math, now I love math, I have always been good at math, why didn’t I see this at the time?

@honey cowl but see i’m fascinated by the PROCESS. you “yadda yadda yadda’ed” over the best part.

@Ester Bloom : I also have many feelings about this, and am also in the “used to hate math, now love math” group. I will un-yadda my experience for you.

A couple of years ago, I went back to school part-time to do the prerequisites for an engineering-style BSc. I knew I’d have to take math (higher math!), and I knew I was going to hate it.

I wasn’t bad at math in high school — I went up through AP Calculus, after all — but I didn’t enjoy it. It was rote, mechanical application of equations and theorems that seemed like they’d been passed down on stone tablets from some math Moses. As soon as I stopped using them, the theorems went right out of my head because they didn’t really mean anything. They were just tools for solving problems, and if you could remember what tool to use, you could solve a problem.

So I signed up for Calc I at the community college where I’d been taking courses, and … it was great. Our professor taught math as something to be thought about, rather than just as something to be done, and that made all the difference. She had two techniques, which I will share with you.

Her first technique (which I later recognized in the few really good math books I’ve read) was to teach every new concept three times, all the way through each time : once in standard mathematical notation with a derivation as needed, once visually as a graph or animation, and once as applied to a concrete problem. Her experience had been that most students learn best through only one of these approaches, and a student (at least at Calc I level) has to see it “their way” in order to learn it correctly. Most importantly, this also means that the student sees it the other two ways, and becomes familiar with translating from one to the other … which, of course, is what someone who “thinks mathematically” has learned to do.

Her second technique was to introduce each new theorem or concept not as an entity in and of itself, but rather as the product of a (historical) process. So, let’s say we were being introduced to L’Hôpital’s rule — she’d sketch out what the state of mathematical knowledge was at the time, and why L’Hôpital was interested in a certain problem, and then go on to work through the sequence of operations he used to extend previous work, and only then did she present the finished theorem. This was exactly opposite from what I’d seen in high school (theorem first, followed by its derivation) and was much more intuitive, as well as pretty closely replicating the experience of how mathematicians work.

So, tl;dr, but in high school, it was a bit like we were handed a toolbox full of tools and taught “you use a screwdriver for this job, and you use a hammer for this job” etc. etc. In this class, by contrast, we were learning more than just matching the right tool to the right job — we were learning how to think about tools and jobs in the abstract, and how to build tools when we needed them … which is exactly what mathematicians do. It was a very concrete exposure to what it means to really do math, rather than to just solve problems, and it absolutely made me a “math person”.

honey cowl (#1,510)

@Ester Bloom Sorry Ester! I appreciate you! But the billfold comment section != my therapist’s office sooooo I don’t wanna get too real.

Ester : Of course, I have a book recommendation! Back in 1965, a fellow named Roy Hartkopf wrote the best single math book I’ve ever read, titled “Math Without Tears”. I recommend it to everyone, without reservations.

In it, Hartkopf covers basically all the core aspects of higher math (complex numbers, derivatives, etc.). It requires no mathematical background, there are no problem sets, and it is a pleasure to read, but it absolutely will make you familiar with higher math.

Pick up a used copy, and if you’re like me you’ll read each chapter twice — first quickly, to get the structure of it, and second, more slowly, to work through the thought process he’s laid out on the page. It’s a very idiosyncratic work (imaginary numbers are taught in the first chapter!) but you will come away with much more than just a casual understanding of math and “mathematical thinking”.

callmeprufrock (#5,158)

I got through honors math and quite liked a lot of science classes, with the exception of phsyics, which busted my butt. But in my adult life I really flourish with applied math: calculating voltage load per circuit when drawing up lighting plots for theater, using trig and geometry to make plans for woodworking and bricklaying projects, understanding the complex financial instruments my colleagues deal with every day. I realize we had to learn the basics before getting to the fun stuff, but I wish more math homework was ‘in the field.’

aesir (#5,963)

There are very few people in the world who are naturally gifted enough to survive a PhD program in math or publish papers, but certainly everyone is capable of reaching a baseline level of competency (everything up to calculus and linear algebra). I didn’t particularly have strong feelings towards math growing up; it was just another subject that with a little practice, I did well on, just like English, science, history, whatever. It’s just like any other skill; time and repetition will eventually clarify previously impenetrable concepts, and I don’t think you need any innate gifts to achieve competency.

More than anything though, higher level or abstract math is just a language that you need to understand if you want to do science. That realization didn’t kick in until college, and now I’m in grad school for statistics, which is basically just math applied to other concepts that I happen to be interested in. It might help for students to receive earlier exposure to the things you can do (which is everything) with a solid foundation in mathematical expression.

At the same time, on a somewhat self-interested note, a lower level of mathematical competency in the population just means more job security for me.

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