One of my biggest pet peeves is when I try to explain something mathematical to a peer and they interupt, explaining that they “don’t understand it because I’m not good at math like you are.”

Good at math? This implies some innate differences in our analytical skills. If I’m “good” at math it’s only because I’ve spent tons of time hunched over my calculus book struggling to understand the concepts.

For a handful of geniuses out there, math comes naturally. The other 98% of us who are “good at math” are simply patient enough to stare at a problem for hours, hitting it with all of our favorite math tricks until it’s beaten into submission. Days of hard work and gallons of coffee does a mathematician make.

A false dichotomy has been created between those who are “good at math” and those who aren’t. People hide behind the excuse that math is hard for them before they’ve even put in the appropriate hours of sweat and toil. Spending an hour looking at a problem without seeing the solution does not mean that you’re bad at math, it only means that the problem is going to require more than an hour of your time.

Unfortunately, I think the structure of our educational system exacerbates the problem. Plenty of people who are really good at solving math problems need more than a few hours to do it. Giving people a night or two to solve a homework set or a few hours to complete an exam is a poor way of testing a person’s ability to comprehend complex math concepts and fosters the belief that your’e not good at math unless you can solve math problems quickly.

Just about anyone can be good at math given enough hours of hard work. True, some people solve a problem more quickly than others, but it certainly isn’t the case that quick problem solvers are good at math while everyone else is not.

To anyone who would argue that they’re “not good at math”, I would argue that you haven’t put in enough time.

“A mathematician is a tool for turning coffee into theorems.” – Alfred Renyi

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I can relate. I always get annoyed when people talk about how I’m ‘good at math’. Whenever someone says “I’m not good at math” I’ve always had a “Oh, so you’re an idiot” feeling. Not that I’m somehow better, it’s just always seemed like they’re saying “oh noz math r hardz 😥 im not gona even try tat stuf”. I always want to say “Yeah, it was hard for me too – when I stopped paying attention in class for a semester! Then I decided NOT to be an idiot and actually LEARN things, and it was the easiest thing in the world! RAAAAHHHH!” You put it much more… calmly, though. That’s probably a good thing.

So thanks for mentioning that. I think it’s probably lots of people’s pet peeve. <.<

Nearly anyone can solve most common math problems; computers can solve most common math problems. It’s a matter of following instructions. But I wouldn’t say that being good at following instructions, and by sheer perseverance solving math problems, really qualifies as being “good at math”; it doesn’t even really require understanding the problem (which is why computers can do it). Which, come to think of it, makes it all the more sad that many people can’t seem to do even this.

To my mind being good at math lies in the extent to which you can use your understanding of the problem to deviate from the standard recipe for solving problems, and solve them faster and better by adding your own flavor to it. Good math is creative math.

Of course most people don’t need to be good at math anyway; they just need to be competent at getting the answers to their problems.

I absolutely disagree. Math is all about internalizing, by bludgeoning yourself with problem after problem, mathematical identities and whatnot. After you’ve internalized them, “creative” solutions become obvious, but I’d say there’s little to no creativity in the more traditional sense here. This is not to disparage math at all. I love it myself. I merely think there are simpler, and more productive explanations, than any inherent aptitudes. People develop “creativity”, in this sense, by having internalized different ways of thinking about something, not by “being creative.”

Well, I in turn have to completely disagree with that.

Maths is a matter of skill, not knowledge. Internalizing all the identities in the world won’t tell you when best to apply them; anymore than knowing the keys on a piano and memorizing sheet music is sufficient to allow you to play it well. That’s a matter of experience and intuition.

If you don’t think there’s any “traditional” creativity in math, then I’m afraid you haven’t seen much real math, but mostly the kind better left to computers. Sure, creative solutions become obvious in hindsight when you’ve internalized them; so does any chord or music, or brush stroke, or line of poetry; once you know it everything is obvious. But finding them in the first place is another matter. Being good lies in going beyond what you know and have seen before; not in reproducing what you’ve seen before, that’s just competence.

And, honestly, I don’t recall saying it comes down to inherent aptitude. Like all skills, you can develop it a long way with effort. All I’m saying is that eventually getting an answer doesn’t make you good at math any more than playing a recognizable tune on a piano makes you good at music, or not poisoning your guests makes you good at cooking.

Apparently I can’t reply directly to you. WordPress doesn’t allow nested comments that deep? Weird.

I’d say creativity is absolutely a function of what you’ve internalized. You haven’t a hope of creative expression in any arts without knowledge of the technique as well as having internalized the more abstract elements of your art. It’s the same with math. Simply knowing and having memorized identities and laws is useful, but only in a very limited way. When you have internalized them, you can see the problem in different ways instantly, because the forms are transparently identical to you. That is to say, when facts are internalized, they are new ways of perceiving the world, rather than knowledge about the world. Given the new perception, old problems become trivial. It’s when the new way of seeing combines aspects of one’s knowledge in unexpected ways that we deem the solution “creative”. Fundamentally, however, there is no qualitative difference between a creative solution and a boring one.

As for whether I’ve seen only math better left to computers, I’d think not, but I also really can’t claim to very well studied in math. A smattering of algebra, logic, calculus, number theory, and statistics. Some category theory, when I feel like it. I certainly have seen examples of what you are calling “creative” in many places in math, but I simply disagree about the nature of this creativity. I think it’s simply what I described above, and nothing so special as we seem to like to think. Not that it’s any less special for that. =P

Totally. For years, I’ve been bothered by the broken way we assess mathematical ability via exams. I mean, when is someone going to grab you, stuff you in a closet, and demand you solve differential equations in real life?

Although the above point applies to a lot of sciences, actually.

Years of hanging around teachers (and thereby parents) led me to observe, at least where I’m from, that there is a tacit acceptance of the “not good at maths” argument. If a child finds maths hard, then their parents can be supportive of this viewpoint, encouraging their children to believe they can’t do maths. Course, that’s just anecdotal, so I don’t really trust it.

I agree, but I think that a lot of people lack a natural interest in math, regardless of a presence or absence of actual skill or aptitude. If someone can’t motivate themselves to do the work until they understand the methods, then they’ll never learn, even if on some level they do want to do the math. And then they’ll confuse a lack of motivation or concentration with an actual lack of skill. I think that’s where the “I’m not good at math” thing comes from. (This is also the opinion of my fiancée, who is a math teacher and probably hears “I’m just not good at math” more than most people.)

This is probably a general rule for most areas of skilled activity. From the physical to mental: Example juggling. People say you are good at juggling and how they are not. BS. If they are willing to practice the majority of people can juggle –even the blind (via contact juggling normally). A top few are naturally superb at it but most just grind away until they appear to novices as a natural.

So basically what I am saying is that it is a matter of people being lazy (or unmotivated or interested in other goals etc.) about learning competence in a skill set then using a simple mental defense against admitting that laziness to others via the passive-aggressive mechanism of complimenting another person’s “innate gifts.”

WARNING Diatribe:

Hmmm….

while I appreciate your perspectives on the laziness of your peers I have a certain level of empathy too. I recently fought my way out of this exact head space and since it sounds like neither you nor the other commenters have ever been stuck in this belief system it might be useful to hear the perspective of a formerly “I am bad at math” person to perhaps invoke a bit more sympathetic response.

I believed for years I was bad at math. I could never pass a timed test on multiplication for example. The standards by which math competency are measured (assume that “in US schools” is added as a qualifier to all statements) align poorly with my skill set.

When I faced these difficulties I would drill, for hours, often in tears of frustration, with one of my parents trying to memorize “basic facts” that my peers appeared to understand with no or minimal additional effort. So I certainly have a self perception of having tried to “do the work” as you so blithely describe it.

I believe looking both back at my own education and at my 12 year old daughter’s education today that teachers are ill equipped to help students struggling with math. That kids will either get it or not and if they don’t too bad for them. I haven’t noticed this happen in reading, but then I was an excellent reader as is my daughter, so it may be a blind spot.

What made me realize that I am not bad at math, but “bad” (meaning painfully slow) at calculations was trying to understand matrices for a personal interest in Quantum Physics. I wanted to understand the math behind a pop-sci volume on the subject I was reading and found an antiquated text at a library sale then attempted to teach myself matrices, even believing I was bad at math. Since I was learning fundamental principles and not calculation it made sense! For the first time ever I experienced a since of accomplishment and understanding in math. Took me 20 years to EVER have that experience in math, to feel like I “got it” just once. I have “good at math” friend to level of degrees in the stuff and so I began asking them to teach me stuff. I got walked through the basic principles of Calculus one afternoon, leaned the ‘ugly’ calculations hidden behind a number of equations and while I am not facile with these concepts I no longer fear them.

Add, subtract, divide, multiple… I am still painfully slow to this day, even when I’ve been practicing regularly. However hand me a formula and tell me how it works and I LOVE playing with math. I learned that “higher” math where one is not enslaved to odious calculation is grand and glorious and tons of fun.

But back to the “bad at math” people. Why on earth would anyone, but the most dedicated and stubborn, spend any time actually working on something they have been told they are inherently bad at? That is the sort of psychological self-brutality most people don’t go in for unless they see it as an inherent part of something else they desire more than they hate/fear math.

Personally I now feel sorry for people who believe they are bad at math, they’ll never understand how cool it is that some little string of numbers and symbols represents some amazing concept in a wonderful elegant (okay sometimes elegant) shorthand that can then be passed to someone around the world with whom one doesn’t even share a verbal language…

So pity the mathless, perhaps take the time to tell them they can be good at math if they work at it. Go so far as to offer to help, tell them how. Otherwise, from my perspective, you’re just contributing to the problem by maintaining an elitist hierarchical grip on the beauty of math. Be willing to sit down with the mathless and show them how to go from calculation to calculus. A patient enthusiastic math-o-phile can do wonders to break the illusion and emotional crap that goes with accepting the label of “I’m no good at math”.

The last time I went back to college, which I do intermittently, I got straight A’s in math for the first time in my life. As you say, it took work, but if I had still had the self perception as “bad at math” I doubt I would have tried as hard to understand. It’s psychology, not cognition that is at stake here.

END Diatribe…

Love reading your blog, it always makes me think

The issue here is fixed vs. growth mindsets. It’s not that people who keep working at something they’ve been told they’re bad at are necessarily stubborn, but rather, perhaps, they believe they will improve. I think most people have (and our society encourages) the fixed mindset in regards to math. This is just silly, anyone can improve immensely in higher level mathematics by practice and hard work.

That being said, I’ve also had the same problems. Arithmetic has only become easier to me by manipulating the problems algebraicly in my head and using the fact that I have a natural talent for memorization. But for things like counting stuff, for example, I’m still hopelessly lost after around seven.

In fact, from fifth grade until I dropped out of highschool my senior year, I only passed a math class once. Currently I play around with whatever math I want, teaching myself. I strongly believe it was only because of the school system instilling in me a belief that I was bad at math that I avoided it for years, until I had to learn it again for my interest in programming.

Also, I plan on posting about this motivation/ability issue tomorrow in my blog, so feel free to check it out if you’d like. Not spamming, just mentioning it since it seems relevant.

Oh, I meant to link to this as well. carol dweck seems to be the psychologist behind the bulk of the fixed vs. growth mindset research.

Staring at a problem for hours because you know success is inevitable is different than staring at a problem for hours and thinking there is a significant chance of never having whatever insight the exercise is trying to manufacture. I’m a “good at math” person, and I share your view about it being time spent in the material, becoming fluent with it. So it’s true, “good at math” is a function of “time invested.”

But “amount of time available for investment” is a function of expected payoff. While I do think that “math learned per hour” is less variable than most people assume, it does vary, and I think most people have a good idea where they fall on the range.

I tried to read this blog post but I’m not good at reading

ha

I not good at flying airplanes but if I take the test often enough I will eventually pass.

While I do agree that people are too dismissive of their mathematical abilities, I don’t fault people for preferring other areas of study. Why brow beat yourself into doing something you have no passion for when you could spend that time reading literature or some other such pursuit that comes more naturally to you? Of course some mathematical understanding is required for everyone, and it’s necessary for any sort of scientific understanding, but I’m not going to get angry at a poet or journalist who calls themselves bad at math.

I have a friend who used to teach high school math. When she started,the other teachers sometimes asked her what she taught. When she told them, she often got the reaction of them taking a step back and going “Oh. I don’t do math.” She started responding “Yeah? Do you ‘do’ reading?”

As someone who teaches English, I hear the exact same argument. The concept is the same: proficiency in English is just time invested, save the occasional genius.

So don’t worry; you’re not alone.

Yeah, well the same thing is true with writing – as a prior poster has just asserted. Really, inborn talent doesn’t enter into the picture until you talk about world-class efforts. Inborn deficiencies, of course (such as dyslexia), are another matter.

i thoroughly agree with this post. i would also like to add that everyone has an innate ability to do math, which is to say that, as an easy example, when you throw someone a ball, you subconsciously perform some very complex math. (i hate to say this, because it’s not quite true, i would argue that it is very much conscious, it just isnt represented in the brain in a numerical form which resembles the simple language we use in every day “maths”….all of the information is there, it’s just in a different form, which most closely resembles instructions for your arm, fingers, and torso, which when performed, throw a ball accurately)

that got longer than i expected….

at any rate, kindergarten students have actually been taught founding principles of calculus before, using experimental teaching methods, with amazing success.

Maths. Fascinating and currently unintelligible. So where would you suggest we start?

I’ve always wanted a reason to use the “Sorry, I am too lazy to understand you” excuse.

My personal irritation with people being bad at Maths is that it seems to be socially accepted for a person not to be able to do really quite simple mathematics whereas a person who struggles to read and write is looked upon as an idiot. I don’t see how basic maths is a less necessary skill than basic reading and writing, but that’s how it seems to be percieved.

My personal irritation with people being bad at Maths is that it seems to be socially accepted for a person not to be able to do really quite simple mathematics whereas a person who struggles to read and write is looked upon as an idiot. I don’t see how basic maths is a less necessary skill than basic reading and writing, but that’s how it seems to be perceived.

As one of the “handful” that you mentioned to whom math comes naturally, I would like to say that I have nothing but respect for individuals who “are simply patient enough to stare at a problem for hours, hitting it with all of our favorite math tricks until it’s beaten into submission.” I had the (mis?)fortune (and guilt) of being able to cruise through each of my math classes, with differential equations as the only exception. I discovered that I do not possess the patience to extend my math skills beyond those which come naturally to me. Also, the quote at the end of your post reminds me of one of my favorite definitions: “Programmer: n. An organism that converts caffeine into computer code”

I forgot to mention something: You touched on something I have believed for a long time, that the “education” system is flawed. I believe it extends into every subject, in that the students are only “tested” on their ability to regurgitate information only obtained (relatively) recently. The education system trains and tests our memories, not our knowledge. This isn’t to say that knowledge cannot be gained from school, just that it isn’t the driving force behind the methods.

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