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"I can't do math" (2001)

149 points by mejakethomas 13y ago

My favorite professor's take on the ever-increasing "I can't do math" statement.

Derbasti 13y ago
Indeed, it is often beneficial to state your preferences up front instead of sputtering nonsense trying to be "diplomatic". Everyone can interpret what I have to say about text editors much more usefully if I state up front that I love Emacs. The same goes for programming languages, frameworks, operating systems and math.
mjn 13y ago
I see his larger point, but the conflation of "understanding math" and "being able to do simple arithmetic" is something of a pet peeve. The latter may be a useful life skill, but is not very closely related to understanding mathematics. In fact it's not only non-technical office workers who can be proud of not being able to do it: if you walk into any math department you will find accomplished mathematicians almost gleefully recounting how bad they are at doing simple arithmetic. They can prove things about topological spaces but can't balance a checkbook! That makes the comparison to literacy more complex. Clearly mathematicians think mathematics is important, or they wouldn't be studying it. But many of them consider ability to do arithmetic, as a skill, essentially irrelevant, to the point where they don't even learn it themselves. Then a question might be: what is the relevant literacy-like skill? I think it comes closer to logic and analytical thinking than specifically mathematics, although understanding of statistical arguments fits into that category.
- Derbasti 13y ago
  I think being able to interpret common mathematical writing in your area of expertise is a valuable skill. I think this is what is meant by "understanding math". I don't know much about anything but signal processing, but I am able to read and understand vector/matrix notation and differential equations. This enables me to read most papers published in signal processing. Just like being able to at least roughly read most C-derived programming languages, this is a valuable skill. I have seen coworkers "not understanding" my work because it involved problem descriptions in mathematic notation. Frankly, it annoys the hell out of me.
  - ebiester 13y ago
    How about I write my comments in Turkish? It's your fault you don't understand them, after all. The art of programming, and of comments, is the ability to communicate to another human, and incidentally to computers. (I believe that was a paraphrase of Knuth.) If the terminology gets in the way of their understanding, then use a different terminology. (I can fight my way through a mathematics paper, myself. But why be obtuse in your communications?)
    - jarrett 13y ago
      Mathematics offers a standardized, internationally accepted notation for its various problem domains. Turkish is not the standard language of software comments. So I don't think the analogy holds.
      - frenchy 13y ago
        Neither is math. My guess is that you will find many more Chinese programmers who understand English comments than those that understand high-school mathematics symbols.
        jarrett 13y ago
        I would venture that any such programmers ought not work on a math-intensive domain like signal processing. Sure, not every programmer has to know high school math. You can, for example, do great work with HTML, CSS, and JavaScript without knowing high school math. But there are certain fields where math is unavoidable. Signal processing is one of them. And the internationally accepted notation for such math is part of what you're expected to know. BWT, I assume you're not saying China uses different mathematical notation. I wouldn't know about that. If so, then that does undermine my argument.
    - akiselev 13y ago
      "If the terminology gets in the way of their understanding, then use a different terminology." Literally the reason mathematics exists.
- mercuryrising 13y ago
  It's just a theory, but I think some mathematicians intentionally 'unlearn' or 'forget' arithmetic when they start to understand what math is about because people who don't understand math will ask them if they add and multiply all day. Theoretical mathematics is an entirely different beast than what most people think it is, so mathematicians get a lot of dumb questions about it. When someone asks if they add and subtract all day, if they say 'I can't even do arithmetic', people may be more inclined to rethink that stereotype.
  - VLM 13y ago
    "ask them if they add and multiply all day" A good example, but you should have thrown in an analogy to the general population thinking anyone who does anything with electronics is automatically a microsoft windows admin/personal trainer with special focus on virus removal.
  - SteveGerencser 13y ago
    My wife is one of those 'math people' that struggles with simple arithmetic. She has calculators and excel for things like that. But for her it wasn't a case of unlearning it. She struggled in school with arithmetic and didn't start to excel until they started introducing variables and all of the other aspects that separate math from arithmetic.
- klibertp 13y ago
  > what is the [maths] relevant literacy-like skill? I'm deeply convinced that the answer to this is easy - the ones that programmers use.
- pcl 13y ago
  > the conflation of "understanding math" and "being able to do simple arithmetic" is something of a pet peeve Agreed. I'm horrible at simple arithmetic -- I've just never gotten the knack for it, despite clear life benefits to being good at it. But I'm decent at math-with-letters. If I'm in a social setting and someone wants me to do the arithmetic on something, I'll happily say "I can't do math" because it makes more sense than saying the above. I bet there are others like me out there.
- hammock 13y ago
  > Then a question might be: what is the relevant literacy-like skill? How about "I'm terrible with names."
wtvanhest 13y ago
The key problem with math is that the learning keeps going and at some point, every single person fails to either have the ability or time to learn more math. Everyone becomes "bad at math" relative to other people. This same thing doesn't happen with reading because once you are a pretty good reader you feel like you have mastered it. 3 examples: 1) Kid who never completes pre-calc. "can't do math" 2) Adult who gets through calc, but doesn't go any further "can't do math"... like an engineer 3) Math PhD. who gets stuck on something they can't solve. Person 1 and 2 are both stating they can't do math, and both people are relatively right. Relatively being the key word. If we rephrased the way math is taught, it would never be labeled as math at all. This would box people in to saying things like "I don't do calculus" which would be correct in many cases, whereas it would be alarming if someone said "I can't add". Really, whether people say "I don't do math" or "my bad" doesn't really matter and being stressed over it is probably just as ridiculous as saying those things.
- CamperBob2 13y ago
  This can't be overemphasized. My favorite (apocryphal) Einstein anecdote is the one where a society matron approaches him at a party and exclaims, "I don't know how you can deal with all that math. I have so much trouble with math." Einstein replies, "Lady, you can't imagine how much trouble I have with it." s/math/computers, and that line comes in very handy in my own social life.
- adventureloop 13y ago
  I think you have hit this point on the head. It is very hard to compare mathematics education between countries. Eastern Bloc countries seem to go a lot further with the secondary level mathematics education, my point of caparison is to Scotland cavet emptor. I am constantly embarrassed by my level of mathematics, I like to play with 3D graphics on the weekend.
- dagw 13y ago
  I have a Masters in applied math, but I still put myself in the Bad At Math camp compared to many of my class mates, especially those who went on to pure math PhD's. And even among that group, I know a couple who would also classify themselves as Bad At Math because they couldn't pull off the more hard core PhD research topics and had to drop down to easier problems.
swinnipeg 13y ago
I went through this exact issue with a junior employee moved to my team to do some analysis that required a basic understanding of medians/means and a little intro stats. It took about 8 weeks of tasks with incremental mathematical challenges to overcome this, and at least reach the point where he could do his work, and apply the fundamentals learned to solving more complex problems. In the end he "could do math", the real issue was he had never "put any work into math".
shawndumas 13y ago
"I can't do math [at a university level]..."
jpwagner 13y ago
Indeed there is something wrong with someone saying "I can't do math..." but it is not what the author identifies. In blunt summary, the author says "you may not be able to do the specific math you claim, but don't worry I'll teach you." In my experience this is not at all what the complaint is saying and the solution "I'll teach you" is not at all what they are looking for. The comparison to illiteracy is completely off-target. In my experience, "I can't do math" is simply "I don't know" in disguise. Ask most children: "what's 300 times 248" and you get a knee-jerk "I don't know". Ask also "what's a balloon made of"; "I don't know". Same goes for many other questions that appear to them to have a definite answer. We excuse children for saying this, but it becomes less and less acceptable as an answer because we learn of tools for finding the correct answers. The real lesson that needs to be taught is: Your worldview of can/can't do math is wrong. Doing math is learning what tools to use after we've broken down our question to its core...kind of like everything else.
- chrisdone 13y ago
  Saying “I don't know” is a fantastic skill that children are born with but have it beaten out of them into adulthood and the beating never stops. I have deep respect for people who can say “I don't know.” That person is one step away from learning something new.
  - jpwagner 13y ago
    It's great when adults who do not usually say "I don't know" can admit to not knowing something. Other than that, I cannot agree with anything else you say.
devgutt 13y ago
But If a person says "I can't \"do\" mathematics" also could imply that the person would like to like it, or maybe the person at least respect the subject as important.
- easy_rider 13y ago
  how did these added slashes slip in?
  - fyi80 13y ago
    Java/C++ programmer who observed that English lacks Perl's qq operator or python's r''
timmm 13y ago
Neil Degrasse Tyson made this point. He basically said that imagine if instead of people saying at cocktail parties "I can't do math" they said "I can't read..."
- zecho 13y ago
  Sure, but "I can't do math" is a shorthand for "I can't do math beyond arithmetic, and even then, I often can't do that in my head." That is not equivalent to "I can't read." It is more equivalent to "I can't read Proust without getting bored and confused." The author in the OP acknowledges this substitution of "I can't" for "I currently struggle with." It's complaint about semantics that misses the point, I think. Rather than complaining when people say they can't do math, we should find out why they feel that way. I suspect a large part of the reason is that math education is pedantic and boring (memorizing axioms and doing rote calculations, when we should prove them, for example, or apply math in ways that doesn't involve trains leaving stations) and when people do speak their minds about their difficulties with mathematics, they often face snooty responses like this one in the OP, rather than a lighter touch.
  - hudibras 13y ago
    One of the OP's main gripes is that many people will gleefully, happily tell you that they can't do math. Nobody will ever admit to a stranger at a cocktail party that they're illiterate but being bad at math is, for some reason, a conversation starter.
- VLM 13y ago
  There are three other defense mechanisms at play: 1) I already made up my mind based on emotion or tradition or the salesperson was cute or whatever, and I was hoping the math proves my select decision is correct, but its not looking good and/or I've found a easier / better justification so "I can't do math" 2) I'm getting totally financially reamed over this (housing bubble / car lease / rent / mortgage / tuition / credit card) but its less painful to say I can't do math than admit I have awful financial judgment. 3) I suspect the result of this decision is going to be a minefield, and the other party is more traditionally mathematical than my side's ethnic / school major / gender / job title / whatever so I automatically come out ahead regardless of result by not making any decision and defer via "I can't do math" because first I don't have to put in the effort and secondly I can't be blamed.
sbashyal 13y ago
This reminds me of my experience with people in China when I was there. My friends there told me that many young people in China do understand English. But every time I approached them with "Do you speak English?" They usually took two steps backward and replied "no". They hesitate speaking English (because they find it difficult) despite knowing enough to serve my purpose. I have had similar experience with "Do you know maths?" in the US.
6d0debc071 13y ago
We seem to accept what's essentially illiteracy in all the subjects that require more precise thinking as the status quo. Most people don't seem to understand much about chemistry, physics, logic or computers either, and that doesn't get them in for a lot of stick. If people are poorly taught and have gaps in their understanding that are never adequately addressed, then I can see how they'd think that the problem was them - that they couldn't do maths. Couldn't make the connections that were expected of them and portrayed as normal functioning for maths. Maths is different to history, and many other subjects, in that regard. If you don't understand something in history, it probably doesn't have a massive list of dependencies that you're going to fail a lot of stuff in the future on. If you don't understand something in English, the worst that's going to happen is you have an esoteric interpretation of the text. You can still do those subjects if you don't really understand them, as long as you use the right buzzwords and hook them off the right things. I suspect part of the answer may just be that admitting you can't do history or the like is different to admitting that you can't do maths in that it's unclear what someone would even mean by claiming that they can do history. Certainly the claim that someone knows a lot about the broad strokes of history would rarely be justified these days.
- deleted 13y ago
  [deleted]
ssw1n 13y ago
Totally relevant: http://www.phdcomics.com/comics/archive.php?comicid=1356 http://www.phdcomics.com/comics/archive.php?comicid=1356
edtechdev 13y ago
It traces back to cultural and educational issues. Math has typically been taught devoid of any context or relevance to our everyday lives. Even in college, you just mindlessly plug and chug formulas to get by. Some students don't see the use in it, beyond perhaps the parts needed for basic financial literacy (which many do not have, either). Better and more engaging and relevant and effective ways to teach math have already been developed, such as Realistic Mathematics Education. But people actually say things like "I can't do math" in regards to all forms of literacy, I believe. It depends what standards you are mentally comparing yourself to, I guess, such as professional vs. social standards. "I'm not good with money, or I'm not good with the business stuff" - financial literacy "I can't write" - as in, I can't write books or novels or easily do other professional writing tasks. Again, there are pedagogical techniques that can help students write more, write better, and have more interest and confidence in writing. "I don't read" - most folks nowadays don't really read books or novels anymore, what with TV, movies, and the Internet. "I don't know computers" - how often do we hear that - that's computer literacy. I hear it less and less though nowadays. To tell you the truth, maybe it will be nice when one day people feel forced to admit "I can't code." Because that would mean that programming and computational literacy is something taught in most schools.
- derleth 13y ago
  > most folks nowadays don't really read books or novels anymore, what with TV, movies, and the Internet. Reading off of a screen is still reading. I don't know why some people think paper is magical.
  - will_work4tears 13y ago
    Sadly, most of what is on the internet counts as reading the same as watching a spongebob episode and "The Stand" both count as watching a 'show.' It's telling when writing a 3-4 paragraph article requires a ;TLDR section. Usually when a person says they are a "reader," or the like, are specifically talking about long works, not articles in Maxim magazine.
    - 13y ago
speeder 13y ago
I only think the author forgot that there are people that REALLY cannot do math. It might sound bizarre and weird, but I met more than once person, that did their best to learn, and were intelligent with many other things (one of these persons had a degree in law, another in international relations, and was doing a masters in international law), yet could not do 29/3 without a calculator... Or even worse, I knew people (in that case usually working with more low level work, like burger flipping) that even trying, or even if needed (ie: cashiers) cannot do it right even with a calculator, their grasp of math is so weak (even if they want to have a grasp) that they cannot even use the correct operations. Also the same apply to many other fields, I knew intelligent people that could not read, or that could not grasp history, or geography, and so on... People keep forgetting that brains CAN be very specialized, and be great with something, and terrible with other, and I personally believe that the old way of teaching professions (ie: throw the kid to work with a Master in that profession) was better because of that, currently you throw kids on the school, and the ones that might excel at some things that are not on school (like Music) reach adulthood thinking they are dump and they don't make a effort even in thinks they do have a talent to do.
- Jtsummers 13y ago
  I don't think the author forgot that, he seems to refer a lot to 'most people' and 'usually' enough to acknowledge that his assertion is not a truism. Besides that, it's a rant, those are often filled with generalities that need to be pared down before we can get to the real discussion.
- umsm 13y ago
  I don't think the author meant that people aren't walking calculators. I believe he implies that people don't want to understand how to evaluate a math problem. Most people that "can do" math still use a calculator; additionally, they understand what's happening and they can identify an answer that is absurd (because of a key-press mistake).
- com2kid 13y ago
  > It might sound bizarre and weird, but I met more than once person, that did their best to learn, and were intelligent with many other things (one of these persons had a degree in law, another in international relations, and was doing a masters in international law), yet could not do 29/3 without a calculator... There are multiple ways to learn even something like arithmetic. Some people can naturally juggle a lot of numbers in their head and can basically brute force problems. Others can break problems down into component pieces, work out each individual piece, and reassemble them into an answer. This requires a different type of mental juggling than the above. And then there are those who just have to memorize a lot of problems. When I was in school, we started off with memorization (multiplication tables and such), which requires a large time investment that I am sure many students did not make. (My peer group tended to stay inside during recces and practice our multiplication!) After that I think we were supposed to "naturally" progress to breaking problems down into parts, but that was never really covered all that well. From what I understand, other countries make this part of learning arithmetic very explicit. A good deal of this involves training ones working memory. Right at the end of college my working memory for numbers was amazing, I could do 3 digit divides in my head, and at one point I could even do a binary search to find logarithms down to a decimal place or two! But as with many other skills, they degrade from a lack of use. 29/3? I have a minor on mathematics. If you give me that problem, I'd honestly type "win-r calc 29/3 enter". Now days I have problems just adding up large strings of numbers, I play a bunch of D10 games and I have to actually do math rather than it coming to me instantly! > People keep forgetting that brains CAN be very specialized, and be great with something, and terrible with other, Well yes of course, but we choose what to specialize in! I really do believe that anyone can learn math if they put the time and effort into it. My math classes took 2-3 hours a day of studying a good 4 days a week in order for me to completely grasp the concepts being taught. Repetition of hundreds of problems, as much as I hated it, was the only real way to burn technique into my head, and even then most of those techniques have fallen by the way side! A few still bounce around inside my skull, but it has been a good 8 years since my last math class, so the amazing feats of mental gymnastics I could perform are long gone. On the flip side, ask me to design a test infrastructure for code sometime, and I'm right on it! How about a custom memory allocation scheme? No problem! Specialization indeed.
skittles 13y ago
I believe that lots of people really can't do math. Most people are fine until fractions. Many people never gain any intuitive feel for what "2/5 * 7/8" even means. It only gets worse with algebra. They can often learn the mechanics of fraction arithmetic and solving equations, but they will never understand how to apply the knowledge later in life.
mathiasben 13y ago
Surely if effort and attention to detail were applied most of these people could work their way through whatever math task was set before them. What they should instead be saying is; "I don't do math".
brudgers 13y ago
Telling people they can do math because they can add is disingenuous at best. "Ciphering" is the term that used to be used for figuring sums and such. Nobody pretended that was math. At the school house it was called "arithmetic". It was one of the three "R's" not something with it's own Phd granting departments at universities. People who say they cannot do math are speaking with the knowledge that they are looking up toward a massive intellectual edifice containing ideas they do not understand - whether they are looking up to high-school trigonometry or differential equations or Bayesian statistics is irrelevant. What is relevant is that they are not looking up to ciphering as unobtainable - at least not those people likely to be conversing causally or academically with a tenure track academic.
Irregardless 13y ago
People who say "I can't do math" are lazy? Sorry, but I think that's a gross oversimplification of the issue (which is also evidenced by the comparison to physical exercise) and the two assumptions fundamental to that opinion are just plain wrong. Namely: > So what do people actually mean when they say that they can’t “do” math? Usually they are really stating one of two things. First, that they don’t like mathematics. Secondly, that mathematics is more difficult for them than other subjects, and that it takes a great deal more effort on their part to learn it. He conveniently chose the two reasons that are easiest to dismiss (irony, anyone?). What he fails to account for is the fact that math education is so poor that many people don't truly understand what math is. Beyond arithmetic and algebra, they think it's some really complicated stuff with big numbers and funny symbols that geeky people with glasses do -- it's practically a foreign language to them, except it has a reputation for being much harder. Why is this? If I had to guess, I'd say it's based on the fact that math involves a lot of critical thinking and critical thinking is very difficult to teach. Those who attempt to do so often do it very poorly, which leads students to the false belief that math is extremely difficult. On the other hand, it's very easy to teach someone to memorize formulas and plug in numbers, so that's what we're most often taught in math class. That's good enough to get us through the standardized test so we can graduate from high school, but memorizing formulas and plugging in numbers is not "doing math". So I believe many people are completely justified in saying "I can't do math". What's more, people who "can do math" should be taking the blame for those who say "I can't do math" rather than using pointless semantics to wag a finger at them.
- diminoten 13y ago
  How is it my fault (as someone who "can do math") that someone else can't/won't do math? What do you believe I am morally obligated to do that I'm not doing with regard to someone else's preference/understanding of mathematics?
  - Irregardless 13y ago
    That's mainly directed at the person who wrote the essay (a math professor) and others like him who blame the students rather than themselves. I think he should be examining the state of math education in this country rather than chastizing the people it has failed.
ltnately 13y ago
Really good book on the subject that deals with why/ramifications of a society that's okay with "I can't do math" as a reasonable thing for an otherwise educated person. Innumeracy: Mathematical Illiteracy and Its Consequences John Allen Paulos http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405 http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its...
a_p 13y ago
My favorite story about how Ernst Kummer [1] did arithmetic, from Hoffman's The Man Who Loved Only Numbers[2]: "One story has him standing before a blackboard, trying to compute 7 times 9. "Ah," Kummer said to his high school class, "7 times 9 is eh, uh, is uh...." "61," one of his students volunteered. "Good," said Kummer, and wrote 61 on the board. "No," said another student, "it's 69." "Come, come, gentlemen," said Kummer, "it can't be both. It must be one or the other." (Erdos liked to tell another version of how Kummer computed 7 times 9: "Kummer said to himself, 'Hmmm, the product can't be 61 because 61 is a prime, it can't be 65 because that's a multiple of 5, 67 is a prime, 69 is too big-that leaves only 63.' ") " [1] https://en.wikipedia.org/wiki/Ernst_Kummer https://en.wikipedia.org/wiki/Ernst_Kummer [2] http://www.amazon.com/The-Man-Loved-Only-Numbers/dp/B004R6HXRQ/ http://www.amazon.com/The-Man-Loved-Only-Numbers/dp/B004R6HX...
- fyi80 13y ago
  > Erdos liked to tell another version of how Kummer computed 7 times 9: "Kummer said to himself, 'Hmmm, the product can't be 61 because 61 is a prime, it can't be 65 because that's a multiple of 5, 67 is a prime, 69 is too big-that leaves only 63.' That's how I do problems like that, too (I am not a genius mathematician), and it is exactly the sort of thinking that kids should be doing all through K-12. Estimation, intuitive reasoning, analogy, pattern matching, logic, etc.
  - rimantas 13y ago
    > Estimation, intuitive reasoning, analogy, pattern > matching, logic, etc. Alas, most of the things on your list require a pretty solid foundation to work. You need patterns already committed into your brain to do pattern matching and to see analogy, you need to have internalized experience for intuition to work, you need to have previous exposure for any meaningful estimation. All to often people forget foundation when they move to the upper layers and sadly sometimes this leads to thinking that foundation is not necessary. And now matter how you look at it there will always be bits of the foundation that require rote learning.
R_Edward 13y ago
I had a trig/pre-calc teacher in high school who I really respected. He had a catchphrase in his classes, especially in the earlier math classes. "In my class, there are only two kinds of people: those who love math, and those who are going to learn to love math." I only had the one class with him, but he left a huge impression on my life. He was convinced that computers were going to become essential to education, so he spent his department's entire budget for a year on two spankin' new Apple ][+ computers. Just set them on carts in his classroom and didn't touch them. He knew he didn't need to. Eventually, a handful of us approached him to ask if he could teach us to use them. "No," he responded. "I don't know anything about them myself... but they came with a tutorial, so maybe you could teach yourself how to write programs, and then maybe help me out." That changed the course of my life. I was planning to be a lawyer, catering to artists and performers. My time spent learning to write programs led to my taking a number of computer science classes in my undergrad, for the easy grades they represented, which then led to majoring in CS, and, eventually, opting for a career in software development. All of which is just to say that, if someone feels that they cannot "do" math, maybe they missed out on the right math teachers; those who understand kids and know how to motivate them and who have their own love for the subject matter and are able to infect others with it. If their math teacher(s) couldn't be bothered to make personal connections with their students, nor find any way at all to make math relevant to their lives, it shouldn't come as a surprise if they wind up being uninterested in "doing" math.
- duopixel 13y ago
  What a wonderful person. I sometimes take the time to contact teachers that have made an impact in my professional/personal life and thank them for setting me on the right course. It's a really simple gesture but they are always thrilled to hear they've made a difference.
btilly 13y ago
The underlying problem is two-fold in my opinion. #1 We focus on teaching procedures rather than understanding. Most people therefore view math as a list of memorized fixed procedures, and that's intrinsically very hard to remember and become good at. #2 Math is simple in a way our brains are not wired to be good at, yet we have a mistaken belief that simple is easy. It is not. Adding 1000 numbers by hand and getting the right answer is very simple, but hard. Recognizing my voice is very complex, but easy. Be aware that your brain is working in a way it is not designed to work and have patience with it. Otherwise you'll get frustrated, and mistake "It took me this long to understand something THIS simple?" for, "I'm stupid!" The result is that most people understand math in a way that is hard, and their experience of math is an experience of repeatedly confirming the message that they are stupid. Is there any wonder that they take that frustration out on the entire subject of mathematics?
haubey 13y ago
I think these people mean "I can't do arithmetic" which is much more acceptable, in my opinion. If you asked me to find a derivative, I could probably do it faster than I could find 123*26. It's not because the multiplication is harder, but because I don't have to do it in my head that often anymore. I have a calculator, and I use it. However, I have to do derivatives in math class everyday and at this point I'm probably faster at it. Not being able to do arithmetic is fine by me, I can't do it.
- learc83 13y ago
  That's just because there are fewer steps for finding a simple derivative. If you evaluate 12326 in your head, most people probably end up thinking through something like this 123 * 20 + 123 * 6 123 * 20 123 * 10 * 2 1230 * 2 2460 Now remember this part 123 * 6 100*6 + 20*6 + 3*6 100*6 = 600 20*6 = 120 3*6 = 18 600+120+18 738 2460 + 738 = 3198 Now compare that to taking a simple derivative. Although I could ask you to take the derivative of 123x^26.
e3pi 13y ago
When `she' said "I hate math". Read as: I hate the public school/university mathematics rote droning pretentious pedagogy ecosystem. I personally still retain a enthusiastic thread of the childlike wonder and delight 15 contiguous years in classroom minefields attempted to lame, but its `opportunity cost' has been expensive. Today's increasing autodidact free materials eliminates this cost.
RobotCaleb 13y ago
I never learned how to do long division by hand. That doesn't mean I can't do math, though. I could, of course, learn how, but I haven't needed to.
pfortuny 13y ago
It is not that people can't do math. It is that other people (who supposedly can but in fact cannot OR will not do them properly) insist on them doing the math they do not need (like computing the second derivative of the unemployment rate) or doing wrong the math they DO need (like with their mortgages). As long as people can add, subtract, multiply and basically understand what a division is, they can do math. The problem is they are scared at what other people tell them 'math' is. I am a mathematician, a professor of mathematics and witness to what I have said. Of course people cannot do 'math' when 'math' means being able to compute multiple integrals or roots of third degree polynomials. That is not 'math' that is UTTER RUBBISH EXCEPT FOR PROFESSIONALS in all caps. Really. You do not expect the average man to be able to write a sonnet with alliteration, second order metaphors and in iambic, do you? And they call themselves "literate". People are not lazy, they are scared. An the blame falls on BAD MATHS TEACHERS, in all caps. Really.
- piato 13y ago
  Hi, I'm a former (high school & middle school) math teacher. I taught various ages, but was only ever responsible for curriculum with age 10-11. We studied a lot of fractions, decimals, percentages & converting between them. There was a bit of angle stuff mixed in there, too. I love mathematics, so I think I'd be the sort of teacher you could see eye-to-eye with. What should I be doing differently?
  - pfortuny 13y ago
    Hi! That is exactly what they need: fractions are just a way to explain division and it helps them a lot (actually they are the basis for the "rule of three" which is the "fifth rule"). Proportions. Trying to start with square (?) triangles and the idea of similarity of triangles so that they can later (when 12-13) understand trigonometry (the basics) which, once again, is PROPORTIONALITY. There is little more to 'maths' than that. What I object to is the unnecessary abstraction. Getting 10-11s to perform correct computations is hard but exactly what they need: lots of exercises (no sweat no learn or whatever). You are a HERO. Really. In all caps My respect. I teach undergrads and this is way easier.
nnq 13y ago
I sympathize with the OP on all he says, but what does he mean by this, aren't these expressions synonymous, the only difference being the tone?: > although saying “my bad” when you mean “my mistake” comes close ...and going further on the linguistic ambiguity route, most people saying "can't do" actually mean simply "I hate it / I'm not good at it, and because it's so much effort for met o do it I'd rather not have to do it"... and the only bad thing in it is the uberannoying implied "I don't want to learn it, don't try and teach it to me"...
- ameister14 13y ago
  'My bad' is a foolish thing to get upset about people saying. People have said it for thousands of years and they're going to keep saying it. See: "Mea Culpa"
jcampbell1 13y ago
When I hear, "I can't do math...", it gets immediately translated in my head to, "My math skill are on the level of a typical 5th grader, and I don't want to be asked to do math because it will expose an embarrassing ignorance." The author's approach to people that feel this way is likely to humiliate them further.
piato 13y ago
One fun parallel - not to literacy, but to another skill at which artsy types are often better than mathematicians - is the oft-repeated, and completely acceptable, "I can't read minds". Lots of people can read minds. Not literally, of course, but they've put in the work (and perhaps it was work that they found easy and pleasant, much as many programmers found math) to be able to essentially tell what people want, don't want, are implying, will be offended by, etc. Yet I've certainly heard plenty of people, and especially STEM-types, making a point of pride about lacking this skill: "I'm a straight-shooter" and the like. There's aspergers and there's dyscalculia, but many STEM types who happily admit to lacking this skill are just like those whom the author bemoans - they find it difficult and uninteresting. And that's okay! But it's no truer, really, than "I can't do maths".
akiselev 13y ago
I do like the author's comparison to illiteracy. Language, just like mathematics, tries to solve the problem of communication but while language is more about the expression of emotions, thoughts, and feelings, mathematics is meant to describe precise ideas and abstractions in a quantified way. While language can be ambiguous in how it relays our true intentions, mathematics is anything but. It is the only method humanity has that, through experiment and observation, can help us reach for and perhaps even attain absolute truth. Just like reading/writing, you don't learn mathematics (real maths, not arithmetic) to be able to scribble symbols on a piece of paper. You learn it to develop a way of thinking that promotes certainty and helps you develop and understand complex abstract ideas that describe how the world works. When you dive deep into math (or programming for that matter), you don't just learn a subject, your brain actually reconfigures itself and fundamentally changes how you act and think. This effect, called neuroplasticity, functions pretty much until you die so it's never too late to learn math. When someone says that they can't "do" math it says nothing about their intellect. All it says is that they didn't like the mathematical equivalent of "The Cat in the Hat" taught in primary school and are now going to live (many quite proudly) without the mental faculties to express and grok abstract and complicated ideas and systems. Sadly, now more than ever, we need each and every human to have these faculties if we are going to survive and thrive as individuals and as a species.
300bps 13y ago
This sounds like an extension of the recently widely covered practice of not telling your kids they're smart. Basically, studies have shown that praising your child for intelligence as opposed to hard work can cause them to undervalue effort. They start to separate subjects into things they are "good" at and things they are "bad" at. They then avoid the things they've labeled themselves as bad at doing. On the contrary, praising a child for their hard work seems to not be associated with this same negative behavior. http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-shouldnt-tell-your-kids-theyre-smart/ http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-should...
mberning 13y ago
There is an idea that pervades their rant that all people are more or less equally educable in all subjects. In my experience this is simply not true.
gyardley 13y ago
"I can't do math" actually means "I both don't like to and don't believe I really need to do any math, so I'm going to say 'I can't do math' to cut you off before you propose I do any." Of course college-educated people can do a little math - but they don't like to, so they don't.
Tycho 13y ago
Maybe they should teach it as 'modelling' instead of 'mathematics.' When you start thinking of it in terms of interpreting real world dynamics and relationships, curiosity takes over and it becomes a much more compelling subject to learn. IMO.
losethos 13y ago
after calculus comes DIFF EQ After DIFF EQ comes nonlinear control systems I got an A in nonlinear control systems. God says... servants, Have me away; for I am sore wounded. 35:24 His servants therefore took him out of that chariot, and put him in the second chariot that he had; and they brought him to Jerusalem, and he died, and was buried in one of the sepulchres of his fathers. And all Judah and Jerusalem mourned for Josiah. 35:25 And Jeremiah lamented for Josiah: and all the singing men and the singing women spake of Josiah in their lamentations to this day, and made them an ordinance in Israel: and, behold, they are written in the lamentations. 35:26 Now the rest of the acts of Josiah, and his goodness, according to that which was written in the law of the LORD, 35:27 And his deeds, first and last, behold, they are written in the book of the kings of Israel and Judah.
droidist2 13y ago
Yeah, it's interesting that people will proudly admit "I can't do math" but you don't nearly as often hear them say "I don't understand politics, government, or world affairs." People will do their damnedest to appear knowledgeable about those things.
- chrisdone 13y ago
  That's true. “I don't really understand national politics in any deep way,” is something I've said many times and has been responded to often with “me neither”, but I'm quite sure had I not said it, the person would've kept quiet about their ignorance and feigned insight in other conversations.
egutesman 13y ago
Seymour Papert (http://www.papert.org/ http://www.papert.org/), inventor of Logo in his seminal work Mindstorms (1980) did a very good job on analyzing this phenomena. Not only he did a great analysis on children but also came up with Logo, one of the best paradigm-changing environments for teaching math. On his second book, The Children's Machine (1991), almost 11 years later he went deeper into the issue of computer's at schools and what should or shouldn't be taught at school on math lectures. There's a nice section on an experiment involving hat he called "Kitchen Math" which served to evidence that a constructivist approach is inevitably better than memorizing formulas, rules and formal stuff. I recommend both books to anyone interested in this topic. Here is a link to an essay written by Dr. Papert in 1996: http://papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html http://papert.org/articles/AnExplorationintheSpaceofMathemat...
cupcake-unicorn 13y ago
Yeah, I didn't like this article. It's overly harsh and doesn't take into account other situations. I have dyscalculia, the math version of dyslexia. People generally don't say "I can't do English" if they have dyslexia, but they can say, "I can't spell" which I wonder would be assessed as harshly by the author as this article. Also, it was pointed out that what math is can be fuzzy - I always thought I was BAD at math, when I was young and it was still adding numbers together and stuff, which I only can do with great difficulty. Once I got into algebra, I was already devising my own ways to solve equations and acing the class (although they told me to stop solving the equations in my own way...)
tokenadult 13y ago
As I did the last time I posted a reply about mathematics education, I read the original post and the comments here before posting this reply. First things first. Mathematical notation is now universal. A student in China learns in middle school (junior high) most of the mathematical notation that an American is expected to learn by graduation from high school. I know a large number of Chinese people who have taken the GRE test for admission to United States graduate schools. All of them, even those pursuing graduate studies in humanities, deride the GRE math section as "junior high math," which it literally is in terms of the standard school curriculum in China. Not all people in China have access to schooling beyond junior high, but through junior high the instruction in mathematics is generally excellent, and the United States could learn from the methods of mathematics teaching used in schools in China. http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles/www/readings/ma-review.pdf http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles... http://www.ams.org/notices/199908/rev-howe.pdf http://www.ams.org/notices/199908/rev-howe.pdf Second things second. There is indeed a distinction between doing the kinds of calculations in arithmetic that may be tested in elementary school, are often done by adults with electronic calculators, and may or may not be a practiced skill of professional mathematicians and the kind of mathematical reasoning that makes up university-level study of mathematics and quantitative sciences. But that is not to say that learning arithmetic is not important. W. Stephen Wilson, a professor of mathematics at Johns Hopkins University, surveyed mathematics researchers about a year after the webpage submitted here was written, and asked them to agree or disagree with the statement "In order to succeed at freshmen mathematics at my college/university, it is important to have knowledge of and facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, (without having to rely on a calculator." http://www.math.jhu.edu/~wsw/ED/list http://www.math.jhu.edu/~wsw/ED/list His colleagues around the world unanimously agreed, answered him in terms such as "I am shocked that there is any issue here. I absolutely agree with your statement." "That it is even slightly in doubt is strong evidence of very distorted curriculum decisions. I do not know even one university-level teacher of mathematics who would disagree with it. I would be truly astonished to meet a person who disagrees." The charming story about Kummer is one I tell my own students, but I also tell them that the mathematics I teach them (prealgebra mathematics, in a class for self-selected elementary-age pupils looking for a challenging mathematics course) is based on their doing their own calculations with their minds alone, or with pencil and paper, never with a calculator. Other mathematicians point out that learning the long division algorithm is itself a basis for the development of mathematical understanding. http://www.csun.edu/~vcmth00m/longdivision.pdf http://www.csun.edu/~vcmth00m/longdivision.pdf The late mathematician W. W. Sawyer spent decades thinking about how to teach mathematics effectively. http://www.marco-learningsystems.com/pages/sawyer/sawyer.htm http://www.marco-learningsystems.com/pages/sawyer/sawyer.htm Back in 2004, when I joined the Art of Problem Solving forums, I chose the screen name "tokenadult" (which so annoys some people here, chosen there because many participants on the forums are much younger than I am), and also chose a tagline quotation from Sawyer: "The proper thing for a parent to say is, 'I did badly at mathematics, but I had a very bad teacher. I wish I had had a good one.'" W. W. Sawyer, Vision in Elementary Mathematics (1964), page 5. Sawyer didn't want parents to give their children an excuse for thinking "I don't have a head for mathematics." Instead, a learner can keep searching for an effective teacher, and learn more than at first seems possible. The curriculum expectations in much of the English-speaking world are meager. In both Singapore and Taiwan (and in some other countries), every seventh grader is expected to learn algebra, and a fair amount of geometry--even all of the below-average students. That is possible. Not everyone in those countries is brilliant in mathematics, but many, many people in those countries have a day-by-day correct understanding of mathematics that helps in their daily life activities. My wife received that kind of mathematical education back when Taiwan is wretchedly poor. Taiwan is no longer poor, in part because it has developed rapidly through its educated workforce.
Detrus 13y ago
> But many people feel the same way about, for example, physical exercise: they don’t enjoy doing it and find it to be very hard work when they try. But it would be strange indeed to say that you can’t “do” exercise. You may not want to do it. You may be unwilling to invest the time and effort into doing it. But you aren’t incapable of doing it. And the same is true, in my experience, in mathematics. The way physical exercise is often presented to people, it's no surprise they give up on it. A lot of gimmicky exercise programs and contraptions designed to take money from you in exchange for no visible results. And even time tested exercise programs like P90X won't teach you the fundamentals. You'll spend a lot of time doing crunches which is the least effective and most time consuming way of working abs. The same is certainly true for math and when people say they can't do any moderately complex math, they're saying "fuck you" to the establishment that wasted their time while teaching them nothing. They also do just fine without complex math, just like most people who never exercise.
forrestpitz 13y ago
I feel like the sentiment of "I can't do math" stems mostly from the way math is taught. To contrast we can look at how reading is taught to elementary students. Students read books at their "level." Once they are comfortable with the words and concepts in a given level then the difficulty of the content is scaled up appropriately. In math, students are often pulled along with the rest of the class. It is very difficult to understand division when you are still struggling to understand subtraction. This happens for a number of reasons but mostly because it is more difficult to teach math on an individual level the way reading can be though. I think that the solution to issues like this will/would look similar to the reverse model that the folks at KahnAcademy are creating. It's clear that it is difficult to teach math of every student is at a different point and understands a different amount of math. By transferring the teaching onto prerecorded videos the students are able to learn at their own pace and rewatch the lessons for more difficult concepts without exasperating the teacher. Salman Kahn has stated that his cousin (that he first started making videos for) told him that she liked learning from him in his videos more because he wouldn't get frustrated when she didn't understand a concept. She could just watch it again. This also frees the teacher to help the students who are learning at a slower rate or have gotten stuck with a difficult concept.
pvaldes 13y ago
> So what do people actually mean when they say that they can’t 'do' math? That I "can't". That my brain is differently "shaped", simply, and that this a common variation. Personally I think in spatial 3d structures, classify images, read superfast recognising words by the shape of the contour of the letters, learn at a good rate and can accurately drawn what I see in the real world... But in the other hand I find deadly boring to express, in a unnecesarily complicated formulae drawn in 2d with many arcane symbols, a simple concept that could be introduced and expressed instead in two or three simple phrases... or logically, graphically... The "atoms" of my thinking process are shapes and relationships between shapes, not abstract quantities. Is as simply as this. Other people "think in sounds" and are very good at music, and other "think in mathematical structures". I'm not blaming nobody, not excuses... I'm just a perfectly normal human with an intelligence basically visual (... And I prefer not spend much time with this when a machine can do the math part for me in the blink of an eye).
pshin45 13y ago
> But many people feel the same way about, for example, physical exercise: they don’t enjoy doing it and find it to be very hard work when they try. But it would be strange indeed to say that you can’t “do” exercise. You may not want to do it. You may be unwilling to invest the time and effort into doing it. But you aren’t incapable of doing it. And the same is true, in my experience, in mathematics. I think a more apt comparison might be to sports, rather than to exercise. Everyone can get reasonably good at "exercise" i.e. be able to run a mile in a reasonable time, but I think we can all agree that there are certainly many people who simply "can't do" a sport. For example, I am pretty bad at baseball. I was a terrible batter and an even worse fielder. I "persevered" and played Little League Baseball for several years, eventually realized I didn't have much if any aptitude for it, and stopped playing altogether. Does this mean I'm lazy or that the Little League coaching system is broken? No, it just means I'm not that good at baseball and probably never will be, and I don't think any amount of great coaching would have changed that. Are there some people who could have been good at a given sport but "slip through the cracks" due to laziness or bad teaching? Maybe, but I doubt it's a significant number. It's easy to take mathematics ability for granted on a focused forum like HN, but perhaps being good at math is no different from being a great sports athlete - Some people are really good at it, but most aren't and it's pretty unrealistic to expect everyone to change their expectations and opinions on the matter.
tempire 13y ago
Math is just another word for structured thought. When people say they're not good at math, what they really mean is that they attempted learn something without understanding the underlying principles, and therefore found it difficult. They're not lazy, they're just ignorant to the process because they were taught incorrectly.
gridmaths 13y ago
I think part of the problem is we don't teach Math in a way that is visual/obvious enough, which means early math is experienced as 'mechanics' not 'understanding'. For example, we should explain commutative rule [ a(b+c)=ab+ac ] by drawing the rectangles. My efforts to help this in some way : GridMaths.com [ sample pics + blurb : quantblog.wordpress.com ]
Kekeli 13y ago
I wish i could do math

149 points by mejakethomas 13y ago

My favorite professor's take on the ever-increasing "I can't do math" statement.

Indeed, it is often beneficial to state your preferences up front instead of sputtering nonsense trying to be "diplomatic". Everyone can interpret what I have to say about text editors much more usefully if I state up front that I love Emacs. The same goes for programming languages, frameworks, operating systems and math.

mjn 13y ago

I see his larger point, but the conflation of "understanding math" and "being able to do simple arithmetic" is something of a pet peeve. The latter may be a useful life skill, but is not very closely related to understanding mathematics. In fact it's not only non-technical office workers who can be proud of not being able to do it: if you walk into any math department you will find accomplished mathematicians almost gleefully recounting how bad they are at doing simple arithmetic. They can prove things about topological spaces but can't balance a checkbook! That makes the comparison to literacy more complex. Clearly mathematicians think mathematics is important, or they wouldn't be studying it. But many of them consider ability to do arithmetic, as a skill, essentially irrelevant, to the point where they don't even learn it themselves. Then a question might be: what is the relevant literacy-like skill? I think it comes closer to logic and analytical thinking than specifically mathematics, although understanding of statistical arguments fits into that category.

Derbasti 13y ago
I think being able to interpret common mathematical writing in your area of expertise is a valuable skill. I think this is what is meant by "understanding math". I don't know much about anything but signal processing, but I am able to read and understand vector/matrix notation and differential equations. This enables me to read most papers published in signal processing. Just like being able to at least roughly read most C-derived programming languages, this is a valuable skill. I have seen coworkers "not understanding" my work because it involved problem descriptions in mathematic notation. Frankly, it annoys the hell out of me.
- ebiester 13y ago
  How about I write my comments in Turkish? It's your fault you don't understand them, after all. The art of programming, and of comments, is the ability to communicate to another human, and incidentally to computers. (I believe that was a paraphrase of Knuth.) If the terminology gets in the way of their understanding, then use a different terminology. (I can fight my way through a mathematics paper, myself. But why be obtuse in your communications?)
  - jarrett 13y ago
    Mathematics offers a standardized, internationally accepted notation for its various problem domains. Turkish is not the standard language of software comments. So I don't think the analogy holds.
    - frenchy 13y ago
      Neither is math. My guess is that you will find many more Chinese programmers who understand English comments than those that understand high-school mathematics symbols.
      - jarrett 13y ago
        I would venture that any such programmers ought not work on a math-intensive domain like signal processing. Sure, not every programmer has to know high school math. You can, for example, do great work with HTML, CSS, and JavaScript without knowing high school math. But there are certain fields where math is unavoidable. Signal processing is one of them. And the internationally accepted notation for such math is part of what you're expected to know. BWT, I assume you're not saying China uses different mathematical notation. I wouldn't know about that. If so, then that does undermine my argument.
  - akiselev 13y ago
    "If the terminology gets in the way of their understanding, then use a different terminology." Literally the reason mathematics exists.
mercuryrising 13y ago
It's just a theory, but I think some mathematicians intentionally 'unlearn' or 'forget' arithmetic when they start to understand what math is about because people who don't understand math will ask them if they add and multiply all day. Theoretical mathematics is an entirely different beast than what most people think it is, so mathematicians get a lot of dumb questions about it. When someone asks if they add and subtract all day, if they say 'I can't even do arithmetic', people may be more inclined to rethink that stereotype.
- VLM 13y ago
  "ask them if they add and multiply all day" A good example, but you should have thrown in an analogy to the general population thinking anyone who does anything with electronics is automatically a microsoft windows admin/personal trainer with special focus on virus removal.
- SteveGerencser 13y ago
  My wife is one of those 'math people' that struggles with simple arithmetic. She has calculators and excel for things like that. But for her it wasn't a case of unlearning it. She struggled in school with arithmetic and didn't start to excel until they started introducing variables and all of the other aspects that separate math from arithmetic.
klibertp 13y ago
> what is the [maths] relevant literacy-like skill? I'm deeply convinced that the answer to this is easy - the ones that programmers use.
pcl 13y ago
> the conflation of "understanding math" and "being able to do simple arithmetic" is something of a pet peeve Agreed. I'm horrible at simple arithmetic -- I've just never gotten the knack for it, despite clear life benefits to being good at it. But I'm decent at math-with-letters. If I'm in a social setting and someone wants me to do the arithmetic on something, I'll happily say "I can't do math" because it makes more sense than saying the above. I bet there are others like me out there.
hammock 13y ago
> Then a question might be: what is the relevant literacy-like skill? How about "I'm terrible with names."

wtvanhest 13y ago

The key problem with math is that the learning keeps going and at some point, every single person fails to either have the ability or time to learn more math. Everyone becomes "bad at math" relative to other people. This same thing doesn't happen with reading because once you are a pretty good reader you feel like you have mastered it. 3 examples: 1) Kid who never completes pre-calc. "can't do math" 2) Adult who gets through calc, but doesn't go any further "can't do math"... like an engineer 3) Math PhD. who gets stuck on something they can't solve. Person 1 and 2 are both stating they can't do math, and both people are relatively right. Relatively being the key word. If we rephrased the way math is taught, it would never be labeled as math at all. This would box people in to saying things like "I don't do calculus" which would be correct in many cases, whereas it would be alarming if someone said "I can't add". Really, whether people say "I don't do math" or "my bad" doesn't really matter and being stressed over it is probably just as ridiculous as saying those things.

CamperBob2 13y ago
This can't be overemphasized. My favorite (apocryphal) Einstein anecdote is the one where a society matron approaches him at a party and exclaims, "I don't know how you can deal with all that math. I have so much trouble with math." Einstein replies, "Lady, you can't imagine how much trouble I have with it." s/math/computers, and that line comes in very handy in my own social life.
adventureloop 13y ago
I think you have hit this point on the head. It is very hard to compare mathematics education between countries. Eastern Bloc countries seem to go a lot further with the secondary level mathematics education, my point of caparison is to Scotland cavet emptor. I am constantly embarrassed by my level of mathematics, I like to play with 3D graphics on the weekend.
dagw 13y ago
I have a Masters in applied math, but I still put myself in the Bad At Math camp compared to many of my class mates, especially those who went on to pure math PhD's. And even among that group, I know a couple who would also classify themselves as Bad At Math because they couldn't pull off the more hard core PhD research topics and had to drop down to easier problems.

swinnipeg 13y ago

I went through this exact issue with a junior employee moved to my team to do some analysis that required a basic understanding of medians/means and a little intro stats. It took about 8 weeks of tasks with incremental mathematical challenges to overcome this, and at least reach the point where he could do his work, and apply the fundamentals learned to solving more complex problems. In the end he "could do math", the real issue was he had never "put any work into math".

shawndumas 13y ago

"I can't do math [at a university level]..."

jpwagner 13y ago

Indeed there is something wrong with someone saying "I can't do math..." but it is not what the author identifies. In blunt summary, the author says "you may not be able to do the specific math you claim, but don't worry I'll teach you." In my experience this is not at all what the complaint is saying and the solution "I'll teach you" is not at all what they are looking for. The comparison to illiteracy is completely off-target. In my experience, "I can't do math" is simply "I don't know" in disguise. Ask most children: "what's 300 times 248" and you get a knee-jerk "I don't know". Ask also "what's a balloon made of"; "I don't know". Same goes for many other questions that appear to them to have a definite answer. We excuse children for saying this, but it becomes less and less acceptable as an answer because we learn of tools for finding the correct answers. The real lesson that needs to be taught is: Your worldview of can/can't do math is wrong. Doing math is learning what tools to use after we've broken down our question to its core...kind of like everything else.

chrisdone 13y ago
Saying “I don't know” is a fantastic skill that children are born with but have it beaten out of them into adulthood and the beating never stops. I have deep respect for people who can say “I don't know.” That person is one step away from learning something new.
- jpwagner 13y ago
  It's great when adults who do not usually say "I don't know" can admit to not knowing something. Other than that, I cannot agree with anything else you say.

devgutt 13y ago

But If a person says "I can't \"do\" mathematics" also could imply that the person would like to like it, or maybe the person at least respect the subject as important.

easy_rider 13y ago
how did these added slashes slip in?
- fyi80 13y ago
  Java/C++ programmer who observed that English lacks Perl's qq operator or python's r''

timmm 13y ago

Neil Degrasse Tyson made this point. He basically said that imagine if instead of people saying at cocktail parties "I can't do math" they said "I can't read..."

zecho 13y ago
Sure, but "I can't do math" is a shorthand for "I can't do math beyond arithmetic, and even then, I often can't do that in my head." That is not equivalent to "I can't read." It is more equivalent to "I can't read Proust without getting bored and confused." The author in the OP acknowledges this substitution of "I can't" for "I currently struggle with." It's complaint about semantics that misses the point, I think. Rather than complaining when people say they can't do math, we should find out why they feel that way. I suspect a large part of the reason is that math education is pedantic and boring (memorizing axioms and doing rote calculations, when we should prove them, for example, or apply math in ways that doesn't involve trains leaving stations) and when people do speak their minds about their difficulties with mathematics, they often face snooty responses like this one in the OP, rather than a lighter touch.
- hudibras 13y ago
  One of the OP's main gripes is that many people will gleefully, happily tell you that they can't do math. Nobody will ever admit to a stranger at a cocktail party that they're illiterate but being bad at math is, for some reason, a conversation starter.
VLM 13y ago
There are three other defense mechanisms at play: 1) I already made up my mind based on emotion or tradition or the salesperson was cute or whatever, and I was hoping the math proves my select decision is correct, but its not looking good and/or I've found a easier / better justification so "I can't do math" 2) I'm getting totally financially reamed over this (housing bubble / car lease / rent / mortgage / tuition / credit card) but its less painful to say I can't do math than admit I have awful financial judgment. 3) I suspect the result of this decision is going to be a minefield, and the other party is more traditionally mathematical than my side's ethnic / school major / gender / job title / whatever so I automatically come out ahead regardless of result by not making any decision and defer via "I can't do math" because first I don't have to put in the effort and secondly I can't be blamed.

sbashyal 13y ago

This reminds me of my experience with people in China when I was there. My friends there told me that many young people in China do understand English. But every time I approached them with "Do you speak English?" They usually took two steps backward and replied "no". They hesitate speaking English (because they find it difficult) despite knowing enough to serve my purpose. I have had similar experience with "Do you know maths?" in the US.

6d0debc071 13y ago

We seem to accept what's essentially illiteracy in all the subjects that require more precise thinking as the status quo. Most people don't seem to understand much about chemistry, physics, logic or computers either, and that doesn't get them in for a lot of stick. If people are poorly taught and have gaps in their understanding that are never adequately addressed, then I can see how they'd think that the problem was them - that they couldn't do maths. Couldn't make the connections that were expected of them and portrayed as normal functioning for maths. Maths is different to history, and many other subjects, in that regard. If you don't understand something in history, it probably doesn't have a massive list of dependencies that you're going to fail a lot of stuff in the future on. If you don't understand something in English, the worst that's going to happen is you have an esoteric interpretation of the text. You can still do those subjects if you don't really understand them, as long as you use the right buzzwords and hook them off the right things. I suspect part of the answer may just be that admitting you can't do history or the like is different to admitting that you can't do maths in that it's unclear what someone would even mean by claiming that they can do history. Certainly the claim that someone knows a lot about the broad strokes of history would rarely be justified these days.

deleted 13y ago
[deleted]

ssw1n 13y ago

Totally relevant: http://www.phdcomics.com/comics/archive.php?comicid=1356 http://www.phdcomics.com/comics/archive.php?comicid=1356

edtechdev 13y ago

It traces back to cultural and educational issues. Math has typically been taught devoid of any context or relevance to our everyday lives. Even in college, you just mindlessly plug and chug formulas to get by. Some students don't see the use in it, beyond perhaps the parts needed for basic financial literacy (which many do not have, either). Better and more engaging and relevant and effective ways to teach math have already been developed, such as Realistic Mathematics Education. But people actually say things like "I can't do math" in regards to all forms of literacy, I believe. It depends what standards you are mentally comparing yourself to, I guess, such as professional vs. social standards. "I'm not good with money, or I'm not good with the business stuff" - financial literacy "I can't write" - as in, I can't write books or novels or easily do other professional writing tasks. Again, there are pedagogical techniques that can help students write more, write better, and have more interest and confidence in writing. "I don't read" - most folks nowadays don't really read books or novels anymore, what with TV, movies, and the Internet. "I don't know computers" - how often do we hear that - that's computer literacy. I hear it less and less though nowadays. To tell you the truth, maybe it will be nice when one day people feel forced to admit "I can't code." Because that would mean that programming and computational literacy is something taught in most schools.

derleth 13y ago
> most folks nowadays don't really read books or novels anymore, what with TV, movies, and the Internet. Reading off of a screen is still reading. I don't know why some people think paper is magical.
- will_work4tears 13y ago
  Sadly, most of what is on the internet counts as reading the same as watching a spongebob episode and "The Stand" both count as watching a 'show.' It's telling when writing a 3-4 paragraph article requires a ;TLDR section. Usually when a person says they are a "reader," or the like, are specifically talking about long works, not articles in Maxim magazine.
  - 13y ago

speeder 13y ago

I only think the author forgot that there are people that REALLY cannot do math. It might sound bizarre and weird, but I met more than once person, that did their best to learn, and were intelligent with many other things (one of these persons had a degree in law, another in international relations, and was doing a masters in international law), yet could not do 29/3 without a calculator... Or even worse, I knew people (in that case usually working with more low level work, like burger flipping) that even trying, or even if needed (ie: cashiers) cannot do it right even with a calculator, their grasp of math is so weak (even if they want to have a grasp) that they cannot even use the correct operations. Also the same apply to many other fields, I knew intelligent people that could not read, or that could not grasp history, or geography, and so on... People keep forgetting that brains CAN be very specialized, and be great with something, and terrible with other, and I personally believe that the old way of teaching professions (ie: throw the kid to work with a Master in that profession) was better because of that, currently you throw kids on the school, and the ones that might excel at some things that are not on school (like Music) reach adulthood thinking they are dump and they don't make a effort even in thinks they do have a talent to do.

Jtsummers 13y ago
I don't think the author forgot that, he seems to refer a lot to 'most people' and 'usually' enough to acknowledge that his assertion is not a truism. Besides that, it's a rant, those are often filled with generalities that need to be pared down before we can get to the real discussion.
umsm 13y ago
I don't think the author meant that people aren't walking calculators. I believe he implies that people don't want to understand how to evaluate a math problem. Most people that "can do" math still use a calculator; additionally, they understand what's happening and they can identify an answer that is absurd (because of a key-press mistake).
com2kid 13y ago
> It might sound bizarre and weird, but I met more than once person, that did their best to learn, and were intelligent with many other things (one of these persons had a degree in law, another in international relations, and was doing a masters in international law), yet could not do 29/3 without a calculator... There are multiple ways to learn even something like arithmetic. Some people can naturally juggle a lot of numbers in their head and can basically brute force problems. Others can break problems down into component pieces, work out each individual piece, and reassemble them into an answer. This requires a different type of mental juggling than the above. And then there are those who just have to memorize a lot of problems. When I was in school, we started off with memorization (multiplication tables and such), which requires a large time investment that I am sure many students did not make. (My peer group tended to stay inside during recces and practice our multiplication!) After that I think we were supposed to "naturally" progress to breaking problems down into parts, but that was never really covered all that well. From what I understand, other countries make this part of learning arithmetic very explicit. A good deal of this involves training ones working memory. Right at the end of college my working memory for numbers was amazing, I could do 3 digit divides in my head, and at one point I could even do a binary search to find logarithms down to a decimal place or two! But as with many other skills, they degrade from a lack of use. 29/3? I have a minor on mathematics. If you give me that problem, I'd honestly type "win-r calc 29/3 enter". Now days I have problems just adding up large strings of numbers, I play a bunch of D10 games and I have to actually do math rather than it coming to me instantly! > People keep forgetting that brains CAN be very specialized, and be great with something, and terrible with other, Well yes of course, but we choose what to specialize in! I really do believe that anyone can learn math if they put the time and effort into it. My math classes took 2-3 hours a day of studying a good 4 days a week in order for me to completely grasp the concepts being taught. Repetition of hundreds of problems, as much as I hated it, was the only real way to burn technique into my head, and even then most of those techniques have fallen by the way side! A few still bounce around inside my skull, but it has been a good 8 years since my last math class, so the amazing feats of mental gymnastics I could perform are long gone. On the flip side, ask me to design a test infrastructure for code sometime, and I'm right on it! How about a custom memory allocation scheme? No problem! Specialization indeed.

skittles 13y ago

I believe that lots of people really can't do math. Most people are fine until fractions. Many people never gain any intuitive feel for what "2/5 * 7/8" even means. It only gets worse with algebra. They can often learn the mechanics of fraction arithmetic and solving equations, but they will never understand how to apply the knowledge later in life.

mathiasben 13y ago

Surely if effort and attention to detail were applied most of these people could work their way through whatever math task was set before them. What they should instead be saying is; "I don't do math".

brudgers 13y ago

Telling people they can do math because they can add is disingenuous at best. "Ciphering" is the term that used to be used for figuring sums and such. Nobody pretended that was math. At the school house it was called "arithmetic". It was one of the three "R's" not something with it's own Phd granting departments at universities. People who say they cannot do math are speaking with the knowledge that they are looking up toward a massive intellectual edifice containing ideas they do not understand - whether they are looking up to high-school trigonometry or differential equations or Bayesian statistics is irrelevant. What is relevant is that they are not looking up to ciphering as unobtainable - at least not those people likely to be conversing causally or academically with a tenure track academic.

Irregardless 13y ago

People who say "I can't do math" are lazy? Sorry, but I think that's a gross oversimplification of the issue (which is also evidenced by the comparison to physical exercise) and the two assumptions fundamental to that opinion are just plain wrong. Namely: > So what do people actually mean when they say that they can’t “do” math? Usually they are really stating one of two things. First, that they don’t like mathematics. Secondly, that mathematics is more difficult for them than other subjects, and that it takes a great deal more effort on their part to learn it. He conveniently chose the two reasons that are easiest to dismiss (irony, anyone?). What he fails to account for is the fact that math education is so poor that many people don't truly understand what math is. Beyond arithmetic and algebra, they think it's some really complicated stuff with big numbers and funny symbols that geeky people with glasses do -- it's practically a foreign language to them, except it has a reputation for being much harder. Why is this? If I had to guess, I'd say it's based on the fact that math involves a lot of critical thinking and critical thinking is very difficult to teach. Those who attempt to do so often do it very poorly, which leads students to the false belief that math is extremely difficult. On the other hand, it's very easy to teach someone to memorize formulas and plug in numbers, so that's what we're most often taught in math class. That's good enough to get us through the standardized test so we can graduate from high school, but memorizing formulas and plugging in numbers is not "doing math". So I believe many people are completely justified in saying "I can't do math". What's more, people who "can do math" should be taking the blame for those who say "I can't do math" rather than using pointless semantics to wag a finger at them.

diminoten 13y ago
How is it my fault (as someone who "can do math") that someone else can't/won't do math? What do you believe I am morally obligated to do that I'm not doing with regard to someone else's preference/understanding of mathematics?
- Irregardless 13y ago
  That's mainly directed at the person who wrote the essay (a math professor) and others like him who blame the students rather than themselves. I think he should be examining the state of math education in this country rather than chastizing the people it has failed.

ltnately 13y ago

Really good book on the subject that deals with why/ramifications of a society that's okay with "I can't do math" as a reasonable thing for an otherwise educated person. Innumeracy: Mathematical Illiteracy and Its Consequences John Allen Paulos http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405 http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its...

a_p 13y ago

My favorite story about how Ernst Kummer [1] did arithmetic, from Hoffman's The Man Who Loved Only Numbers[2]: "One story has him standing before a blackboard, trying to compute 7 times 9. "Ah," Kummer said to his high school class, "7 times 9 is eh, uh, is uh...." "61," one of his students volunteered. "Good," said Kummer, and wrote 61 on the board. "No," said another student, "it's 69." "Come, come, gentlemen," said Kummer, "it can't be both. It must be one or the other." (Erdos liked to tell another version of how Kummer computed 7 times 9: "Kummer said to himself, 'Hmmm, the product can't be 61 because 61 is a prime, it can't be 65 because that's a multiple of 5, 67 is a prime, 69 is too big-that leaves only 63.' ") " [1] https://en.wikipedia.org/wiki/Ernst_Kummer https://en.wikipedia.org/wiki/Ernst_Kummer [2] http://www.amazon.com/The-Man-Loved-Only-Numbers/dp/B004R6HXRQ/ http://www.amazon.com/The-Man-Loved-Only-Numbers/dp/B004R6HX...

fyi80 13y ago
> Erdos liked to tell another version of how Kummer computed 7 times 9: "Kummer said to himself, 'Hmmm, the product can't be 61 because 61 is a prime, it can't be 65 because that's a multiple of 5, 67 is a prime, 69 is too big-that leaves only 63.' That's how I do problems like that, too (I am not a genius mathematician), and it is exactly the sort of thinking that kids should be doing all through K-12. Estimation, intuitive reasoning, analogy, pattern matching, logic, etc.
- rimantas 13y ago
  > Estimation, intuitive reasoning, analogy, pattern > matching, logic, etc. Alas, most of the things on your list require a pretty solid foundation to work. You need patterns already committed into your brain to do pattern matching and to see analogy, you need to have internalized experience for intuition to work, you need to have previous exposure for any meaningful estimation. All to often people forget foundation when they move to the upper layers and sadly sometimes this leads to thinking that foundation is not necessary. And now matter how you look at it there will always be bits of the foundation that require rote learning.

R_Edward 13y ago

I had a trig/pre-calc teacher in high school who I really respected. He had a catchphrase in his classes, especially in the earlier math classes. "In my class, there are only two kinds of people: those who love math, and those who are going to learn to love math." I only had the one class with him, but he left a huge impression on my life. He was convinced that computers were going to become essential to education, so he spent his department's entire budget for a year on two spankin' new Apple ][+ computers. Just set them on carts in his classroom and didn't touch them. He knew he didn't need to. Eventually, a handful of us approached him to ask if he could teach us to use them. "No," he responded. "I don't know anything about them myself... but they came with a tutorial, so maybe you could teach yourself how to write programs, and then maybe help me out." That changed the course of my life. I was planning to be a lawyer, catering to artists and performers. My time spent learning to write programs led to my taking a number of computer science classes in my undergrad, for the easy grades they represented, which then led to majoring in CS, and, eventually, opting for a career in software development. All of which is just to say that, if someone feels that they cannot "do" math, maybe they missed out on the right math teachers; those who understand kids and know how to motivate them and who have their own love for the subject matter and are able to infect others with it. If their math teacher(s) couldn't be bothered to make personal connections with their students, nor find any way at all to make math relevant to their lives, it shouldn't come as a surprise if they wind up being uninterested in "doing" math.

duopixel 13y ago
What a wonderful person. I sometimes take the time to contact teachers that have made an impact in my professional/personal life and thank them for setting me on the right course. It's a really simple gesture but they are always thrilled to hear they've made a difference.

btilly 13y ago

The underlying problem is two-fold in my opinion. #1 We focus on teaching procedures rather than understanding. Most people therefore view math as a list of memorized fixed procedures, and that's intrinsically very hard to remember and become good at. #2 Math is simple in a way our brains are not wired to be good at, yet we have a mistaken belief that simple is easy. It is not. Adding 1000 numbers by hand and getting the right answer is very simple, but hard. Recognizing my voice is very complex, but easy. Be aware that your brain is working in a way it is not designed to work and have patience with it. Otherwise you'll get frustrated, and mistake "It took me this long to understand something THIS simple?" for, "I'm stupid!" The result is that most people understand math in a way that is hard, and their experience of math is an experience of repeatedly confirming the message that they are stupid. Is there any wonder that they take that frustration out on the entire subject of mathematics?

haubey 13y ago

I think these people mean "I can't do arithmetic" which is much more acceptable, in my opinion. If you asked me to find a derivative, I could probably do it faster than I could find 123*26. It's not because the multiplication is harder, but because I don't have to do it in my head that often anymore. I have a calculator, and I use it. However, I have to do derivatives in math class everyday and at this point I'm probably faster at it. Not being able to do arithmetic is fine by me, I can't do it.

learc83 13y ago
That's just because there are fewer steps for finding a simple derivative. If you evaluate 12326 in your head, most people probably end up thinking through something like this 123 * 20 + 123 * 6 123 * 20 123 * 10 * 2 1230 * 2 2460 Now remember this part 123 * 6 100*6 + 20*6 + 3*6 100*6 = 600 20*6 = 120 3*6 = 18 600+120+18 738 2460 + 738 = 3198 Now compare that to taking a simple derivative. Although I could ask you to take the derivative of 123x^26.

e3pi 13y ago

When `she' said "I hate math". Read as: I hate the public school/university mathematics rote droning pretentious pedagogy ecosystem. I personally still retain a enthusiastic thread of the childlike wonder and delight 15 contiguous years in classroom minefields attempted to lame, but its `opportunity cost' has been expensive. Today's increasing autodidact free materials eliminates this cost.

RobotCaleb 13y ago

I never learned how to do long division by hand. That doesn't mean I can't do math, though. I could, of course, learn how, but I haven't needed to.

pfortuny 13y ago

It is not that people can't do math. It is that other people (who supposedly can but in fact cannot OR will not do them properly) insist on them doing the math they do not need (like computing the second derivative of the unemployment rate) or doing wrong the math they DO need (like with their mortgages). As long as people can add, subtract, multiply and basically understand what a division is, they can do math. The problem is they are scared at what other people tell them 'math' is. I am a mathematician, a professor of mathematics and witness to what I have said. Of course people cannot do 'math' when 'math' means being able to compute multiple integrals or roots of third degree polynomials. That is not 'math' that is UTTER RUBBISH EXCEPT FOR PROFESSIONALS in all caps. Really. You do not expect the average man to be able to write a sonnet with alliteration, second order metaphors and in iambic, do you? And they call themselves "literate". People are not lazy, they are scared. An the blame falls on BAD MATHS TEACHERS, in all caps. Really.

piato 13y ago
Hi, I'm a former (high school & middle school) math teacher. I taught various ages, but was only ever responsible for curriculum with age 10-11. We studied a lot of fractions, decimals, percentages & converting between them. There was a bit of angle stuff mixed in there, too. I love mathematics, so I think I'd be the sort of teacher you could see eye-to-eye with. What should I be doing differently?
- pfortuny 13y ago
  Hi! That is exactly what they need: fractions are just a way to explain division and it helps them a lot (actually they are the basis for the "rule of three" which is the "fifth rule"). Proportions. Trying to start with square (?) triangles and the idea of similarity of triangles so that they can later (when 12-13) understand trigonometry (the basics) which, once again, is PROPORTIONALITY. There is little more to 'maths' than that. What I object to is the unnecessary abstraction. Getting 10-11s to perform correct computations is hard but exactly what they need: lots of exercises (no sweat no learn or whatever). You are a HERO. Really. In all caps My respect. I teach undergrads and this is way easier.

nnq 13y ago

I sympathize with the OP on all he says, but what does he mean by this, aren't these expressions synonymous, the only difference being the tone?: > although saying “my bad” when you mean “my mistake” comes close ...and going further on the linguistic ambiguity route, most people saying "can't do" actually mean simply "I hate it / I'm not good at it, and because it's so much effort for met o do it I'd rather not have to do it"... and the only bad thing in it is the uberannoying implied "I don't want to learn it, don't try and teach it to me"...

ameister14 13y ago
'My bad' is a foolish thing to get upset about people saying. People have said it for thousands of years and they're going to keep saying it. See: "Mea Culpa"

jcampbell1 13y ago

When I hear, "I can't do math...", it gets immediately translated in my head to, "My math skill are on the level of a typical 5th grader, and I don't want to be asked to do math because it will expose an embarrassing ignorance." The author's approach to people that feel this way is likely to humiliate them further.

piato 13y ago

One fun parallel - not to literacy, but to another skill at which artsy types are often better than mathematicians - is the oft-repeated, and completely acceptable, "I can't read minds". Lots of people can read minds. Not literally, of course, but they've put in the work (and perhaps it was work that they found easy and pleasant, much as many programmers found math) to be able to essentially tell what people want, don't want, are implying, will be offended by, etc. Yet I've certainly heard plenty of people, and especially STEM-types, making a point of pride about lacking this skill: "I'm a straight-shooter" and the like. There's aspergers and there's dyscalculia, but many STEM types who happily admit to lacking this skill are just like those whom the author bemoans - they find it difficult and uninteresting. And that's okay! But it's no truer, really, than "I can't do maths".

akiselev 13y ago

I do like the author's comparison to illiteracy. Language, just like mathematics, tries to solve the problem of communication but while language is more about the expression of emotions, thoughts, and feelings, mathematics is meant to describe precise ideas and abstractions in a quantified way. While language can be ambiguous in how it relays our true intentions, mathematics is anything but. It is the only method humanity has that, through experiment and observation, can help us reach for and perhaps even attain absolute truth. Just like reading/writing, you don't learn mathematics (real maths, not arithmetic) to be able to scribble symbols on a piece of paper. You learn it to develop a way of thinking that promotes certainty and helps you develop and understand complex abstract ideas that describe how the world works. When you dive deep into math (or programming for that matter), you don't just learn a subject, your brain actually reconfigures itself and fundamentally changes how you act and think. This effect, called neuroplasticity, functions pretty much until you die so it's never too late to learn math. When someone says that they can't "do" math it says nothing about their intellect. All it says is that they didn't like the mathematical equivalent of "The Cat in the Hat" taught in primary school and are now going to live (many quite proudly) without the mental faculties to express and grok abstract and complicated ideas and systems. Sadly, now more than ever, we need each and every human to have these faculties if we are going to survive and thrive as individuals and as a species.

300bps 13y ago

This sounds like an extension of the recently widely covered practice of not telling your kids they're smart. Basically, studies have shown that praising your child for intelligence as opposed to hard work can cause them to undervalue effort. They start to separate subjects into things they are "good" at and things they are "bad" at. They then avoid the things they've labeled themselves as bad at doing. On the contrary, praising a child for their hard work seems to not be associated with this same negative behavior. http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-shouldnt-tell-your-kids-theyre-smart/ http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-should...

mberning 13y ago

There is an idea that pervades their rant that all people are more or less equally educable in all subjects. In my experience this is simply not true.

gyardley 13y ago

"I can't do math" actually means "I both don't like to and don't believe I really need to do any math, so I'm going to say 'I can't do math' to cut you off before you propose I do any." Of course college-educated people can do a little math - but they don't like to, so they don't.

Tycho 13y ago

Maybe they should teach it as 'modelling' instead of 'mathematics.' When you start thinking of it in terms of interpreting real world dynamics and relationships, curiosity takes over and it becomes a much more compelling subject to learn. IMO.

losethos 13y ago

after calculus comes DIFF EQ After DIFF EQ comes nonlinear control systems I got an A in nonlinear control systems. God says... servants, Have me away; for I am sore wounded. 35:24 His servants therefore took him out of that chariot, and put him in the second chariot that he had; and they brought him to Jerusalem, and he died, and was buried in one of the sepulchres of his fathers. And all Judah and Jerusalem mourned for Josiah. 35:25 And Jeremiah lamented for Josiah: and all the singing men and the singing women spake of Josiah in their lamentations to this day, and made them an ordinance in Israel: and, behold, they are written in the lamentations. 35:26 Now the rest of the acts of Josiah, and his goodness, according to that which was written in the law of the LORD, 35:27 And his deeds, first and last, behold, they are written in the book of the kings of Israel and Judah.

droidist2 13y ago

Yeah, it's interesting that people will proudly admit "I can't do math" but you don't nearly as often hear them say "I don't understand politics, government, or world affairs." People will do their damnedest to appear knowledgeable about those things.

chrisdone 13y ago
That's true. “I don't really understand national politics in any deep way,” is something I've said many times and has been responded to often with “me neither”, but I'm quite sure had I not said it, the person would've kept quiet about their ignorance and feigned insight in other conversations.

egutesman 13y ago

Seymour Papert (http://www.papert.org/ http://www.papert.org/), inventor of Logo in his seminal work Mindstorms (1980) did a very good job on analyzing this phenomena. Not only he did a great analysis on children but also came up with Logo, one of the best paradigm-changing environments for teaching math. On his second book, The Children's Machine (1991), almost 11 years later he went deeper into the issue of computer's at schools and what should or shouldn't be taught at school on math lectures. There's a nice section on an experiment involving hat he called "Kitchen Math" which served to evidence that a constructivist approach is inevitably better than memorizing formulas, rules and formal stuff. I recommend both books to anyone interested in this topic. Here is a link to an essay written by Dr. Papert in 1996: http://papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html http://papert.org/articles/AnExplorationintheSpaceofMathemat...

cupcake-unicorn 13y ago

Yeah, I didn't like this article. It's overly harsh and doesn't take into account other situations. I have dyscalculia, the math version of dyslexia. People generally don't say "I can't do English" if they have dyslexia, but they can say, "I can't spell" which I wonder would be assessed as harshly by the author as this article. Also, it was pointed out that what math is can be fuzzy - I always thought I was BAD at math, when I was young and it was still adding numbers together and stuff, which I only can do with great difficulty. Once I got into algebra, I was already devising my own ways to solve equations and acing the class (although they told me to stop solving the equations in my own way...)

tokenadult 13y ago

As I did the last time I posted a reply about mathematics education, I read the original post and the comments here before posting this reply. First things first. Mathematical notation is now universal. A student in China learns in middle school (junior high) most of the mathematical notation that an American is expected to learn by graduation from high school. I know a large number of Chinese people who have taken the GRE test for admission to United States graduate schools. All of them, even those pursuing graduate studies in humanities, deride the GRE math section as "junior high math," which it literally is in terms of the standard school curriculum in China. Not all people in China have access to schooling beyond junior high, but through junior high the instruction in mathematics is generally excellent, and the United States could learn from the methods of mathematics teaching used in schools in China. http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles/www/readings/ma-review.pdf http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles... http://www.ams.org/notices/199908/rev-howe.pdf http://www.ams.org/notices/199908/rev-howe.pdf Second things second. There is indeed a distinction between doing the kinds of calculations in arithmetic that may be tested in elementary school, are often done by adults with electronic calculators, and may or may not be a practiced skill of professional mathematicians and the kind of mathematical reasoning that makes up university-level study of mathematics and quantitative sciences. But that is not to say that learning arithmetic is not important. W. Stephen Wilson, a professor of mathematics at Johns Hopkins University, surveyed mathematics researchers about a year after the webpage submitted here was written, and asked them to agree or disagree with the statement "In order to succeed at freshmen mathematics at my college/university, it is important to have knowledge of and facility with basic arithmetic algorithms, e.g. multiplication, division, fractions, decimals, and algebra, (without having to rely on a calculator." http://www.math.jhu.edu/~wsw/ED/list http://www.math.jhu.edu/~wsw/ED/list His colleagues around the world unanimously agreed, answered him in terms such as "I am shocked that there is any issue here. I absolutely agree with your statement." "That it is even slightly in doubt is strong evidence of very distorted curriculum decisions. I do not know even one university-level teacher of mathematics who would disagree with it. I would be truly astonished to meet a person who disagrees." The charming story about Kummer is one I tell my own students, but I also tell them that the mathematics I teach them (prealgebra mathematics, in a class for self-selected elementary-age pupils looking for a challenging mathematics course) is based on their doing their own calculations with their minds alone, or with pencil and paper, never with a calculator. Other mathematicians point out that learning the long division algorithm is itself a basis for the development of mathematical understanding. http://www.csun.edu/~vcmth00m/longdivision.pdf http://www.csun.edu/~vcmth00m/longdivision.pdf The late mathematician W. W. Sawyer spent decades thinking about how to teach mathematics effectively. http://www.marco-learningsystems.com/pages/sawyer/sawyer.htm http://www.marco-learningsystems.com/pages/sawyer/sawyer.htm Back in 2004, when I joined the Art of Problem Solving forums, I chose the screen name "tokenadult" (which so annoys some people here, chosen there because many participants on the forums are much younger than I am), and also chose a tagline quotation from Sawyer: "The proper thing for a parent to say is, 'I did badly at mathematics, but I had a very bad teacher. I wish I had had a good one.'" W. W. Sawyer, Vision in Elementary Mathematics (1964), page 5. Sawyer didn't want parents to give their children an excuse for thinking "I don't have a head for mathematics." Instead, a learner can keep searching for an effective teacher, and learn more than at first seems possible. The curriculum expectations in much of the English-speaking world are meager. In both Singapore and Taiwan (and in some other countries), every seventh grader is expected to learn algebra, and a fair amount of geometry--even all of the below-average students. That is possible. Not everyone in those countries is brilliant in mathematics, but many, many people in those countries have a day-by-day correct understanding of mathematics that helps in their daily life activities. My wife received that kind of mathematical education back when Taiwan is wretchedly poor. Taiwan is no longer poor, in part because it has developed rapidly through its educated workforce.

Detrus 13y ago

forrestpitz 13y ago

I feel like the sentiment of "I can't do math" stems mostly from the way math is taught. To contrast we can look at how reading is taught to elementary students. Students read books at their "level." Once they are comfortable with the words and concepts in a given level then the difficulty of the content is scaled up appropriately. In math, students are often pulled along with the rest of the class. It is very difficult to understand division when you are still struggling to understand subtraction. This happens for a number of reasons but mostly because it is more difficult to teach math on an individual level the way reading can be though. I think that the solution to issues like this will/would look similar to the reverse model that the folks at KahnAcademy are creating. It's clear that it is difficult to teach math of every student is at a different point and understands a different amount of math. By transferring the teaching onto prerecorded videos the students are able to learn at their own pace and rewatch the lessons for more difficult concepts without exasperating the teacher. Salman Kahn has stated that his cousin (that he first started making videos for) told him that she liked learning from him in his videos more because he wouldn't get frustrated when she didn't understand a concept. She could just watch it again. This also frees the teacher to help the students who are learning at a slower rate or have gotten stuck with a difficult concept.

pvaldes 13y ago

> So what do people actually mean when they say that they can’t 'do' math? That I "can't". That my brain is differently "shaped", simply, and that this a common variation. Personally I think in spatial 3d structures, classify images, read superfast recognising words by the shape of the contour of the letters, learn at a good rate and can accurately drawn what I see in the real world... But in the other hand I find deadly boring to express, in a unnecesarily complicated formulae drawn in 2d with many arcane symbols, a simple concept that could be introduced and expressed instead in two or three simple phrases... or logically, graphically... The "atoms" of my thinking process are shapes and relationships between shapes, not abstract quantities. Is as simply as this. Other people "think in sounds" and are very good at music, and other "think in mathematical structures". I'm not blaming nobody, not excuses... I'm just a perfectly normal human with an intelligence basically visual (... And I prefer not spend much time with this when a machine can do the math part for me in the blink of an eye).

pshin45 13y ago

> But many people feel the same way about, for example, physical exercise: they don’t enjoy doing it and find it to be very hard work when they try. But it would be strange indeed to say that you can’t “do” exercise. You may not want to do it. You may be unwilling to invest the time and effort into doing it. But you aren’t incapable of doing it. And the same is true, in my experience, in mathematics. I think a more apt comparison might be to sports, rather than to exercise. Everyone can get reasonably good at "exercise" i.e. be able to run a mile in a reasonable time, but I think we can all agree that there are certainly many people who simply "can't do" a sport. For example, I am pretty bad at baseball. I was a terrible batter and an even worse fielder. I "persevered" and played Little League Baseball for several years, eventually realized I didn't have much if any aptitude for it, and stopped playing altogether. Does this mean I'm lazy or that the Little League coaching system is broken? No, it just means I'm not that good at baseball and probably never will be, and I don't think any amount of great coaching would have changed that. Are there some people who could have been good at a given sport but "slip through the cracks" due to laziness or bad teaching? Maybe, but I doubt it's a significant number. It's easy to take mathematics ability for granted on a focused forum like HN, but perhaps being good at math is no different from being a great sports athlete - Some people are really good at it, but most aren't and it's pretty unrealistic to expect everyone to change their expectations and opinions on the matter.

tempire 13y ago

Math is just another word for structured thought. When people say they're not good at math, what they really mean is that they attempted learn something without understanding the underlying principles, and therefore found it difficult. They're not lazy, they're just ignorant to the process because they were taught incorrectly.

gridmaths 13y ago

I think part of the problem is we don't teach Math in a way that is visual/obvious enough, which means early math is experienced as 'mechanics' not 'understanding'. For example, we should explain commutative rule [ a(b+c)=ab+ac ] by drawing the rectangles. My efforts to help this in some way : GridMaths.com [ sample pics + blurb : quantblog.wordpress.com ]

Kekeli 13y ago

I wish i could do math