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I am miles away from Eric or Linus, but the "curse of the gifted" is very real. Thankfully I wasn't smart or gifted enough that I could ride it for long, but w

I am miles away from Eric or Linus, but the "curse of the gifted" is very real. Thankfully I wasn't smart or gifted enough that I could ride it for long, but when it comes to math and problem-solving I rode it well into my high school years. I never learned to do algebra "by the book," because I didn't need to. Or maybe because I wasn't smart enough to. The math teacher would teach "3x + 6 = 9." Basic algebraic problem-solving says you subtract the 6 from both sides, then divide by 3. So "3x = 3" then "x = 1." Easy. But I learned pretty early on that I could do it in my head. It was a little bit challenging, but then I wouldn't have to waste the time of writing it out, and I wasn't handicapped like all of those suckers who had to go through the motions no matter how simple the problem was. If the teacher wrote "x + 1 = 6" I didn't have to subtract 1 from each side, I just thought about it logically and knew the answer. Of course, the math got more complex, but I was good enough at doing it in my head that, at least for a long time, it never really mattered. I thought it was because I just "got" math, and the other kids were on a lower level. But as the math grew in complexity, I fell behind. By the time we reached Calculus I was still doing most of it in my head, as I had never really learned to write it out on paper. And the complexity of the math outgrew my capacity to visualize. I showed up to my AP calculus test without a calculator, partially because I was forgetful and partly for fun, and it wasn't until I got my score back (a failing 2 of 5) that it finally hit me: I was actually behind. In school. I was cocky enough that this was a slap in the face. I had to start from scratch, and I'm still not sure if I've made up for a lot of that. I ended up in more creative fields, mostly because I felt inferior to those who had learned the rules and not been cocky douchebags like I had been in the beginning. This really sucks to write. I frequently wonder what could have been.

TrainedMonkey 13y ago
I got burned by this too. Problem, unfortunately, goes deeper than just not learning how to do math. You skip learning ability to structurally learn new things at a young age, because you simply "get" how things work. So by the time you hit the wall you not only not know how to do math correctly, but also have no idea how to structurally learn correct way and must do both at the same time. Here most people give up and say they are bad at math.
- Varcht 13y ago
  My daughter has gotten burnt in a similar way. She's grown up in the teach to the test era. She has been a straight A student and sadly I did not see it but what she is gifted in is memorization. You tell her 300 answers to the upcoming test and she will be able to recall them. It is now becoming apparent that she is stunted when it comes to actually reasoning and learning, PSAT kicked her butt and as a HS Junior she is struggling to maintain a B. Not sure how to fix this...
  - legacy2013 13y ago
    Try and find something she's interested in. I was this way all throughout high school because nothing ever interested. When I got to college and started studying CS though, I was extremely interested and always wanted to know how things worked, I still knew most of the answers without trying, but I would dig in to see why the answer worked. This saved me my Junior year when we started getting into complex concept that I couldn't just "figure out". Having something of interest (to the person) to study will almost always lead to better study habits.
  - enjo 13y ago
    I can tell you what worked for a friends daughter: Music. They steered her (somewhere around her sophmore year) into playing piano and eventually she found the guitar. As she described it "I needed to rewire my brain and music was the way to do that". From her perspective learning to play music helped her begin to understand how things "fit" together in her head. Her ability to memorize things was incredibly helpful (so she was initially a step-up in confidence), but as she played more she began to see how chords build on each other to form songs. She went from rote memorization to actually building a mental model of music. In the end she became not only a fantastic musician but a MUCH better student.
- selimthegrim 13y ago
  This. I managed to keep this up through even the reasonably prestigious STEM school I attended for undergrad. It was only when taking reasonably challenging graduate physics courses in grad school and having to do research that I finally was forced to break myself down and learn how to learn.
delluminatus 13y ago
Yes, it's real. In my case, overconfidence in high school led me to not devote the effort -- to not know how to devote the effort -- to securing acceptance to a prestigious college. It ended up OK -- I graduated a year early at the college I did attend -- so I'm not complaining, but I still notice effects of the "curse" impacting my behavior every day, especially when faced with intimidating work or with looking the fool.
ToastyMallows 13y ago
> I showed up to my AP calculus test without a calculator In my Calculus class we weren't even allowed to use a calculator on the test. Actually, almost all my math classes through college wouldn't let us use calculators during tests.
- delluminatus 13y ago
  Yes, but if a test is designed to be taken with a calculator, not bringing one is an invitation to disaster (especially if the test is timed), because the arithmetic is probably not designed to be easy. I once forgot a calculator in my discrete math class and ended up having to do long division in the test margins.
  - ToastyMallows 13y ago
    Believe me I've been there before. My point was rather that I think the person who was giving the test was wrong to offer that students use calculators.
    - jeorgun 13y ago
      That calculators are used on the AP calc test isn't exactly one teacher's decision, though. (I actually did the same thing on mine, but fortunately extra calculators were provided, possibly because of their past experiences with students pulling this kind of stunt).
    - LukeShu 13y ago
      Since 1995, the AP Calculus exam has been designed to require a graphing calculator. In my opinion, that's silly, as none of the 3 semesters of college calculus I took allowed the use of a calculator, but that's the test that was mentioned.
    - cosmie 13y ago
      I believe the parent was referring to the AP Calculus exam, based off of his 2 out of 5 score[1]. For non-Americans, AP exams are standardized tests administered by the College Board (company behind the SAT university entrance exams)[2]. Most universities will accept passing AP exam scores as the equivalent college credit (e.g. a score of 3/5 is usually accepted as college credit for Calculus I). AP Exams/Courses are offered in many subject areas and each have very strict guidelines (like which calculators to allow), which are dictated to the instructor by the College Board. [1] http://en.wikipedia.org/wiki/AP_Calculus#Exam http://en.wikipedia.org/wiki/AP_Calculus#Exam [2] http://en.wikipedia.org/wiki/College_Board http://en.wikipedia.org/wiki/College_Board
bradleyjg 13y ago
It's bad in more ways than one. Not only do you eventually hit a wall in the subjects you are naturally gifted in and find yourself without the skills to keep going, you also probably avoided the subjects your weren't naturally gifted in. So for example, maybe you can't keep going in math because you can no longer do it in your head and never learned how to do it on paper, but you also never learned to write well, so moving over to some liberal arts major isn't going to be any walk in the park either. Even if you find something else that you are really good at, you are only keeping the house of cards standing a little longer. Although this may be just deflecting the blame, I do think that the educational system in the US by and large poorly serves gifted children. The underlying notion seems to be that gifted children are already ahead of the game and so don't deserve any special attention. Another piece of the puzzle is grading-as-certification rather than grading-as-progress report or some other scheme. Straight As can mask a lot of problems.
- ejk314 13y ago
  >Straight As can mask a lot of problems. I've got a room mate who was put ahead a grade in middle?late-elementary school and missed the whole foundation of algebra. They did so because he got straight A's so obviously he's smart enough; he could just skip that. (They promised to give him a text book so he could learn on his own that summer, but never got around to giving it to him.) Of course, he started struggling in school the next year. Now math is one of his worst subjects. They completely screwed him over because they were distracted by his grades.
  - bunderbunder 13y ago
    I have never, ever, ever met someone who was well-served by skipping a grade. Myself included. Ever. Skipping a grade means giving up a full year of education. If that proposition doesn't give you pause, you probably don't have enough respect for the value of education. Even if you you get absolutely nothing out of that year aside from the soft skills you develop by sitting in a class with other kids and listening to lectures and grinding through homework (even stupid and boring homework), it's still vastly more valuable than the fleeting ego boost you get in exchange when you sacrifice it in order to skip a grade. Parents, please, this is one marshmallow test[1] you and your kids really don't want to fail. [1]: http://en.wikipedia.org/wiki/Stanford_marshmallow_experiment http://en.wikipedia.org/wiki/Stanford_marshmallow_experiment
bluedino 13y ago
I did the same thing and would get 0 credit for assignments or tests because I didn't "show my work". It made the 15 year old me furious and I basically swore math off after that.
- alxndr 13y ago
  Me too, but it meant that I ended up learning how to fake showing-the-work after I knew what the answer was, which I think in turn taught me what they were trying to get across in the first place...
- smky80 13y ago
  This stuff makes me laugh looking back on it. Also teachers saying stuff like, "If you do all of your homework, no matter what you will get at least a B." Pretty much high school was an obedience test. "Monkeys, if you do exactly what I tell you, when I tell you, I will rate you all 'Above Average'."
colechristensen 13y ago
For me it was never exactly learning-how-to-learn, but struggling with the anxiety of difficulty once I got past the level where everything was trivially easy. It's not something I've entirely conquered either, frustration leading to shut-down still happens from time to time.
ChuckMcM 13y ago
We home schooled our kids prior to high school and one of the more interesting challenges was this 'doing the steps' part. My eldest was very much like you, look at the problem, tell you the answer. Which was 99% of the time correct, and 1% of the time wrong. She was really annoyed that we focused on that 1% but eventually we got to the point where by writing down all the steps you could then see where in your thinking you had been mislead. The trick was differentiating between "doing math" versus "learning math." (and the nice thing about math at this level is that if you get all the steps right you cannot help but get the right answer). Once we got past the big fight about "always showing your work" not being a 'for all time, forever' edict but instead for a 'these problems while you are learning' edict, it became possible to do math in this ponderous way, but only when learning and only when training our minds on the steps and alerting ourselves to the places we were likely to make mistakes.
- renovaatio 13y ago
  I was (and still am in many ways) this undisciplined kid. I never learned the value of a good work ethic, of effort. One of the most important thing I want to teach my 4 months old son, is the value of effort. I am glad you shared your experience, I will keep it as one of the many tools I am gathering so that I can be able to teach what I haven't learned to my children.
- exhilaration 13y ago
  Thank you, this is especially useful advice when your child is able to get the kind of one-on-one attention that home schooling can provide.
- deleted 13y ago
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hcarvalhoalves 13y ago
I can relate to that. College-level calculus burned me so much, I didn't had the algebra background necessary to grok it, much of it is memorizing heuristics and "tricks", and college professors (specially in my public uni) didn't had much patience either. I even did well in other math-related classes, but calculus was a chimera. Unfortunately, I fell so much behind the curriculum that I had to drop out of college to start working full-time. Lately I've been picking up other math-related online classes, and I finally realized that I had never had real exposure to mathematics, and that high-school curriculum is something else. So, there's that too... we are mostly scammed into thinking we've learned something during high-school, and then life happens and you actually figure out you don't know shit. Hopefully I'm a curious person, so I'm always learning something by myself, mostly to broaden my knowledge in other topics, but to not let the gears grind too.
- taternuts 13y ago
  I definitely remember the first time I could no longer slack off, take 0's on homeworks, and ace tests to get a C+/B and it was in high-school :( I jumped to AP Calculus without taking the pre-requisite AP class everyone else had taken, and I thought I was so cool and smart. By the weeks end I no longer felt so cool and smart - I was completely lost.
  - hcarvalhoalves 13y ago
    Calculus sucked more for me because here in Brazil the education system doesn't include it in the high-school curriculum, so unless you're on some top private school, you only first hear about "calculus" in college. In the USA and other places there's exposure to it prior to college, which I believe is sensible. As a side note, I can't stress enough how bad the education system is in Brazil (in the sense of lack of structure, motivation, etc.), even at college level. Almost everything I know is self-taught (including English). I sometimes hear complaints about public school in the USA, and there's a meme that americans are "dumb", but it seems miles ahead to what I had access to.
    - tjr 13y ago
matwood 13y ago
I'm with you. I made it to hardware architecture in undergrad without ever pulling out a book to study. Then I had a rude awakening and ended up on academic probation and failed a few classes while I figured out how to study. Luckily I was friends with a couple of girls who were driven (finished school with 4.0s after finishing HS with 4.0s, etc...) who basically taught me how to study. They also showed me the effort required to really learn something. I think in the end, the slap in the face came at the right time and made me more capable later. No matter how smart a person is, there are things they do not know and have to go learn. Learning how to learn it skill, and like all skills it takes practice.
mgkimsal 13y ago
Almost exact same here, except I failed college calculus - twice. It's always been a sore point for me that people who are obviously not as 'smart' as I am somehow all managed to pass it - I couldn't even understand it. Can I lay a little blame on bad professors? perhaps. others complained about the profs too, but ... they still managed to grok enough to pass. I only managed to satisfy degree requirements by taking 'logic' (a philosophy class) instead of calculus. I was warned off trying this route by a few people though, as it was "hard". I'd been hobby programming for... 10 years at that point - there's little about 'logic' that could possibly be 'hard' in a logic 101 class, so I passed by doing something I was naturally good at. I simply couldn't afford (financially) taking calculus another 2-3 times to keep trying to pass. It's still a sore point even now... 20+ years later, and a source of secret (perhaps not so secret now that I post this!) shame. :( I'd never even had to try at anything (except music, perhaps) until well in to high school, at which point I'd mostly just given up. I scored in the top 2% of the ACT test (back when it was scored differently, in the 80s), and I'm not actually 100% sure I finished all the questions - I know I didn't study for it, nor was I particularly well rested. Yeah, as someone else wrote, schools are simply not oriented towards helping 'gifted' students, assuming that they're already 'ahead' of others, and seem to be left on their own - I know I was.
- thisrod 13y ago
  Did you ever read Calculus Made Easy? If you just want to understand enough calculus to know why a thrown ball follows a parabola, that really isn't hard. The typical university course aims higher than that - it's trying to instill a way of thinking that's required to progress towards a third year course in Generalised Nonsense Theory. That way of thinking is quite unnatural, and makes the calculus course harder than it needs to be.
  - mgkimsal 13y ago
    no - have not revisited it at all. I've been encouraged to, and may do that later this year or next depending on my schedule. thanks for the tip.
    - 13y ago
nicholas73 13y ago
It happened to me during second semester Calculus. In first semester, the professor found out that I didn't do the assigned homework (worth no points) and said that I would "die" in next semester. Sure enough, it happened. What I learned over the years since that time is that some things just take practice or effort. The difference in Calc 2 was that the problems became non-intuitive and virtually everyone is forced to learn some identity or transformation to solve a problem (usually involving trig functions). Basically second-order formula plug and chug, but "effort" required to be able to do it right with time constraint. I still didn't espouse the value of hard work until I've gotten out of college. I tried to cruise by like I always did, though it increasingly became untenable. What made me really understand working hard was actually through sports. There, I had no illusion of being superior, and it's established that you get better through practice. You get to see yourself getting better each time, and put yourself to the test. True iteration.
- livingparadox 13y ago
  I had a similar experience. Breezed through my first calculus class. No studying, no homework (also no points), not even necessarily paying attention in class. Easy A. Then I took Calc 2. I don't think I've ever failed so hard in my life. ... Except freaking english...
  - mullingitover 13y ago
    Integrals are the devil's handiwork. Derivatives are almost too easy, and then you get to Calc II and suddenly you're supposed to be able to do it inside out and backwards, with the help of all those dozens of identities you must now memorize. I went from an A+ in Calc I to a C- in Calc II.
    - eropple 13y ago
      Yup. I bombed calculus twice simply because I have a lot of trouble memorizing things like that. I ended up taking the sucker's way out: I took it online in a class where Mathematica was encouraged. I use derivatives and integrals pretty often now, but I've yet to need to do them by hand since.
josephschmoe 13y ago
I never hit a wall with mathematics. My approach was to write down what I have to and do everything else in my head. I hit a wall within the first five minutes of programming. I know I will mistakes and I make up for that by making small, clear code commits and trying to make my code easy to read. I'm a much better programmer than I am a physicist. I am also much happier working as a programmer than I was studying physics.
- gknoy 13y ago
  I definitely make mistakes, so one tactic I use is liberal use of code comments. I start with a comment about what the overall task is about, so that I can keep perspective, and then I will use a series of "TODO ..." comments to break things down into smaller steps. The nice thing about this is, some of those survive revisions and can then be line comments which explain the next few lines of code: # Frob the Foo.womble, so that Bar gets its input # in the format it expects Similarly, I have grown to use commit messages longer than one line, even if I expect to later rebase it together with something else.
  - 72deluxe 13y ago
    I tend to design stuff on paper with logical boxes and arrows, then add that as a large comment at the beginning of a complex section, then implement it without any comments in the code. That way, the code is still readable but there is a reference above it. Just like you have in books on programming languages.
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larrys 13y ago
"I am miles away from Eric..." ESR "grandpa" was at the Wharton Computer Center when I was there. [1] http://www.catb.org/~esr/resume.html http://www.catb.org/~esr/resume.html At Wharton, at the time, this was definitely true: "When you were in college, did you ever meet bright kids who graduated top of their class in high-school and then floundered freshman year in college because they had never learned how to study? It's a common trap. A friend of mine calls it "the curse of the gifted"" I was lucky that I had to work hard in high school. I definitely noticed a bunch of kids that were actually depressed when they were surrounded by others equally gifted and got their first "b" grade. No adversity experience. [1] APL was big back then. http://en.wikipedia.org/wiki/APL_%28programming_language%29 http://en.wikipedia.org/wiki/APL_%28programming_language%29
tempestn 13y ago
I was lucky enough to get hit by this early. I always cruised through math with very little effort, doing any required homework in the 5 minute break before class, etc, and getting near 100%. In grade 9, I didn't fail hard or anything, but I did struggle with the final exam, and ended up with a B in the course. Fortunately that was enough of a wake-up for me, and at that point it was still early enough to correct course without a massive upheaval. I'm thankful I didn't continue to cruise until hitting a real wall in university.
dools 13y ago
I would highly recommend going back and learning maths properly. In my case, I actually gave up on maths in year 7 because I wanted to hang out with friends more than study. I consistently failed in high school despite being pretty promising in primary school ... but that's just 'cause I "wasn't trying", right? Well, maybe so, but maths is a skill. You can't ignore it for 4 years and then pick it up in the same way you can with English or Japanese or Sociology. So when it came to year 11 and 12, when I actually wanted to do well at maths, I couldn't, so I borderline failed high school maths. A foible of the (Australian) state in which I went to year 11/12 meant that, despite not using maths towards my university entrance score, I was still allowed to use it as a pre-requisite to get into a university course. I didn't go to uni straight away because I didn't really know what I wanted to do. At age 21 and on a whim, on the last day that you could mail your applications in, I picked Mechatronic Engineering from the handbook and sent in my application. Why? Because I thought it sounded cool (I used to love Robotech :) but I had no idea that Engineering was so maths heavy (that's how ignorant I was of the field). First year I failed everything. The only thing I did well in was programming, so I took 2 years off and got a job as a programmer. In the last 6 months before I started uni again, I went through my Calculus text book from the beginning, going over my first year uni notes and assignments at the same time. Answering all the problems in the book, etc. As it turns out, the things that were most nobbling my ability to do calculus was lack of understanding of algebra, trigonometry, geometry ... things like logs and graphs and functions, factorisation, all that stuff. Once I'd learned that, I discovered the rest wasn't so bad. I re-did my first year subjects in summer school that year and passed (even got some Credits which is 65+!) and then managed to get a low distinction in one of my second year courses. You never saw a guy so happy with his 75 in Vector Calculus :) all the engineering geeks were crying in their pillows because they got a 98 instead of a 100 but I was punching some serious air. Getting past this personal myth that I was "just bad at maths" is one of the most important things I've ever done. It really taught me that, with persistent execution and incremental improvement, you can learn and do anything (within reason: ie. I probably can't learn to levitate although I'd love to be proven wrong :)
urs2102 13y ago
Reiterating austennailred, despite being miles way from ESR or Linus, the "curse of the gifted" is 100% real, but I think it can actually be beneficial in the long run for a certain type of "gifted". There is one on hand the "gifted" who runs on his own fumes with no other form of external effort. Much like @austennailred notes about his efforts in high school mathematics, this type of "gifted" often suffers from something similar to the Dunning-Kruger effect in the long run --> in other words, a sense of superiority can potentially drive you into believing you are better than you actually are. This, I believe, can happen when people attempt to pursue things which do not particularly satisfy their innate curiosity or their genuine interests. Sure you can be great at math naturally, but your view of how good you are limited by the population size of those you compare yourself against can leave you damagingly unprepared when you realize that you actually aren't as great as you thought you were. What makes the "curse of the gifted" the "blessing of the gifted" on the other hand, is when that moment where you realize your own fallibility seems to provide a moment of illumination rather than a sense of dejection. For me, my first attempts at genuine college level discrete mathematics versus having used basic counting, permutations, probability, number theory principles in the past showed that computer science or at least the mathematics of computer science can be difficult. I had a similar issue in chemistry as well. The difference was even though I was always a strong math and science student, approaching college level chemistry made me just feel inferior and made me drop it. On the other hand, when faced with adversity in mathematics/CS I tended to take the difficulty as a challenge. Rather than drop it, realizing that perhaps there were others who could be better at mathematics, CS in this new environment drove me to pushing myself to a place of intense focus I had had before. Now this is where I think passion crosses with the concept of the "curse of the gifted" to make it more of a blessing than a curse. When you love something and you know what it feels like to be best, realizing your own shortcomings can sometimes cause you to miss that feeling. Now in order to get back to a place where you "feel gifted" you have to be in love with the work to get there over "the idea of being gifted" and this I think can happen to those who are put in a position where the feeling of "being gifted" is compromised. Anyway, just my view, first "longer" post I've written on HN but I thought austennailred had a great point and just wanted to comment. Great piece by both Eric and Linus and crazy to think how 14 years later, we have Git.
joyeuse6701 13y ago
Hear you on that, I had no discipline in high school compared to my contemporaries. Then I went to college and had my first CS classes. I couldn't handle the load, couldn't get the discipline to study between the distractions of college life and stubborn refusal to learn how to study. I ended up getting really into martial arts and that discipline transferred over. When I went back to school. Thank God for that, because I'd be in a very different place without it.
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graycat 13y ago
When he was about 20, Yehudi Menuhin, one of the best concert violinists of the 20th century, concluded that suddenly he didn't know how to play violin. Why? Because before his teachers, back to his age 7 or so, had carefully walked him through the music note by note and bar by bar and, likely then, the artistic expression. But, still he was darned gifted. So, a few years later, relearning violin, he was fine again for the rest of his life. Being able to do arithmetic, algebra, and other mathematical operations in your head is fine. E.g., during WWII, John von Neumann, one of the best mathematicians of the 20th or any century, sometimes went to people working on war projects to see if he could help them out. At one stop, a guy was unsure about how to find a solution, so von Neumann suggested, "Let's try a local solution via infinite series and look at a few terms. So, von Neumann did the arithmetic in his head [he could take two eight digit numbers and multiply them together in his head]. When von Neumann left, the guy was near tears. Why? Because he had been up all night using a mechanical desk calculator to get just some of that arithmetic right! I found in doing research in math (I've published such stuff), once get into the problem well then do most of the thinking for the actual research just between the ears and writing very little. Can even do some of the algebraic derivations just between the ears. The actual research, at least the way I do it, is heavily 'conceptual' where writing isn't very efficient anyway. From what you wrote, I see nothing wrong with your abilities. If you are not handy with paper and pencil, then it is not too much to expect you to become handy with just some usage. So, try, and soon you will 'get it'. It sounds like your problem with calculus was mostly just a problem with paper and pencil -- so, 'get it' with paper and pencil. Unless are, say, another von Neumann, can't expect to do significant derivations in calculus, say, integration by parts or multiple integrals, without writing down the expressions step by step. But, of course, for calculus, long ago some software efforts for integration worked out what expressions could be integrated in closed form and what ones could not and wrote software to do the integrations for all the ones that could. The results are in at least one of the old computer algebra packages! So, with that software, "Look, Ma, no pencil or paper!". About your suspected faults, don't be the least discouraged about them! Some are just your imagination. Some can be easily enough corrected. Essentially all the rest can be circumvented. In particular, it appears that you are concerned about some skills that were supposed to take you from a few days to at most a few months to get good enough with way back long before you shaved! Doing catch up on that material now should be a few days' walk in the park. E.g., in K-12, I didn't learn English grammar and punctuation very well. In college I was in math and physics where this gap was not very important, and otherwise I just wrote only sentences where I did understand the grammar and punctuation. Now I've long had a 12th grade English grammar book right at hand and look up details when I'm in doubt; long ago I got nearly everything I missed in K-12. Back to working without writing, in plane geometry I refused to do the homework the way the teacher wanted, write out in full detail proofs of just three problems. Instead I worked all the non-trivial problems and then also the more challenging ones in the back of the book, often writing nothing, sometimes writing in the margin of the book, sometimes on scraps of paper, and only for a few of the most difficult problems in the book, actually writing out a complete proof. Worked fine! When the teacher wanted to see my homework, I showed her nothing, and she was torqued. When I came in second in the class on the state test, she was 'confused' since she thought that I didn't do any of the homework! Heck, I solved every non trivial problem in the book and, thus, likely did the most homework of anyone in the class. Also, I slept in class -- I learned from the book in a quiet room, not when she was making noise in front of the class! Being able to learn math just from a book proved crucial, the main way I got my Ph.D.! Lesson: You don't always have to do it their way!
puredemo 13y ago
It's also an example of why it's poor practice to teach the gifted along side of lower performing students -- they realize they can get by easily without working hard and it becomes a habit. Ideally, the gifted should have their own programs where they are forced to compete with other exceptional students the entire time they're in school, rather than follow a program meant to pander to the lowest common denominator students in society. Also, I'm with you bro, fell into the same trap. It sucks.
berto99 13y ago
ugh, the way you did it, I thought that was the way most people did it. Usually you see the answer and only "show working". Though the mechanical approach can facilitate more complex problems.
loganu 13y ago
I think we're the same person. Up until grade 12, I could show up late, stoned, or not at all, skip all the homework, and end up at the top of the class due to tests. I was on-track/ pre-accepted into engineering until calculus came, and my natural "getting" math completely tapered off. When the problems became abstract enough that I couldn't understand what they were asking for (or more importantly, why) I dropped out of my first course. Switched to a more creative field, and circled back towards engineering-type jobs 10 years later. Happy (enough) with where I am now, but can't help but think things would have been better if laziness, hubris and structure of the school system didn't keep me from learning how to learn earlier.
pydave 13y ago
> "x + 1 = 6" I didn't have to subtract 1 from each side, I just thought about it logically and knew the answer. I don't see the difference. In my mind, thinking about it logically is recognizing that one side has an excess and removing it from the other side. That's subtracting. To you is it like looking at 5 * 4 and knowing it's 20 rather than thinking about 2 * 5 is 10 and two of those is 20? I was the kind of rule-following kid who went through the algebra steps because you were supposed to rather than out of necessity. (Or so I like to think: I'm not good at math in my head because I always wrote it out or maybe I relied on paper since I couldn't do it in my head.) I recall rebelling against memorizing multiplication tables in grade ~4 because I thought my time was better spent leaning new stuff (or maybe understanding how to multiply faster -- wouldn't that be ironic!). It's always interesting to hear how someone else's brain works. Thank you.
- dllthomas 13y ago
  But there's doing it, and there's knowing how you're doing it.

TrainedMonkey 13y ago

I got burned by this too. Problem, unfortunately, goes deeper than just not learning how to do math. You skip learning ability to structurally learn new things at a young age, because you simply "get" how things work. So by the time you hit the wall you not only not know how to do math correctly, but also have no idea how to structurally learn correct way and must do both at the same time. Here most people give up and say they are bad at math.

Varcht 13y ago
My daughter has gotten burnt in a similar way. She's grown up in the teach to the test era. She has been a straight A student and sadly I did not see it but what she is gifted in is memorization. You tell her 300 answers to the upcoming test and she will be able to recall them. It is now becoming apparent that she is stunted when it comes to actually reasoning and learning, PSAT kicked her butt and as a HS Junior she is struggling to maintain a B. Not sure how to fix this...
- legacy2013 13y ago
  Try and find something she's interested in. I was this way all throughout high school because nothing ever interested. When I got to college and started studying CS though, I was extremely interested and always wanted to know how things worked, I still knew most of the answers without trying, but I would dig in to see why the answer worked. This saved me my Junior year when we started getting into complex concept that I couldn't just "figure out". Having something of interest (to the person) to study will almost always lead to better study habits.
- enjo 13y ago
  I can tell you what worked for a friends daughter: Music. They steered her (somewhere around her sophmore year) into playing piano and eventually she found the guitar. As she described it "I needed to rewire my brain and music was the way to do that". From her perspective learning to play music helped her begin to understand how things "fit" together in her head. Her ability to memorize things was incredibly helpful (so she was initially a step-up in confidence), but as she played more she began to see how chords build on each other to form songs. She went from rote memorization to actually building a mental model of music. In the end she became not only a fantastic musician but a MUCH better student.
selimthegrim 13y ago
This. I managed to keep this up through even the reasonably prestigious STEM school I attended for undergrad. It was only when taking reasonably challenging graduate physics courses in grad school and having to do research that I finally was forced to break myself down and learn how to learn.

delluminatus 13y ago

Yes, it's real. In my case, overconfidence in high school led me to not devote the effort -- to not know how to devote the effort -- to securing acceptance to a prestigious college. It ended up OK -- I graduated a year early at the college I did attend -- so I'm not complaining, but I still notice effects of the "curse" impacting my behavior every day, especially when faced with intimidating work or with looking the fool.

ToastyMallows 13y ago

> I showed up to my AP calculus test without a calculator In my Calculus class we weren't even allowed to use a calculator on the test. Actually, almost all my math classes through college wouldn't let us use calculators during tests.

delluminatus 13y ago
Yes, but if a test is designed to be taken with a calculator, not bringing one is an invitation to disaster (especially if the test is timed), because the arithmetic is probably not designed to be easy. I once forgot a calculator in my discrete math class and ended up having to do long division in the test margins.
- ToastyMallows 13y ago
  Believe me I've been there before. My point was rather that I think the person who was giving the test was wrong to offer that students use calculators.
  - jeorgun 13y ago
    That calculators are used on the AP calc test isn't exactly one teacher's decision, though. (I actually did the same thing on mine, but fortunately extra calculators were provided, possibly because of their past experiences with students pulling this kind of stunt).
  - LukeShu 13y ago
    Since 1995, the AP Calculus exam has been designed to require a graphing calculator. In my opinion, that's silly, as none of the 3 semesters of college calculus I took allowed the use of a calculator, but that's the test that was mentioned.
  - cosmie 13y ago
    I believe the parent was referring to the AP Calculus exam, based off of his 2 out of 5 score[1]. For non-Americans, AP exams are standardized tests administered by the College Board (company behind the SAT university entrance exams)[2]. Most universities will accept passing AP exam scores as the equivalent college credit (e.g. a score of 3/5 is usually accepted as college credit for Calculus I). AP Exams/Courses are offered in many subject areas and each have very strict guidelines (like which calculators to allow), which are dictated to the instructor by the College Board. [1] http://en.wikipedia.org/wiki/AP_Calculus#Exam http://en.wikipedia.org/wiki/AP_Calculus#Exam [2] http://en.wikipedia.org/wiki/College_Board http://en.wikipedia.org/wiki/College_Board

bradleyjg 13y ago

It's bad in more ways than one. Not only do you eventually hit a wall in the subjects you are naturally gifted in and find yourself without the skills to keep going, you also probably avoided the subjects your weren't naturally gifted in. So for example, maybe you can't keep going in math because you can no longer do it in your head and never learned how to do it on paper, but you also never learned to write well, so moving over to some liberal arts major isn't going to be any walk in the park either. Even if you find something else that you are really good at, you are only keeping the house of cards standing a little longer. Although this may be just deflecting the blame, I do think that the educational system in the US by and large poorly serves gifted children. The underlying notion seems to be that gifted children are already ahead of the game and so don't deserve any special attention. Another piece of the puzzle is grading-as-certification rather than grading-as-progress report or some other scheme. Straight As can mask a lot of problems.

ejk314 13y ago
>Straight As can mask a lot of problems. I've got a room mate who was put ahead a grade in middle?late-elementary school and missed the whole foundation of algebra. They did so because he got straight A's so obviously he's smart enough; he could just skip that. (They promised to give him a text book so he could learn on his own that summer, but never got around to giving it to him.) Of course, he started struggling in school the next year. Now math is one of his worst subjects. They completely screwed him over because they were distracted by his grades.
- bunderbunder 13y ago
  I have never, ever, ever met someone who was well-served by skipping a grade. Myself included. Ever. Skipping a grade means giving up a full year of education. If that proposition doesn't give you pause, you probably don't have enough respect for the value of education. Even if you you get absolutely nothing out of that year aside from the soft skills you develop by sitting in a class with other kids and listening to lectures and grinding through homework (even stupid and boring homework), it's still vastly more valuable than the fleeting ego boost you get in exchange when you sacrifice it in order to skip a grade. Parents, please, this is one marshmallow test[1] you and your kids really don't want to fail. [1]: http://en.wikipedia.org/wiki/Stanford_marshmallow_experiment http://en.wikipedia.org/wiki/Stanford_marshmallow_experiment

bluedino 13y ago

I did the same thing and would get 0 credit for assignments or tests because I didn't "show my work". It made the 15 year old me furious and I basically swore math off after that.

alxndr 13y ago
Me too, but it meant that I ended up learning how to fake showing-the-work after I knew what the answer was, which I think in turn taught me what they were trying to get across in the first place...
smky80 13y ago
This stuff makes me laugh looking back on it. Also teachers saying stuff like, "If you do all of your homework, no matter what you will get at least a B." Pretty much high school was an obedience test. "Monkeys, if you do exactly what I tell you, when I tell you, I will rate you all 'Above Average'."

colechristensen 13y ago

For me it was never exactly learning-how-to-learn, but struggling with the anxiety of difficulty once I got past the level where everything was trivially easy. It's not something I've entirely conquered either, frustration leading to shut-down still happens from time to time.

ChuckMcM 13y ago

We home schooled our kids prior to high school and one of the more interesting challenges was this 'doing the steps' part. My eldest was very much like you, look at the problem, tell you the answer. Which was 99% of the time correct, and 1% of the time wrong. She was really annoyed that we focused on that 1% but eventually we got to the point where by writing down all the steps you could then see where in your thinking you had been mislead. The trick was differentiating between "doing math" versus "learning math." (and the nice thing about math at this level is that if you get all the steps right you cannot help but get the right answer). Once we got past the big fight about "always showing your work" not being a 'for all time, forever' edict but instead for a 'these problems while you are learning' edict, it became possible to do math in this ponderous way, but only when learning and only when training our minds on the steps and alerting ourselves to the places we were likely to make mistakes.

renovaatio 13y ago
I was (and still am in many ways) this undisciplined kid. I never learned the value of a good work ethic, of effort. One of the most important thing I want to teach my 4 months old son, is the value of effort. I am glad you shared your experience, I will keep it as one of the many tools I am gathering so that I can be able to teach what I haven't learned to my children.
exhilaration 13y ago
Thank you, this is especially useful advice when your child is able to get the kind of one-on-one attention that home schooling can provide.
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hcarvalhoalves 13y ago

I can relate to that. College-level calculus burned me so much, I didn't had the algebra background necessary to grok it, much of it is memorizing heuristics and "tricks", and college professors (specially in my public uni) didn't had much patience either. I even did well in other math-related classes, but calculus was a chimera. Unfortunately, I fell so much behind the curriculum that I had to drop out of college to start working full-time. Lately I've been picking up other math-related online classes, and I finally realized that I had never had real exposure to mathematics, and that high-school curriculum is something else. So, there's that too... we are mostly scammed into thinking we've learned something during high-school, and then life happens and you actually figure out you don't know shit. Hopefully I'm a curious person, so I'm always learning something by myself, mostly to broaden my knowledge in other topics, but to not let the gears grind too.

taternuts 13y ago
I definitely remember the first time I could no longer slack off, take 0's on homeworks, and ace tests to get a C+/B and it was in high-school :( I jumped to AP Calculus without taking the pre-requisite AP class everyone else had taken, and I thought I was so cool and smart. By the weeks end I no longer felt so cool and smart - I was completely lost.
- hcarvalhoalves 13y ago
  Calculus sucked more for me because here in Brazil the education system doesn't include it in the high-school curriculum, so unless you're on some top private school, you only first hear about "calculus" in college. In the USA and other places there's exposure to it prior to college, which I believe is sensible. As a side note, I can't stress enough how bad the education system is in Brazil (in the sense of lack of structure, motivation, etc.), even at college level. Almost everything I know is self-taught (including English). I sometimes hear complaints about public school in the USA, and there's a meme that americans are "dumb", but it seems miles ahead to what I had access to.
  - tjr 13y ago

matwood 13y ago

I'm with you. I made it to hardware architecture in undergrad without ever pulling out a book to study. Then I had a rude awakening and ended up on academic probation and failed a few classes while I figured out how to study. Luckily I was friends with a couple of girls who were driven (finished school with 4.0s after finishing HS with 4.0s, etc...) who basically taught me how to study. They also showed me the effort required to really learn something. I think in the end, the slap in the face came at the right time and made me more capable later. No matter how smart a person is, there are things they do not know and have to go learn. Learning how to learn it skill, and like all skills it takes practice.

mgkimsal 13y ago

Almost exact same here, except I failed college calculus - twice. It's always been a sore point for me that people who are obviously not as 'smart' as I am somehow all managed to pass it - I couldn't even understand it. Can I lay a little blame on bad professors? perhaps. others complained about the profs too, but ... they still managed to grok enough to pass. I only managed to satisfy degree requirements by taking 'logic' (a philosophy class) instead of calculus. I was warned off trying this route by a few people though, as it was "hard". I'd been hobby programming for... 10 years at that point - there's little about 'logic' that could possibly be 'hard' in a logic 101 class, so I passed by doing something I was naturally good at. I simply couldn't afford (financially) taking calculus another 2-3 times to keep trying to pass. It's still a sore point even now... 20+ years later, and a source of secret (perhaps not so secret now that I post this!) shame. :( I'd never even had to try at anything (except music, perhaps) until well in to high school, at which point I'd mostly just given up. I scored in the top 2% of the ACT test (back when it was scored differently, in the 80s), and I'm not actually 100% sure I finished all the questions - I know I didn't study for it, nor was I particularly well rested. Yeah, as someone else wrote, schools are simply not oriented towards helping 'gifted' students, assuming that they're already 'ahead' of others, and seem to be left on their own - I know I was.

thisrod 13y ago
Did you ever read Calculus Made Easy? If you just want to understand enough calculus to know why a thrown ball follows a parabola, that really isn't hard. The typical university course aims higher than that - it's trying to instill a way of thinking that's required to progress towards a third year course in Generalised Nonsense Theory. That way of thinking is quite unnatural, and makes the calculus course harder than it needs to be.
- mgkimsal 13y ago
  no - have not revisited it at all. I've been encouraged to, and may do that later this year or next depending on my schedule. thanks for the tip.
  - 13y ago

nicholas73 13y ago

It happened to me during second semester Calculus. In first semester, the professor found out that I didn't do the assigned homework (worth no points) and said that I would "die" in next semester. Sure enough, it happened. What I learned over the years since that time is that some things just take practice or effort. The difference in Calc 2 was that the problems became non-intuitive and virtually everyone is forced to learn some identity or transformation to solve a problem (usually involving trig functions). Basically second-order formula plug and chug, but "effort" required to be able to do it right with time constraint. I still didn't espouse the value of hard work until I've gotten out of college. I tried to cruise by like I always did, though it increasingly became untenable. What made me really understand working hard was actually through sports. There, I had no illusion of being superior, and it's established that you get better through practice. You get to see yourself getting better each time, and put yourself to the test. True iteration.

livingparadox 13y ago
I had a similar experience. Breezed through my first calculus class. No studying, no homework (also no points), not even necessarily paying attention in class. Easy A. Then I took Calc 2. I don't think I've ever failed so hard in my life. ... Except freaking english...
- mullingitover 13y ago
  Integrals are the devil's handiwork. Derivatives are almost too easy, and then you get to Calc II and suddenly you're supposed to be able to do it inside out and backwards, with the help of all those dozens of identities you must now memorize. I went from an A+ in Calc I to a C- in Calc II.
  - eropple 13y ago
    Yup. I bombed calculus twice simply because I have a lot of trouble memorizing things like that. I ended up taking the sucker's way out: I took it online in a class where Mathematica was encouraged. I use derivatives and integrals pretty often now, but I've yet to need to do them by hand since.

josephschmoe 13y ago

I never hit a wall with mathematics. My approach was to write down what I have to and do everything else in my head. I hit a wall within the first five minutes of programming. I know I will mistakes and I make up for that by making small, clear code commits and trying to make my code easy to read. I'm a much better programmer than I am a physicist. I am also much happier working as a programmer than I was studying physics.

gknoy 13y ago
I definitely make mistakes, so one tactic I use is liberal use of code comments. I start with a comment about what the overall task is about, so that I can keep perspective, and then I will use a series of "TODO ..." comments to break things down into smaller steps. The nice thing about this is, some of those survive revisions and can then be line comments which explain the next few lines of code: # Frob the Foo.womble, so that Bar gets its input # in the format it expects Similarly, I have grown to use commit messages longer than one line, even if I expect to later rebase it together with something else.
- 72deluxe 13y ago
  I tend to design stuff on paper with logical boxes and arrows, then add that as a large comment at the beginning of a complex section, then implement it without any comments in the code. That way, the code is still readable but there is a reference above it. Just like you have in books on programming languages.

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larrys 13y ago

"I am miles away from Eric..." ESR "grandpa" was at the Wharton Computer Center when I was there. [1] http://www.catb.org/~esr/resume.html http://www.catb.org/~esr/resume.html At Wharton, at the time, this was definitely true: "When you were in college, did you ever meet bright kids who graduated top of their class in high-school and then floundered freshman year in college because they had never learned how to study? It's a common trap. A friend of mine calls it "the curse of the gifted"" I was lucky that I had to work hard in high school. I definitely noticed a bunch of kids that were actually depressed when they were surrounded by others equally gifted and got their first "b" grade. No adversity experience. [1] APL was big back then. http://en.wikipedia.org/wiki/APL_%28programming_language%29 http://en.wikipedia.org/wiki/APL_%28programming_language%29

tempestn 13y ago

I was lucky enough to get hit by this early. I always cruised through math with very little effort, doing any required homework in the 5 minute break before class, etc, and getting near 100%. In grade 9, I didn't fail hard or anything, but I did struggle with the final exam, and ended up with a B in the course. Fortunately that was enough of a wake-up for me, and at that point it was still early enough to correct course without a massive upheaval. I'm thankful I didn't continue to cruise until hitting a real wall in university.

dools 13y ago

I would highly recommend going back and learning maths properly. In my case, I actually gave up on maths in year 7 because I wanted to hang out with friends more than study. I consistently failed in high school despite being pretty promising in primary school ... but that's just 'cause I "wasn't trying", right? Well, maybe so, but maths is a skill. You can't ignore it for 4 years and then pick it up in the same way you can with English or Japanese or Sociology. So when it came to year 11 and 12, when I actually wanted to do well at maths, I couldn't, so I borderline failed high school maths. A foible of the (Australian) state in which I went to year 11/12 meant that, despite not using maths towards my university entrance score, I was still allowed to use it as a pre-requisite to get into a university course. I didn't go to uni straight away because I didn't really know what I wanted to do. At age 21 and on a whim, on the last day that you could mail your applications in, I picked Mechatronic Engineering from the handbook and sent in my application. Why? Because I thought it sounded cool (I used to love Robotech :) but I had no idea that Engineering was so maths heavy (that's how ignorant I was of the field). First year I failed everything. The only thing I did well in was programming, so I took 2 years off and got a job as a programmer. In the last 6 months before I started uni again, I went through my Calculus text book from the beginning, going over my first year uni notes and assignments at the same time. Answering all the problems in the book, etc. As it turns out, the things that were most nobbling my ability to do calculus was lack of understanding of algebra, trigonometry, geometry ... things like logs and graphs and functions, factorisation, all that stuff. Once I'd learned that, I discovered the rest wasn't so bad. I re-did my first year subjects in summer school that year and passed (even got some Credits which is 65+!) and then managed to get a low distinction in one of my second year courses. You never saw a guy so happy with his 75 in Vector Calculus :) all the engineering geeks were crying in their pillows because they got a 98 instead of a 100 but I was punching some serious air. Getting past this personal myth that I was "just bad at maths" is one of the most important things I've ever done. It really taught me that, with persistent execution and incremental improvement, you can learn and do anything (within reason: ie. I probably can't learn to levitate although I'd love to be proven wrong :)

urs2102 13y ago

Reiterating austennailred, despite being miles way from ESR or Linus, the "curse of the gifted" is 100% real, but I think it can actually be beneficial in the long run for a certain type of "gifted". There is one on hand the "gifted" who runs on his own fumes with no other form of external effort. Much like @austennailred notes about his efforts in high school mathematics, this type of "gifted" often suffers from something similar to the Dunning-Kruger effect in the long run --> in other words, a sense of superiority can potentially drive you into believing you are better than you actually are. This, I believe, can happen when people attempt to pursue things which do not particularly satisfy their innate curiosity or their genuine interests. Sure you can be great at math naturally, but your view of how good you are limited by the population size of those you compare yourself against can leave you damagingly unprepared when you realize that you actually aren't as great as you thought you were. What makes the "curse of the gifted" the "blessing of the gifted" on the other hand, is when that moment where you realize your own fallibility seems to provide a moment of illumination rather than a sense of dejection. For me, my first attempts at genuine college level discrete mathematics versus having used basic counting, permutations, probability, number theory principles in the past showed that computer science or at least the mathematics of computer science can be difficult. I had a similar issue in chemistry as well. The difference was even though I was always a strong math and science student, approaching college level chemistry made me just feel inferior and made me drop it. On the other hand, when faced with adversity in mathematics/CS I tended to take the difficulty as a challenge. Rather than drop it, realizing that perhaps there were others who could be better at mathematics, CS in this new environment drove me to pushing myself to a place of intense focus I had had before. Now this is where I think passion crosses with the concept of the "curse of the gifted" to make it more of a blessing than a curse. When you love something and you know what it feels like to be best, realizing your own shortcomings can sometimes cause you to miss that feeling. Now in order to get back to a place where you "feel gifted" you have to be in love with the work to get there over "the idea of being gifted" and this I think can happen to those who are put in a position where the feeling of "being gifted" is compromised. Anyway, just my view, first "longer" post I've written on HN but I thought austennailred had a great point and just wanted to comment. Great piece by both Eric and Linus and crazy to think how 14 years later, we have Git.

joyeuse6701 13y ago

Hear you on that, I had no discipline in high school compared to my contemporaries. Then I went to college and had my first CS classes. I couldn't handle the load, couldn't get the discipline to study between the distractions of college life and stubborn refusal to learn how to study. I ended up getting really into martial arts and that discipline transferred over. When I went back to school. Thank God for that, because I'd be in a very different place without it.

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graycat 13y ago

When he was about 20, Yehudi Menuhin, one of the best concert violinists of the 20th century, concluded that suddenly he didn't know how to play violin. Why? Because before his teachers, back to his age 7 or so, had carefully walked him through the music note by note and bar by bar and, likely then, the artistic expression. But, still he was darned gifted. So, a few years later, relearning violin, he was fine again for the rest of his life. Being able to do arithmetic, algebra, and other mathematical operations in your head is fine. E.g., during WWII, John von Neumann, one of the best mathematicians of the 20th or any century, sometimes went to people working on war projects to see if he could help them out. At one stop, a guy was unsure about how to find a solution, so von Neumann suggested, "Let's try a local solution via infinite series and look at a few terms. So, von Neumann did the arithmetic in his head [he could take two eight digit numbers and multiply them together in his head]. When von Neumann left, the guy was near tears. Why? Because he had been up all night using a mechanical desk calculator to get just some of that arithmetic right! I found in doing research in math (I've published such stuff), once get into the problem well then do most of the thinking for the actual research just between the ears and writing very little. Can even do some of the algebraic derivations just between the ears. The actual research, at least the way I do it, is heavily 'conceptual' where writing isn't very efficient anyway. From what you wrote, I see nothing wrong with your abilities. If you are not handy with paper and pencil, then it is not too much to expect you to become handy with just some usage. So, try, and soon you will 'get it'. It sounds like your problem with calculus was mostly just a problem with paper and pencil -- so, 'get it' with paper and pencil. Unless are, say, another von Neumann, can't expect to do significant derivations in calculus, say, integration by parts or multiple integrals, without writing down the expressions step by step. But, of course, for calculus, long ago some software efforts for integration worked out what expressions could be integrated in closed form and what ones could not and wrote software to do the integrations for all the ones that could. The results are in at least one of the old computer algebra packages! So, with that software, "Look, Ma, no pencil or paper!". About your suspected faults, don't be the least discouraged about them! Some are just your imagination. Some can be easily enough corrected. Essentially all the rest can be circumvented. In particular, it appears that you are concerned about some skills that were supposed to take you from a few days to at most a few months to get good enough with way back long before you shaved! Doing catch up on that material now should be a few days' walk in the park. E.g., in K-12, I didn't learn English grammar and punctuation very well. In college I was in math and physics where this gap was not very important, and otherwise I just wrote only sentences where I did understand the grammar and punctuation. Now I've long had a 12th grade English grammar book right at hand and look up details when I'm in doubt; long ago I got nearly everything I missed in K-12. Back to working without writing, in plane geometry I refused to do the homework the way the teacher wanted, write out in full detail proofs of just three problems. Instead I worked all the non-trivial problems and then also the more challenging ones in the back of the book, often writing nothing, sometimes writing in the margin of the book, sometimes on scraps of paper, and only for a few of the most difficult problems in the book, actually writing out a complete proof. Worked fine! When the teacher wanted to see my homework, I showed her nothing, and she was torqued. When I came in second in the class on the state test, she was 'confused' since she thought that I didn't do any of the homework! Heck, I solved every non trivial problem in the book and, thus, likely did the most homework of anyone in the class. Also, I slept in class -- I learned from the book in a quiet room, not when she was making noise in front of the class! Being able to learn math just from a book proved crucial, the main way I got my Ph.D.! Lesson: You don't always have to do it their way!

puredemo 13y ago

It's also an example of why it's poor practice to teach the gifted along side of lower performing students -- they realize they can get by easily without working hard and it becomes a habit. Ideally, the gifted should have their own programs where they are forced to compete with other exceptional students the entire time they're in school, rather than follow a program meant to pander to the lowest common denominator students in society. Also, I'm with you bro, fell into the same trap. It sucks.

berto99 13y ago

ugh, the way you did it, I thought that was the way most people did it. Usually you see the answer and only "show working". Though the mechanical approach can facilitate more complex problems.

loganu 13y ago

I think we're the same person. Up until grade 12, I could show up late, stoned, or not at all, skip all the homework, and end up at the top of the class due to tests. I was on-track/ pre-accepted into engineering until calculus came, and my natural "getting" math completely tapered off. When the problems became abstract enough that I couldn't understand what they were asking for (or more importantly, why) I dropped out of my first course. Switched to a more creative field, and circled back towards engineering-type jobs 10 years later. Happy (enough) with where I am now, but can't help but think things would have been better if laziness, hubris and structure of the school system didn't keep me from learning how to learn earlier.

pydave 13y ago

> "x + 1 = 6" I didn't have to subtract 1 from each side, I just thought about it logically and knew the answer. I don't see the difference. In my mind, thinking about it logically is recognizing that one side has an excess and removing it from the other side. That's subtracting. To you is it like looking at 5 * 4 and knowing it's 20 rather than thinking about 2 * 5 is 10 and two of those is 20? I was the kind of rule-following kid who went through the algebra steps because you were supposed to rather than out of necessity. (Or so I like to think: I'm not good at math in my head because I always wrote it out or maybe I relied on paper since I couldn't do it in my head.) I recall rebelling against memorizing multiplication tables in grade ~4 because I thought my time was better spent leaning new stuff (or maybe understanding how to multiply faster -- wouldn't that be ironic!). It's always interesting to hear how someone else's brain works. Thank you.

dllthomas 13y ago
But there's doing it, and there's knowing how you're doing it.