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I rewired my brain to become fluent in math (2014)

• DarkNova6 3y ago
  Wow. That author sure loves to talk about herself. I kept reading, but the whole article feels like an overdrawn introduction without payoff. If you want to know how you can become better in math and rewire your brain to be math compatible I‘m afraid you will be none the wiser after reading this.
  • eviks 3y ago
    Maybe one needs another brain rewiring job to become fluent in learning from blogs like this
    • chankstein38 3y ago
      Or the author needs to rewire their brain again to learn to write in a way that actually teaches lol
    • DarkNova6 3y ago
      Oh. Do please enlighten me a put the deep wisdom that lies just beneath the surface a pleb like me doesn’t understand.
    • gnicholas 3y ago
      I tried reading one or two of her books and found them similarly lacking. I don't give up on many books, but I left hers for greener pastures.
  • dimitrios1 3y ago
    Quite dissapointing, because I found the authors book "A Mind For Numbers" to be good.
  • dailykoder 3y ago
    >If you want to know how you can become better in math and rewire your brain to be math compatible [...] ... then you just have to do it. And keep working on it, even though it feels awful
    • DarkNova6 3y ago
      No shit
  • keybored 3y ago
    I skipped the purely biographical paragraphs. Some important parts: - Memorization and rote practice are important for learning, not just the current Zeitgeist (2014) of “understanding” without the former. This becomes the foundation that allows you to focus on higher-level things like understanding and applying formulas. - Experts develop “memory chunks” which allows for example chess masters to draw on thousands of different past games, openings, variations.
    • jacobolus 3y ago
      Memorization happens naturally through repeat exposure, and works better if this is exposure in some meaningful context rather than through cramming via flash cards or whatever. The best kind of practice is practice that you are motivated to do because is inherently interesting. The less "rote" you can make this the better. For a primary school example, if you can solve basic arithmetic problems in service of a fun and challenging logic puzzle, that is more motivating than solving a page of arithmetic problems one after the other. More generally, while mathematics certainly requires putting in time and actually doing the work of thinking a whole lot about a variety of hard things in the service of solving hard problems, very little of that is memorization per se. > In the United States, the emphasis on understanding sometimes seems to have replaced rather than complemented older teaching methods that scientists are—and have been—telling us work with the brain’s natural process to learn complex subjects like math and science. The older teaching method also sucked. In my opinion, the single most important thing primary school math education should be teaching is how to attack and solve nontrivial word problems. Unfortunately we did not have any of that before, and still do not have any now. Cf. https://cs-web.bu.edu/faculty/gacs/toomandre-com-backup/travel/sweden05/WP-SWEDEN-NEW.pdf https://cs-web.bu.edu/faculty/gacs/toomandre-com-backup/trav...
      • kaitai 3y ago
        It's important that we marry viewpoints when looking at what we call "meaningful". I spend a lot of time right now with a 6/7 yr old. This child does not care about meaning. This child likes to solve arithmetic problems one after another. It's motivating -- it's like a game -- the kid gets them right and gets a thrill. Word problems? Well, the math ability is outstripping the reading ability right now so 2000 x 2000 x 2000 is way more fun than reading some stupid sentence about tulips. I've spent plenty of time on math (PhD in algebraic geometry) and educating people, and for sure when I taught college freshmen and master's students I spent a lot of time challenging folks to engage their minds, spirits, and intellect. At the same time, we have to admit there is a stage of childhood where kids just love memorization and facts. Dino facts, shark facts, math facts, Pokemon facts, My Little Pony facts, whatever. Let's not force kids to reckon too much with meaning when they're in the facts for facts sake stage -- and once they've got their impressive facts list, they'll make sense of the meaning much more easily, as discussed in the article and here!
  • zero-sharp 3y ago
    I never really know what people mean by "rewiring your brain". You just have to spend a lot of time studying it. The hard part as an adult is probably making the time, especially if your work is already mentally taxing.
    • joelfried 3y ago
      Ok, I'll bite. Thoughts flow through my brain like electrons through wires, both at a speed I cannot truly comprehend. The paths of my thoughts, the way words connect together, the emotions they evoke, the feelings that are associated with - these are all malleable. I have been working to rewire myself away from pessimism and towards optimism for years now. It's not easy, and sometimes I fall back into old patterns. As years have passed, though, I've found the new pathways easier, the new roads getting more familiar. My thoughts have previously wanted to go one way, and I spent time yanking at them to go a different way. I spent enough time at it that I now on good days more naturally go they way I want to go. It's not just sitting and repeating a single thing over and over again, it's working with your own natural inclinations so that you can recognize when you experience X and naturally reach for Y that perhaps Z is what your preference really is, upon reflection. If you can practice that enough then, in the moment, you can sometimes find yourself not following the old pathways but the new. Rewiring seems like a pretty good analogy as when you rewire a house you work hard -- it is dirty, dusty work. Pulling wire is hard and thankless because when you're done you cover it all up and, if you're lucky, it works! Then at the end you're . . . back in a state where nobody but you knows any different what is happening behind the walls. Things work, and others might have no idea anything changed at all. But you put in the hard work and you know how things actually work on the inside now and it's exactly how you want it, not how it was before. If you've got a better analogy, I'd love to hear it.
  • chankstein38 3y ago
    Right?! I want to know "How they rewired their brain to be fluent in math" but so far all I've seen is a bunch of talking about how great they are. This article sucks.
    • CyberDildonics 3y ago
      Most people just call it practice.
    • criddell 3y ago
      There's a chance that the author isn't the person responsible for the title. I searched for rewire on the page and the only instance is in the title. The author, Barbara Oakley, has a free Coursera course that is pretty good: https://www.coursera.org/learn/learning-how-to-learn https://www.coursera.org/learn/learning-how-to-learn
  • vunderba 3y ago
    This was my experience with the article which could be consolidated down to a single sentence: "Manipulate and play with concepts you intend to internalize, rather than relying on rote memorization". I would think that would be obvious to anyone that merely memorizing something like 'f=ma' would be meaningless without deliberate attempts at application (both theoretical and practical). There was a kludgy attempt at tying the study of foreign languages to STEM, but it just amounted to, everything is ultimately a craft. You have to practice to perfect it.
  • intended 3y ago
    feel bad that this article ended up on Hacker News (HN), since it seems additional context is needed. Currently, the emphasis in training and education is on ensuring students understand the material, and rote memorization is viewed as a failure mode. The author acknowledges this but introduces an argument that rote memorization is critical to achieving fluency. I suspect that stating this position among typical education-focused circles will result in pushback. To lend credibility, she adds her lived experience as a way to explain what she means—and to clarify that she isn’t saying everyone is wrong, just that we may be too harsh on memorization. This is apparent to me because, frankly, if it weren't for the additional content she added, I wouldn’t have spent more than a few seconds before dismissing it. The article even made me concerned about an internal project I am involved in, prompting me to verify that I hadn’t overlooked some issues. If you want a TL;DR, the golf analogy matters: If you want to learn math, you need to understand it and then practice it so much that it becomes second nature.
• keybored 3y ago
  Oh, I didn’t connect the dots before after I read where’s she’s a professor at. She’s one of the instructors in Learning How To Learn https://www.coursera.org/learn/learning-how-to-learn https://www.coursera.org/learn/learning-how-to-learn
  • JabavuAdams 3y ago
    Yeah, I had the same realization. Loved that course.
• xchip 3y ago
  Articles that start with "I" are usually about bragging and hence disappointing.
  • JabavuAdams 3y ago
    What did you think of this article?
    • xchip 3y ago
      Too much bragging and disappointing
  • ykonstant 3y ago
    I know, right?
• ltbarcly3 3y ago
  Some people just won't ever be good at math. There are people who have basically no visual intuition and can't predict what an object will look like when rotated in 3 dimensions. It may be possible to practice this but someone who does poorly at this untrained is unlikely to ever reach even median level ability. There are techniques you can learn to perform this task in a multiple choice test situation but they don't train your brain to be better at visualizing 3d rotations at all. This is not to say that object rotation is a proxy for mathematical ability, but just a demonstration that there are cognitive tasks which people vary widely in ability on when untrained and which we don't have an effective way to train, at least at an arbitrary age. Lots of Math seem to be this way.
  • JabavuAdams 3y ago
    Possibly true, but "good enough" is within reach of many more people than realize it. Engineering level calculus is not particularly high-level math, but will get you a long way in terms of applications.
  • yura 3y ago
    > It may be possible to practice this but someone who does poorly at this untrained is unlikely to ever reach even median level ability. There are techniques you can learn to perform this task in a multiple choice test situation but they don't train your brain to be better at visualizing 3d rotations at all. Any source for this claim? I'd like to read more about it.
  • zero-sharp 3y ago
    I know you said object rotation isn't a proxy for mathematical ability. But I just want to add that not all intuition is geometric intuition. And not all math is even geometric. Of course, there isn't a switch that gets flipped which suddenly makes you "good at math". But still, I think most people with an interest can study it, learn something, and make some progress. I'm happy playing a sport, but I know what separates me from an athlete and I know I won't ever be a professional athlete.
  • pokerface_86 3y ago
    [dead]
• keiferski 3y ago
  I wish mathematics education would incorporate more history and philosophy. Personally, I was never great at math in school, less because of aptitude and more because I just found it boring and disconnected from the things I found interesting as a kid. Years later, I’ve been slowly trying to “catch up” with my mathematical knowledge, and I find myself the most interested in topics that relate to the lives of mathematicians (and how events impacted their work) and to the philosophy of mathematics. I didn’t get any of this in school math classes, which focused purely on calculations and formulas. I had the same experience with accounting, as well: boring in isolation but fascinating when connected to the history of double entry accounting in Italy, global trade from the 1500s onwards, and so on.
  • eXpl0it3r 3y ago
    But aren't you then teaching philosophy and history instead of mathematics? I mean it can be a great story hook to start off with a subject, but in the end isn't math about the calculations, formulas and proofs?
    • layer8 3y ago
      The history and philosophy is about giving context and meaning to the calculations, formulas and proofs.
    • keiferski 3y ago
      I don't think that's true at all and would consider the history and deeper structures (philosophy) of something to be integral to that topic. In fact, I think the (very modern) rigid division of subjects into separate categories is part of the problem. Intellectuals from a few centuries ago would find it absurd that we consider the liberal arts and mathematics to be entirely opposite types of things.
  • glitchc 3y ago
    Maybe your true love is history, not accounting or math.
    • 3y ago
• msteffen 3y ago
  I have to say, I actually loved this article. Especially “Understanding doesn’t build fluency; instead, fluency builds understanding.” I love math and majored in it in college. The rest of my family is all scientifically inclined, but I think found/find math itself opaque and somewhat intimidating. I remember my brother asking me at one point how one would ever find, for example, the Pythagorean theorem intuitive. The author’s quote is the response I wish I had. The Pythagorean theorem becomes intuitively true not when you have some deep insight about Euclidean space, but when, on seeing a right triangle, three proofs of it spring instantly to mind. Which happens after a lot of practice. FWIW I think it’s appropriate that the author talks about herself a lot. She’s trying to explain the subjective, cognitive experience of going from math-phobia to math mastery over her career. She can’t explain that without talking about her background and her perception of the process from inside her head.
  • msteffen 3y ago
    This actually calls to mind this great talk by Grand Sanderson (the YouTuber behind 3blue1brown): https://youtu.be/z7GVHB2wiyg?si=jcUtUo-TT3ycpTpD https://youtu.be/z7GVHB2wiyg?si=jcUtUo-TT3ycpTpD That talk is about something superficially different—ego in math—but on reflection, I think the desire to look smart actually really does set one up for success in math in the particular way that the OP article describes. When you just want to look smart, you don’t care whether you know something because you thought of it or because you read it in a book. You just care that you can show off what you know and solve problems easily. So you voraciously read and memorize and try to accumulate a massive mental database of facts to show off. Then at the end you find you’re actually good at the thing.
    • syndicatedjelly 3y ago
      > When you just want to look smart, you don’t care whether you know something because you thought of it or because you read it in a book. You just care that you can show off what you know and solve problems easily. So you voraciously read and memorize and try to accumulate a massive mental database of facts to show off. Then at the end you find you’re actually good at the thing. What should one do instead, in order to avoid merely “looking”/“sounding” smart?
• zora_goron 3y ago
  I commented on this on HN a couple months ago, but I had a similar conclusion regarding the value of memorization when I joined med school after studying computer science in undergrad and grad. It took me a while to buy in to high-volume memorization as a learning technique (especially coming from CS, where memorizing facts is not a huge emphasis). After a while though, I started recognizing how the quick recall encouraged by the system enhanced my understanding of concepts vs replacing it (I wrote about this a couple years ago [0]). [0] https://samrawal.substack.com/p/on-the-relationship-between-memorizing https://samrawal.substack.com/p/on-the-relationship-between-...
  • 2OEH8eoCRo0 3y ago
    That's my takeaway from The Shallows by Nicholas Carr. Knowing how to derive information or where to find information doesn't mean you know the information and knowing the information is necessary to form higher level associations in the mind.
    • JonChesterfield 3y ago
      Huh. That's an interesting premise. I think I would split it though - knowing the basis well enough to derive results is probably fine for later deduction, knowing where to find the information is definitely useless for it.
      • nescioquid 3y ago
        The argument is actually more about insight. You can't have insights about things you don't already have in your head. Insight in this context is noticing some new relationship between two facts. There was a slang term "refrigerator thoughts" that described someone staring into the refrigerator while thinking of a show plot and realizing there is a plot hole, a disturbing implication, etc. In any case, that's an example of insight. Hopefully we have these spontaneous realizations about less trivial things as well. The more stuff you've got in your head, the more insights you'll have, which drive more questions whose investigations puts yet more stuff in your head. I don't think you can split it. The critical piece is actually getting information into your head in the first place.
• bilsbie 3y ago
  How did he do it? I read half and gave up.
  • downrightmike 3y ago
    TL:DR
• dguest 3y ago
  I'd like to know what education reformers would say to the subtitle > Sorry, education reformers, it’s still memorization and repetition we need. It seems needlessly confrontational, and misses what the article is about. The article asserts that practice and repeated use of math is important. I don't think it's really suggesting that we should go back to how math was taught in the US 40 years ago. But maybe I'm just out of touch with math education reform: In high school I was graded on how fast I could do matrix multiplication, and thought matrices were kinda stupid. Then I learned about linear algebra and coupled oscillators in college and thought they were awesome. So I'd assumed the educational reform was about removing the busy work from math and focusing on what you'd actually use it for. Am I wrong?
  • detourdog 3y ago
    I had a same experience with you but there was no algebra at art school. I learned why math was interesting from trying to figure out how a computer works. I know I have huge gaping blind spots but I can use math for what I need. I'm now trying to avoid math and only using the shapes of math.
  • caddemon 3y ago
    I didn't even know what a matrix was until I got to college, and I went to a supposedly well-ranked high school and was on the higher level math track. This was about 10 years ago. I think some of the education reform might've removed concepts altogether instead of actually improving the presentation? Though I suppose in order to present things well you might need to cut back on the total number of topics covered, I'm not sure I'd describe what I did learn as well-presented either.
  • deltarholamda 3y ago
    I remember hearing an interview with a woman who was doing charter school-type work in the UK (IIRC), where most of her students were thought of as "underperforming". She was successful because they emphasized drills, lots of drills, and more drills. Teachers and students hate drills. Teachers, because they're tedious to grade, and students because they're boring. But they work. It's no different than doing the same Super Mario Bros. level again and again until you time your jumps just right. I've often thought that gamification of drills would be a great way to get kids to learn their math facts or whatever, but there seems to be an allergy to doing this in the US education system. What the US education system seems to be addicted to is moving from one hype/fad to the next, as that's where the money trough seems to be.
• johngossman 3y ago
  I think it’s ironic that when we rewire a virtual neural network, we call it training and the field is called by machine learning, but when humans learn something, train themselves, they call it rewiring their brain. At some point the reductionist language just obscures the point and makes it less accessible
  • keiferski 3y ago
    One wonders: will the robo-humanoids of the future use biological metaphors to describe their electronic bodies?
  • syndicatedjelly 3y ago
    What does accessible mean in this context?
    • johngossman 3y ago
      I was actually thinking about a phrase like “it activated my amygdala” instead of “it made me anxious” et al, where you have to know some neuroscience, hence less accessible to the general populace. Another example is “updated my priors” instead of “learned some new information” or “changed my mind.”
      • keybored 3y ago
        I agree. I really dislike technical-sounding jargon that really are just replacements for feeling-talk. Use scientific terms for science. Use normal words for your own experience unless you really were hooked up to a machine and were measured in some way.
• Funes- 3y ago
  I've always loved quick calculation games, learning mathematical principles and concepts, applied mathematics, probability theory, etcetera. However, I developed huge mathematical anxiety throughout all of high-school, because math class followed an appalling, horrifying routine: the teacher would randomly pick any of us to forcibly go up to the blackboard to solve an exercise from the previous lesson's homework, especially when we hadn't done it, and we would get badly scolded in a humilliating manner when we couldn't solve it, getting some laughs or hurtful remarks from our classmates, as well. When we were done, we would get more homework, and so the cycle repeated. The actual teaching always took less than ten minutes, if it took place at all. Teachers were so utterly disparaging, it became an extremely stressful experience. It undermined our ability to focus in the first place, so not instantly getting whatever was being "taught" induced more fear, which made you lose even more focus. It was a terribly negative feedback loop. Later on, I started reading math books on my own and realized that not only I wasn't bad at it, but what kind of motherfuckers were those so-called teachers, and how clueless they were in pedagogical terms.
  • ivansavz 3y ago
    Thanks for sharing. I talk to a lot of people about math and many of them (adults) have intense math anxiety. I always wonder what kind of trauma could have led to this, because I assumed the I-suck-at-math is such a private feeling, at worst maybe your parents might see your grades and scold you about them. None of this is super traumatic, I thought... But the perspective about public shaming by the teacher and other students piling on is much more intense, so I can see how some people really don't want anything to with math in later life. Those motherfucker teachers indeed!
• toss1 3y ago
  OK, the article convinced me that repetition intentionally focused on the full range how to use and not use each small component such as a word, formula term, or concept is the key. Great. So where are some books, programs, or apps that will help us do exactly this? Not impressed that the article focused more on their personal journey and provided no recommendations on how to follow it. Anyone here have recommendations on apps that might help? One HNer a few years ago posted a great little web app to practice rapid addition/subtraction, etc. which I used daily to noticeable benefit until it disappeared. Of course something working up in complexity from there would be good too.
  • mamonster 3y ago
    The university I went to was notorious for having their own textbook for Analysis 1 and 2 that had 1600 or so exercises of just calculations and covering all cases(for example, if a theorem gave you 3 conditions for it to work you would work through 3 examples with one condition not present and how the theorem would fail, and stuff like). It was completely different to a theory textbook like Rudin/Tao, which had fewer exercises that were more focused on "did you understand the abstract object" and "use your knowledge to prove this slightly modified proposition or easy extension of the theorem". If you want to practice addition/subtraction I suggest Zetamac(https://arithmetic.zetamac.com/ https://arithmetic.zetamac.com/), this is what most people use to train for HFT/MM interviews(although I heard there are more specialized tests now).
  • j2kun 3y ago
    If you're a programmer, not just struggling with basic arithmetic, I wrote a book: https://pimbook.org https://pimbook.org that ramps up in complexity.
• constantcrying 3y ago
  When taking mathematics classes in university I always noticed an enormous gap between what I thought I understood compared to how confusing the problems were. I am glad the author mentions that phenomenon. For (the few) students who actually understood the subject the problems are just busywork, for those who didn't it is the most important part of the learning process. There is exactly one way to understand mathematics, which is actually doing it. This can be many things, but actually solving problems is an important part. I believe that problems should be interesting, but repeated recall definitely is important as well.
  • djmips 3y ago
    Same goes for coding. You can go into a problem super well prepared and think you know what you need to do but often only through a lot of repetitive work of experiments and trying multiple times do you gain the knowledge to actually solve the problem smartly.
• the__alchemist 3y ago
  To me, it seems that there are two general categories of things referred to as "math": A: the one used in this article: What people generally refer to as math. What's used by engineers, (most) scientists, etc. B: The one used by math majors and mathematicians. This type is abstract, contains things domains that end in "theory". My question: Do you think an approach like in the article is possible to learn Math B? I have tried several times, unsuccessfully. I'm proficient in most domains of Math A. (Differential equations, linear algebra etc, symbol manipulation, geometry, and how tho apply them to practical problems). Math B seems, in contrast, beyond me. There is a programming analogy: Math B is like Haskell, or pure functional programming, which also is as ungraspable to me. I am wondering if maybe this is partially genetic, partially something you have to learn at an early age. Or maybe it takes a formal learning path.
  • collinrapp 3y ago
    Correct me if I’m wrong, but aren’t you simply referring to “applied mathematics” and “pure mathematics”, respectively? I skimmed through the replies to your comment and I don’t believe anyone mentioned these terms, although I did see one reference to “abstract mathematics” (a term used by you, as well). I thought these were well-known terms and thus that the dichotomy you describe was itself well-known, but I thought I’d add this comment on the chance that you weren’t familiar with them.
  • parpfish 3y ago
    I loved math type A, so I majored in it. Once you're fully ensconced in the major, it pivots into type B. And it turns out that I hate type B but slogged through it with medium-good grades. looking back on it now, I've come to like type B and wish I could go retake those classes with my current perspective. I think my original distaste was largely due to what felt like a bait-n-switch: start out majoring in something you like and are good at, but then pull the rug out and switch to something completely different
    • jacobolus 3y ago
      The real problem is that "type B", despite being much more important of an activity to learn (for mathematics or any other kind of technical problem solving) is almost entirely ignored in primary/secondary education.
• zzzbra 3y ago
  She has a book that expands on this topic substantially. I highly recommend it: https://barbaraoakley.com/books/a-mind-for-numbers/ https://barbaraoakley.com/books/a-mind-for-numbers/
• InPanthera 3y ago
  Poorly written article on wats with the website asking needing to store cookies just to read ?
• croes 3y ago
  Rewired the brain? Isn't that just learning?
• hosh 3y ago
  I’ve come to understand learning math as: 1. First gain the intuition 2. Second develop rigorous understanding 3. Third gain fluency from repetition Repetition without understanding, or even intuition, is not really going to help. There are game-based learning that really gets to the fluency part.
  • comfortabledoug 3y ago
    How do you gain intuition without repetition? I learned math by blindly following algorithms. Over time i gained intuition from seeing how variations in the input changed the output. The deeper understanding kind've slipped in there...I don't know how. I don't think you can build real understanding without rigorous practiced repetition.
    • hosh 3y ago
      Kalid Azad wrote books explaining mathematics in that way with his "Better Explained" series (https://betterexplained.com/ https://betterexplained.com/). For me, that intuition is the seed in the consciousnes from which the rigor can then form a structure around. When I applied it to concepts I was learning on my own -- monoids, monads, semi-groups, semi-lattices, partial orders, etc. what I found was that I'm often overthinking the intuition. The intuition for a specific idea is very, very precise. It is exactly as it is, and yet something so precise and clear seems difficult to get. It helps to approach things from a lot of different angles until you "get it". It's not always about repeitition on manipulating symbols. The Soviet method for teaching math (and remember, the Soviet system was intended to raise enough mathematicians to be able to work with a planned economy) was to let their kids manipulate things with their hands in a concrete way. It was in a way more like Common Core, but you're playing with toys with your hands. I can tell you that I picked up being able to add and subtract things at an early age, but I didn't really get into the deeper stuff until I was exploring monoids and groups. I've met people who tell me, subtraction and negative numbers are difficult. They know how to do the operation arithmatically, even fluently, but they don't "get it". No amount of repetition was going to change that. I had a similar block when I came across the idea of instantaneous rate of change. I get the proofs, the idea of limits, and how it defines instantaneous rate of change, but it was the first thing that I came across that I couldn't get over the idea that this is an abstract idea, not concrete. I didn't know how to handle it. It wasn't until I came across Azad's way of explaining the _intuition_ on instantaneous rate of change that I focused on getting the intuition first before trying to develop rigor.
• melodyogonna 3y ago
  It is like learning Vim.
• _wire_ 3y ago
  A title for a how-to article should offer hope that you can learn something from reading it. "I re-wired my brain" offers no such hope.
• wuj 3y ago
  I didn't grasp the similarity between human and machine learning until I took a machine learning class at Berkeley. Listening to lectures or reading the textbook is akin to fitting a machine learning model: You receive just enough information to begin understanding, but not enough to master it. True mastery requires you to validate your knowledge through homework, quizzes, exams, iteratively tuning your approach based on feedback. Without this practice, similar to a machine, your learning is merely overfitting to training data - you might handle familar problems well, but struggle with new challenges.
• MrDrMcCoy 3y ago
  When I read "memorization and repetition", the first thing that springs to my mind was being unsuccessfully forced to learn multiplication tables in my youth. I have learned over time that I'm simply incapable of memorizing something that I either don't understand to a certain depth or see as unmoored from obvious utility. Even when I comprehend and see the use for something, it's still hard to remember without practice through usage. I think she does mean "use and practice" when she says "memorization", which is fine, but I think that phrasing could lead education in a direction that would be worse for people with memory issues like mine.
  • vundercind 3y ago
    Heh—all that early memorization-heavy arithmetic represents a very high proportion of the applicable value I get out of my decade-and-a-half of mathematics education. Some weeks I bet it’s nearly all the value. (Not that a kid can necessarily see that, it’s just funny because that stuff is about as useful as it gets)
• djeastm 3y ago
  Meanwhile I have a B.S in Mathematics and I'm still just as bad at it as I ever was. I paired it with Computer Science in a Double Major and thankfully I am much more comfortable with that.
• wuliwong 3y ago
  > After all, I’d flunked my way through elementary, middle, and high school math and science. I have to question the veracity of this sentence. How could they possible keep progressing to the next grade if they keep failing math and science? I'm sure it is hyperbole but this doesn't seem like a great way to start off an article like this.
  • the_sleaze9 3y ago
    D's get degrees
    • wuliwong 3y ago
      In my parlance a D is not flunking though. Flunking means you don't get credit for the class. But maybe not where she is from?
  • aegypti 3y ago
    It isn’t hyperbole. You can fail math all year long, but achieve the bare minimum in the subject during your annual standardized test and pass to the next grade. Course credits/grades do not ~~affect~~ limit? progression in many/most? US school districts before high school.
    • wuliwong 3y ago
      Was that the case in the 1960s/1970s because that was when the author was in elementary through high school? I graduated high school in 1995 and what you are describing was not the case at my school nor any other school that I knew of at that time.
    • dragonwriter 3y ago
      I know of districts using some degree of social promotion, but I’ve never heard of one promoting on performance but using standardized tests alone instead of class grades or clearing a certain bar for both grades and standardized test as the performance criteria.
• wuliwong 3y ago
  >students who have been reared in elementary school and high school to believe that understanding math through active discussion is the talisman of learning. I graduated high school in 1995. Was I too early? I don't remember high school math just being a bunch of discussions without problem solving.
• tndibona 3y ago
  Question: After preparing and failing at a faang interview, it seems clear the only way to pass this is to look through leetcode and memorise graph search patterns, bfs and dfs of trees, recursion patterns, etc. Because if I truly use my natural problem solving techniques, it takes me hours to days to solve the leetcode problems. At least according to the article and the tech industry, memorisation is intelligence. I’ve always understood the subject and avoided memorising all my life. I’m suffering massive imposter syndrome at this point. A part of me is considering quitting my existing tech job voluntarily because maybe I’m not supposed be around the smarter people who cleared the interview. Is the tech industry interviewing right? I suppose I need help.
  • vundercind 3y ago
    1) I’ve had a career in tech for—holy shit, way too long. I’ve never had an interview that was terribly close to a FAANG-type one. I’ve also never had a hiring process take more than a week from interview to offer. 2) I don’t make FAANG money but I’ve consistently earned 2.5x+ median for a person my age in my area (I’m in like a 3rd tier US city, couple million people, several tech headquarters, a couple of which are household names) 3) FAANG interviews are a game. The point of how awful it is and how prep-necessary is to selection-bias the pool so the vast majority of candidates are suitable, to select for only those who want it bad enough (and/or have lots of free time), to make jumping to peer companies difficult to keep wages down (if that last weren’t the case, they’d find a way to stop doing it for people who’d already passed it one or more times—the process is expensive) and finally to build esprit de corps via hazing (hazing is very effective at that). Don’t take it personally.
    • tndibona 3y ago
      Thanks mate. Needed to hear this.
  • currymj 3y ago
    most of the leetcode problems are based on material that a new grad CS major would have learned recently from taking a class that uses CLRS as the textbook. if this background is assumed then the key to success becomes building problem solving skills. if you haven't very recently taken a class that uses CLRS as the textbook, then it makes sense you would have to do more memorization and practice with those concepts.
• dang 3y ago
  Related: I Rewired My Brain to Become Fluent in Math - https://news.ycombinator.com/item?id=33890921 https://news.ycombinator.com/item?id=33890921 - Dec 2022 (9 comments) I Rewired My Brain to Become Fluent in Math (2014) - https://news.ycombinator.com/item?id=13674101 https://news.ycombinator.com/item?id=13674101 - Feb 2017 (46 comments) The building blocks of understanding are memorization and repetition - https://news.ycombinator.com/item?id=12508776 https://news.ycombinator.com/item?id=12508776 - Sept 2016 (94 comments) How I Rewired My Brain to Become Fluent in Math - https://news.ycombinator.com/item?id=8402859 https://news.ycombinator.com/item?id=8402859 - Oct 2014 (144 comments) How I Rewired My Brain to Become Fluent in Math - https://news.ycombinator.com/item?id=8400837 https://news.ycombinator.com/item?id=8400837 - Oct 2014 (6 comments)
• SamPatt 3y ago
  I started reading the article and it reminded me of a great book I read, A Mind For Numbers. Then I realized it was the same author! Definitely worth reading if you've been avoiding deepening your math understanding.
• fuzztester 3y ago
  I saw that others have mentioned some points about her. This is the Wikipedia page for Barbara Oakley, which has more details about her: https://en.m.wikipedia.org/wiki/Barbara_Oakley https://en.m.wikipedia.org/wiki/Barbara_Oakley
• piloto_ciego 3y ago
  This is surprisingly similar to my life in a way and how I learned math. Huh. Good find, thank you.
• voidhorse 3y ago
  Great article. I'm in the same boat (though luckily not translating Russian on the Bearing sea) as the author. Grew up getting a fantastic literary education while positively flunking all math classes. In my case, I actually think I failed because teachers only focused on rote mechanics with no attempts to develop understanding. This just made the entire enterprise entirely boring for me as a student. You really do need both. These days I spend my free time reading books on higher mathematics and mathematical logic. Doing exercises certainly is the key to solidifying insight. I've also found adopting an old practice from my literary school days, writing essays, to be extremely helpful. There is a certain sense in which Wittgenstein's later "language is use" philosophy is deeply true when it comes to mastery of any intellectual material. The brain really does work just like the body—if you hit the gym each day you will build muscle and retain it, if you stop you won't.
• phforms 3y ago
  This is interesting and reminds me of the idea of “thinking in action” where insights/understanding happens while interacting with the concrete subject matter in exploration, experimentation, etc., which seems to be exactly what the author described she was doing when learning Russian or physics equations. I don’t think that from “dull” memorization and mindless practice alone (how it was often done in school) understanding at a deeper level somehow magically happens. What I do believe is that both (“smart”) memorization and explorative/playful interaction with the subject matter (turning it upside down, interrogating it, relating it in different ways, etc.) support each other, which, after some time, creates enough structure in ones neural pathways such that deeper insight can emerge from intuition. When we try to learn math conceptually, we focus a lot on metaphorical or contextual understanding (“what is this like?”, “how does this apply to the real world?”, etc.), which may divert attention away from the actual subject matter, which is the symbols, formulas, equations, axioms, theorems, diagrams and so on. It is all one really needs to understand. Sometimes I read texts where the author talks about mathematical ideas in a very vague and abstract language, mystifying and obscuring it or entangling it with other subjects. But then it turns out what they write makes no actual sense in the language of mathematics, which itself is very concrete and clear. Maybe they have fallen into the trap of thinking that they knew about the subject when all they have is a broad conceptual perspective without any grounding in the actual rules of the formal system.
• purpleteam81 3y ago
  I'm still working on rewiring my brain and math. I was at the top of my primary classes until we moved; the new school was a year behind academically. We returned in 6 months, however, it was enough that I struggled with factoring some fractions and percentages because I missed the theory and the stress of moving. My mind embraces set and fractal theory readily and spatial awareness is decent. For me, math is applied using abstract logic. I'm still have math-phobia