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The Greatest Educational Life Hack: Learning Math Ahead of Time

• bell-cot 2y ago
  Within a limited range of academic disciplines, it's a great hack. Outside of that, and situations where being a "math genius" is social cred - not so much. The article's pretty good on why institutionalized education doesn't like students who are seriously ahead in learning math. (Or any other subject.) But it's pretty much silent on the self-discipline and self-study skills (or parent-paid tutors) required, to seriously learn math years ahead. And the former are probably far better indicators of long-term success than the early math skills are.
• trte9343r4 2y ago
  > Learning math early guards you against numerous academic risks and opens all kinds of doors to career opportunities. Learning math, just so you can learn it again is quite pointless! Much better hack is to skip academia completely, and go self educated. No debt, no pointless extra classes, no risk of being misaccused, no politics! You can even move to cheaper country, with nice weather, to have better environment for studying!
  • xattt 2y ago
    You’re oddly specific so I assume you’re speaking to your experience, but your case would be survivor bias. Academia does pander to the masses, and it provides a path to take a person off the street and turn them into a somewhat of a knowledge expert in a range of disciplines. You also hope that your nurse practitioner, physician or surgeon didn’t take a self-taught path.
    • beardedwizard 2y ago
      But a physician or surgeon needs a license to practice, so it's not really a valid comparison. However, I would love to have a doctor who was so passionate about it they taught themselves before going to school.
      • skhunted 2y ago
        In the U.S. getting that license requires med school. Almost no one is capable of learning advanced topics on their own unless they have already been trained to learn an advanced topic. It’s interesting to see the number of comments talking as if self learning is easy or doable for any but a small percent of the population. Self learning a topic is largely an ability of those who have been taught advanced knowledge in some area.
        • lanstin 2y ago
          Also the young with relatively less to do. When I was little, I started reading calculus books in about 4th grade; I couldn't understand them much but with a few years of trying I finally mostly got it at a conceptual level (tho I didn't do the homeworks till I took it in school; but by then it seemed to be the easiest subject of all). I also read this cool book "Metamathematics" by Kleene and then wrote (in MS Basic for the Ohio Scientific C1P, using computed gosubs) a recursive descent parser for numerical math equations, so I could type in like "i ^ (1/i)" (I only had +,-,x,/ and ^ but they all took all complex numbers; I might have had ln as well? I could only implement functions where I could figure out how to evaluate them, which excluded cos and sin unless I used exp(theta i pi) = cos(theta pi) + i sin (theta pi) and see what it was as a complex number. It wasn't ground breaking, but it was self-taught (and I could rewrite that program to this day pretty quickly). But as a grown-up, it's more efficient to get help learning hard things. And some things are harder than others. I think you can learn calculus on your own, and certainly computability theory, and point set topology, but learning finite-group theory, which has a lot of numeric details, or measure theory at a really solid level, would be getting harder. Still doable if you have the inner drive, but lot more efficient to take grad level classes where you turn in homework. Also doing a lot of homework does give you a sort of muscle memory "a function is continuous iff the inverse image of open sets are open". I wouldn't tell everyone to become a professor, but I'd certainly recommend US grad level classes as an extremely efficient way to learn a lot.
          • skhunted 2y ago
            You are not anywhere near the average in learning ability. Your experience is as an outlier.
    • trte9343r4 2y ago
      Academia wasted 5 years of my life. > provides a path to take a person off the street and turn them into That was true maybe 40 years ago. Today students are asking for debt forgiveness! Academia ruins people financially for decades! > somewhat of a knowledge expert in a range of disciplines. University graduates are pretty much useless in practical disciplines. They need years of additional training to become employable. > You also hope that your nurse practitioner, physician or surgeon didn’t take a self-taught path Medical professionals have several years of extra training in hospitals. They have to "self study"!
      • lanstin 2y ago
        Residency isn't independent study, it's pretty tightly directed by the hierarchy. And I'd hire a math major with limited software experience over a boot camp or self-taught person that only knows code any day. In fact, I'd take a math major over most people with MS in CompSci. They know how to learn very difficult stuff, and didn't do it in an environment that is mostly people wanting to be highly paid, but mostly people that have a love of complicated but beautiful abstract structures (hence less weird resume lying and so on; also, tends to be a bit of a salary arbitrage opportunity). (Hiring for experienced people is of course a different problem.) Of course, trying for a professor job in the US is very likely to a difficult career path; I'm taking some math classes just for fun and the professors are usually grading our papers at insane hours, 3 am and then office hours at 9 am). I could not have done that much work and been a good parent. But academia is great training. One of the best project managers I've worked with had a PhD in Anglo-Saxon english; her dissertation was on masculinity in the court of the Anglo-Saxon king (or something, I've not worked with her in a long time); surprisingly relevant to trying to get the mostly male dev teams to coordinate to finish projects when she didin't have the feudal power of the technical managers, just the soft power of the travelling minstral.
      • Suppafly 2y ago
        >Academia wasted 5 years of my life. Nah, you wasted 5 years of your life.
• glitchc 2y ago
  It definitely makes the first couple of years in university that much easier, although limited to the science and engineering disciplines.
• CrazyStat 2y ago
  I’m going to push back on the advice to learn higher grade math rather than competition math, as I feel the author is ignoring an important skill that competition math helps develop. They allude it in passing: > A student can wrestle with a competition problem for long periods of time, and all the teacher needs to do is give a hint once in a while and check the student’s work once they claim to have solved the problem. Wrestling with a problem for long periods of time is not just a convenience for the teacher, it is a skill that will serve students well for decades to come. Sitting with a problem that you don’t know how to solve for hours, trying various approaches, failing and failing and trying again, is a life skill that learning calculus two years early won’t teach you. Many of the tactics used in competition problems are also useful in general quantitative situations: identifying symmetries, invariant quantities, properties that can only increase under perturbations.
  • alephnerd 2y ago
    I did competition math in middle and high school, and the only reason I was able to build the base needed to do decently in the AMC, AIME, and CEMC was because I was introduced to various concepts in math much earlier than when American or Canadian curricula would introduce them. Competition math becomes a zero sum game when you are competing with students who have both built strong fundamentals AND then concentrated on technique and problem solving. You can't run if you can't walk. > failing and failing and trying again, is a life skill that learning calculus two years early won’t teach you But learning Calc for 2 years, and getting a 5 on the AP Calc BC exam means you can take 2 additional courses in college or graduate early. > Many of the tactics used in competition problems are also useful in general quantitative situations Agreed. But at the end of the day, the kids getting into AIME or USAMCO were already doing high school or even college level math by 9th grade
    • CrazyStat 2y ago
      You don't have to "do decently" or worry about beating students who are already doing college level math, though. You can just do it for "fun" (and learning value). It may be a zero sum game if the outcome you're concerned with is beating other people, but that doesn't need to be the objective.
• twic 2y ago
  Is there anything specific to mathematics about this?
  • mamcx 2y ago
    I think learning how read and write is a better fit. Math, despite what some say, is not that fundamental, but reading and writing well is(and then helps to get math and others).
  • criticas 2y ago
    No, I had the same strategy in computer science, foreign language, and elective courses. CS? The first week of the class, I'd read the entire language manual. I wouldn't understand everything, but when a concept was explained in detail, I had a context and baseline familiarity to orient myself. In foreign language and elective courses (such as history) doing the reading before the lecture meant I could focus on what the lecturer thought was important rather than absorbing new information.
    • lanstin 2y ago
      I had a similar strategy as a youth. It definitely makes for a more relaxed education (or gave me a buffer for when the homework becomes really hard and my youthful irresponsibility put me behind). Now I've gone back to grad school (30 years later) and I also have kids (older but not completely ignorable :) and a job and a wife I am determined to keep happy, so I have to optimize for time, so I'm mostly going into lectures blind except for whatever foreshadowing "motivation" they've done, so it's a constant stream of completely new stuff, but a lot of "wow, that's cool" moments.
• ziofill 2y ago
  > why stop learning one year ahead? Ok, I get the principle but learning multiple years worth of university math is starting to sound unrealistic? I understand learning something in advance to have an easier time, but this is almost the same as finishing a degree before starting it.
• litver 2y ago
  The Even Superiorly Greatest and Lovely Educational Life Hack: Learning Latin Ahead of Time
  • blowski 2y ago
    Quicquid latīne dictum sit, altum videtur. Learn Latin and you can fake your way through so many situations.
  • euroderf 2y ago
    It made French grammar a breeze. (Mostly.)
• fnord77 2y ago
  And there are places that have or are trying to ban algebra in Jr. High School (e.g. SFUSD)
  • NotYourLawyer 2y ago
    Haven’t you heard? Math, logic, reading and writing… it’s all white supremacist colonialism. https://www.nationalreview.com/2021/09/the-folly-of-woke-math/amp/ https://www.nationalreview.com/2021/09/the-folly-of-woke-mat...
    • wnolens 2y ago
      You've been downvoted, but the Seattle school system thinks math is racist https://www.edweek.org/teaching-learning/seattle-schools-lead-controversial-push-to-rehumanize-math/2019/10 https://www.edweek.org/teaching-learning/seattle-schools-lea...
    • anthk 2y ago
      >“curricula emphasizing terms like Pythagorean theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans.” Damn Chinese, Arabic, Indian and Mesopotamian people, they ruined everything with their Geometry and Algebra. Oh, wait... Dear Gutierrez, Science and Math doesn't give a crap about race/ethnics and even less to crybabies as you. And as I say this being a Spaniard, an odd blend between an Iberian, an Atlantic/Mid-European (Goth) and Mediterranean (Who knows, point a huge chunk between Tartesos and Rome) people. In the Hispanic world (the actual one, not the joke invented in the US) no one gives a shit about the race. It's all about nurture against nature. Since the old times. (Uno no es de donde nace, sino de donde pace) -Lit. one does not belong from where he was born, but where he is lying - - -> Home is where the heart is. BTW. Latinx -> US creation, not Hispanic. We usually do Science subjects in Spanish AND in English once we reach University/College, thanks. No one it's hurt. Skills on technical English are a must, period. Black and Latino students here (inmigrants from overseas) do it perfectly fine in Spain. First they study in Spanish, and later in English which is much harder to achieve at the age of 18-20. Stop the ethnic bullshit, please. Our country invented Algebra, please. European Spaniards learnt it fine from the Moors in ARABIC more than five centuries ago. Later they translated it into Latin and into Castillian Spanish. Are the American children challenged, or what? You look like the sickos who put "White Only/Colored" labels on everything. The actual struggle for these children is not the race. It's money and parents being underpaid.
• rodolphoarruda 2y ago
  If you are native speaker of any language different from English, the greatest educational life hack is to learn English at the earliest time. It opens one's mind and allows access to content and communication at a global level.
  • M4v3R 2y ago
    And if you’re a non-English parent but speak English consider talking to your child in English from the very beginning. There are many different ways to approach this, one relatively simple way is to have one parent speak their native language while the other speaks English (called “one parent one language”). Even if your pronunciation isn’t perfect it will still yield very good results. Source: I’m a parent of a 3yo who now understands speaks both English and Polish. Me and my wife are Polish and only I speak English. Apart from speaking we also use English audio in all TV content she watches and buy books that contains both English and Polish text. Edit: as pointed out below I should’ve clarified that this applies when you live in a non-English country where your child does not have any other way to learn English (over here you can’t really learn English in schools - not enough hours, plus it starts way too late anyways).
    • et-al 2y ago
      I would clarify this is for parents residing in non-English speaking countries. Because over here in the States folks are doing the opposite: spending thousands a month to send their children to language immersion schools to not speak English.
    • noisy_boy 2y ago
      > And if you’re a non-English parent but speak English consider talking to your child in English from the very beginning. If you are living in a place where people don't speak your mother tongue but English is spoken everywhere and is the main medium of education, don't do this. The kids will pick-up English anyway because they will be exposed to it for 8 hours daily at school but if you don't speak with them in your mother tongue, they will never pick it up. The older they get, the harder it is. First hand experience.
• floatrock 2y ago
  I'm just confused by this article. It's basically "Learn a course before you take the course so the course is easy." Well, yeah, of course. But this is basically the "draw the rest of the horse" meme. What about any discussion of how to learn the material in advance, why self-guided learning is better than course-driven learning, or just how to prioritize advanced learning with everything else going on in your life. Why is this on the front page today?
  • kreetx 2y ago
    > Well, yeah, of course. It tries to substantiate the ahead-of-time learning with how it will benefit you on a larger scale than a course or even a degree.
  • lupire 2y ago
    Those details are second order. What's important is the "flipped classroom". Learning isn't done in neat little buckets of time, checking off skills from a punch list. Learning works when it repeats and spirals over years. This is why hobbiests and apprentices are higher skilled professionals than people with mere educational certifications.
• TuringNYC 2y ago
  If you go to any of the wealthy or upper-middle-class suburbs, especially those with large immigrant populations, you'll see half the students secretly doing this, whether it is via Kumon or RSM or something else. In many ways it skews the ratings of the schools because they can be lazy and not teach as well...but still show great school average scores, since so many kids are already enriching externally. Before you know, the school is just a motion and the real learning is at home. I suppose it is idealistic to think teachers "should" teach well, of course, since in reality not all do.
  • lupire 2y ago
    It's not secret. It's out in the open and people who don't do it are looked at with scorn or dismissal.
    • TuringNYC 2y ago
      >> It's not secret. It's out in the open and people who don't do it are looked at with scorn or dismissal. Amongst the participants, it isnt secret -- you see all the other participants at the center weekly, or more. I think a lot of it is a class thing that runs side by side. For the outsiders, it is a secret. I was part of a group in K12 that didnt even always have consistent nutrition. The Kumon kids were a strange breed -- folks who had money to "splurge" on "private" education.
      • kjkjadksj 2y ago
        All the kids I knew in those programs hated it. Last thing they wanted to do after school was more school. They wanted to play games or sports but their parents decided being an A student in elementary school is better than any potential social or physical development.
        • DowagerDave 2y ago
          Western society loves to make every kid "special" either in their challenges or abilities. We seem to forget that every kid IS special, in the sense they are diverse, inconsistent, immature and range dramatically across different types of skills & abilities. If you're a middle-class or higher new parent in the West, let me give you my parenting book for free: chill the fuck out.
• markus_zhang 2y ago
  My father (a Mathematician) used to teach Math to me early. But somehow I was not motivated to learn Math myself so every year I got a very good mid-term grade but terrible final grade. He also taught competitive Math to me (the Olympics) but to be frank I was totally uninterested. This definitely created a lot of tension along the years. He just couldn't understand why people don't like learning Math, and I just couldn't understand why I couldn't watch TV every night. LOL.
  • lanstin 2y ago
    You could be my kid writing, but I didn't push too hard; I am still disappointed they didn't take up more math, but each person has their own life to live. They understood negative numbers and square roots in early elementary school and optimized later education to be least effort for the grade, not inner inspired learning for the joy of learning.
    • markus_zhang 2y ago
      Yeah different people have different roads. And if someone just doesn't have the inner motivation to crack Math problems, then feeding Math to them, especially in a traditional textbook-homework way, is just going to produce resentment. My father actually wanted to teach me programming too. But similar to teaching Math, he wanted me to go competitive programming, which I absolutely hated and still hate. If he tried teaching me game programming then it was going to be a completely different story. I eventually taught myself programming decades later. My first language was C++ and my first project was a 2d game engine. IMO, all those teaching he tried to feed me, not only did not increase my motivation or learning techniques, but decreased them. Throughout my childhood (starting from maybe 9), I absolutely hated summer and winter vacations. While my friends were enjoying, I had to go through TONs of extra-curriculums. I used to practice piano 4+ hours a day (as long as I don't have school), and some other hours for extra homeworks. I absolutely hated that, to the point that I hated playing piano and completely dropped it after actually achieving a lot. My father simply doesn't understand why would a normal human-being hate piano, music and Math, when he couldn't even get them when he was young. I didn't bother to explain. You were probably not that tough to your children though, so I guess they fared much better.
• johngossman 2y ago
  This is basically an ad
  • lupire 2y ago
    And an attack on the competitors -- opposing competition math because other vendors got their first and it has a narrower addressable market.
• WesleyLivesay 2y ago
  A bit of a sensational title, I would say that Learning to Read as early as possible, then reading well above age level, would be a greater "Educational Life Hack".
  • alephnerd 2y ago
    They're both outcomes of the same action - parental interest in education. Success in early learning is heavily correlated to how invested your parents are in their kid's education. It's not a money thing (as plenty of us 1.5 gen Asian American kids can attest to)
  • supertofu 2y ago
    Most unfortunately, not every child will even have access to this unarguably beneficial life hack. I learned to read early because my immigrant mom read to me in her non-native language every single night, and that's because she came from a culture that lauds education. I wish every child was lucky enough to have a parent like this, but so many kids only get their first exposure to education in public school.
  • bee_rider 2y ago
    Learning to read as an educational lifehack suffers from a couple issues with the target audience.
  • CrazyStat 2y ago
    The author works at a math education company, so the focus on math is understandable.
  • yonaguska 2y ago
    My superpower is that I learned to read at a very young age. It allowed me to find some modicum of success despite a lifetime of undiagnosed adhd. If I hadn't learned how to read early, and thus learned how to read fast- I doubt I would have ever gotten to a point of enjoying reading.
  • dh2022 2y ago
    But doesn't this reading ability plateau quickly? My 13 years old son reads pretty much as well as I do. I am working with him on SAT tests and there are some things he can improve. But not that much. As opposed to Math - which keeps going and going well beyond college....
• grose 2y ago
  My 4th and 5th grade teachers tricked us into learning algebra by calling it "enigmas" and treating it like a fun puzzle instead of a math problem. It definitely worked on me, I was quite shocked when middle school math was just those puzzles under a different name. Made those classes quite easy though.
  • lupire 2y ago
    This is what DragonBox does too. Kids hate math because teachers and textbook writers hate math, who put no fun into it.
    • ghostpepper 2y ago
      It looks like Dragonbox was bought in 2019. It's now called Kahoot! Algebra by Dragonbox and requires accepting a bunch of tracking permissions on the App Store, plus a subscription. Anyone know an alternative?
      • thorncorona 2y ago
        Art of Problem Solving books
  • zozbot234 2y ago
    This is done as standard practice in many countries outside the English-speaking world - complex "word problems" are used to gradually introduce algebraic-style reasoning (often involving multiple "steps" as a matter of course) in the earliest grades as part of the study of both arithmetic and what English-speaking schools call "pre-algebra". Teaching proper algebra after that once the students have the proper level of mathematical maturity becomes almost seamless.
    • 1970-01-01 2y ago
      The way math is taught in the USA is downright disastrous. It's been through several revisions over the last 30 years and still isn't showing average students reaching anywhere near these levels.
• niemandhier 2y ago
  This is a hack to create people wha are successful in the education system, I wonder if it is the right approach to create educated people. I work in science and often work with highly skilled people from China and India. Theses people are much better in applied math than I ever was, but somehow my erratic highly derivative style of problem solving is at least as good at getting the job done and I am much better in thinking out of the box than most of them.
• ChicagoBoy11 2y ago
  I work at a private school and will sadly tell you that the author's points are actually pretty severely understated when it comes to the incentives of schools regarding this phenomenon. Differentiation is a word that gets thrown around as some tremendous necessity for schools to implement, yet in the case of math, where one could fairly easily (compared to other subjects) confidently assess the attainment of prerequisites, gauge student progress, comfort, etc., we comically either bound students who have clearly mastered materials OR happily move them along the math curve in which the deficiencies in mastery build on each other to eventually lead to a child who truly has a strong distaste for math. More even than pre-teaching, I would encourage any parent to very actively be involved to ensuring that their child maintains a reasonable comfort with math throughout their study, and to the extent possible, pitch in to help those gaps beyond "passing" or doing "ok" in class, but to earnestly try to see if their child is comfortable. The reality is schools will very frequently PASS your child and given them fine enough grades, but I would argue that it is oftentimes almost orthogonal to how comfortable your child genuinely feels with what they've learned.
• criticas 2y ago
  My wife was a great example of this. She was an undergraduate math major, then went on to get her master's and PhD in engineering. The first year of the master's was largely remedial engineering courses - statics and dynamics, thermodynamics, controls, simple electrical circuits, etc. I asked if she found them difficult. She quipped, "If you already know the math, it's just nomenclature."
  • supertofu 2y ago
    Ahh, the very definition of isomorphism :)
  • Syzygies 2y ago
    As a sophomore, I took the "barrier" physics intro for my distribution requirement. Sunday night before our first Monday morning exam, I found my professor in a phone book (1970's) and phoned to ask for an extension, explaining that I hadn't started studying. Denied. That test was just multivariate calculus I'd already aced, with funny names. I got one of the top scores in the class. So I decided to study an extra hour next time, just to be responsible. Oops! I flunked a test that was differential equations with funny names. I didn't really learn ODE's till Columbia assigned me to teach them as an assistant professor.
  • trueismywork 2y ago
    Love this quote.
• supertofu 2y ago
  I was a late bloomer in almost every arena of my life. Developing social skills, having relationships, developing an identity independent of my family, etc. I'm also a late bloomer to mathematics. I'm in my 30s and getting a bachelor's degree in Math now after a lifetime of math-phobia. Math was my worst subject because it never came easily or naturally to me, and so I assumed I must have been innately incapable of it. I didn't take a single math class during my first bachelor's degree. I sure wish I could have learned math properly earlier in life, but my point with this comment is that it is never too late to learn math. Learning mathematics "late" over the last couple of years has enriched my life in so many ways. Learning to write proofs has brought a sense of organization and calm to many other areas of my life. Complex problems and challenges in life feel so much more approachable, because I am much more skilled now in breaking down tasks to manageable components. I can see now how mathematics has influenced programming languages and computer science, and every time I can identify the mathematical underpinning of some program I use or write, I feel like I am peering into the heart of the universe. Learning math early is a great hack, but so is learning math late :)
  • chikenf00t 2y ago
    How were you able to learn math later in life? I'm terrible at math and I know it causes my work to suffer.
    • 2snakes 2y ago
      I am planning to use Math Academy after my Master's degree. I did a beta and it was awesome, just wish I had taken more notes.
    • moralestapia 2y ago
      My two cents. Math it's way easier than you think it is, it greatly depends on how you approach it. I really like the style of Robert Ghrist videos on YouTube. A great tutor/video goes a long way. I wish I could share some resources but am a bit outdated on that. The overall idea is that some people can explain math concepts in a very clear and straightforward way, while some others will write up a bunch of symbols and let you figure them out. Avoid the latter. As a note, those are usually the lowest performers in academia, lol.
• ailtjalwiejr 2y ago
  I got good at calculus when I started doing differential equations. I got good at differential equations when I started doing modeling and control theory. In general, you don't get good at a subject when you learn it in class; you get good at a subject when you work on the stuff one level beyond it. So yeah, if you want to be good at the class you're in, start studying for the class after it. This is definitely an effective method. But then again, that's really difficult to actually do. For anyone who grew up surrounded by resources, that might sound like a really easy and obvious suggestion. "Just listen to the tutors your parents bought for you." But for the students who can't afford books for this year's classes, you might as well be telling them to "just grow wings and fly, it's not hard". Me personally, I knew plenty of people who did this, learned a year ahead so they looked extra good in class. Most of them had parents who had PhDs, paid their rent for them, and explained what problems they were going to face far ahead of time. For the students who leave class and go to work to pay their own rent and then go back to campus to study and do research at night, this is not very helpful advice. Like so many educational "one simple tricks", the unspoken prerequisite is "just be born rich".
  • looshch 2y ago
    i had a similar experience. I was understanding the concepts i’ve learnt a year earlier and hardly ever would grasp anything immediately
• hintymad 2y ago
  > Higher Math, Not Competition Math This is very true, especially now. So many families, at least in the competitive places like the Bay Area, push their kids to spend enormous amount of time on AMC, AIME, and etc. Other than viewing competition math as a way for their kids to get into elite universities, they often think that doing competition math as a way to be really good at math and they can cite many examples kids who are good at competition math also would have a bright career. Unfortunately, they got it backwards: kids who are naturally good at maths will like do well in competition math (think about Schulz or Terence Tao), but really not the other way around. For people like me, who have limited talent on maths, focusing on learning higher math and the associated essential problem-solving techniques will have a much higher return on investment.
• fumeux_fume 2y ago
  Slightly galling that people write this kind of drivel without examining any of the shaky premises it's logic relies on. Yes, in a perfect world, we can all learn our course material in advance and skate through our in-class education. More practical advice would be to build strong study habits and networking skills. Being able to get your work done with more time for editing/revisions and having access to other perspectives on the course work would have definitely improved the quality of my education. Building those habits and community take time and energy. I guess no simple hack there.
• falcor84 2y ago
  Reading between the lines in TFA, it seems that they're implying that university learning is really bad, and pretty much any other way you can use to learn the subject matter before getting to university will serve you better. There's a long discussion to be had there, but for the sake of argument, let's take that as a given. Assuming that is true, but that there is still a significant benefit to attending a good university - in terms of connections, social experiences, status etc. - should we maybe strive to decouple the university experience from course enrolment - e.g. make it easier for people who have pre-learned the content, to prove their competency and essentially jump directly into a free-form experience similar to grad school?
  • kjkjadksj 2y ago
    While the thesis based freeform option is liable to lead to practically learned mastery, it is perilous. What you might set out to learn and to do might not pan put. You might have to revise your ideas, redesign your studies. You may very well take a lot longer than 4 years through no fault of your own. It can also feel incredibly demoralizing to be toiling in those trenches. Feeling like you are qualified for the job but you just need to get these damn experiments to finally work so you can actually leave and no longer be impoverished.
• Fatalist_ma 2y ago
  Learning the whole course ahead of time sounds easier said than done. But I definitely recommend pre-learning the next chapter in the course instead of relying on the teacher's explanation. Personally, I could never understand a relatively complicated math concept just by listening to the teacher. I usually need to think about it, draw things, read several different explanations, etc, to really get it. But when I was already familiar with the topic, then I could benefit from another repetition and ask questions if there were some complicated aspects.
• advael 2y ago
  I agree with this tip. Works great for anyone who can autodidact, and if you're good at finding and vetting resources, autodidacting got easier with the internet, and has only gotten a little harder with the proliferation of nonsense on the internet for topics that aren't hot in business or politically charged Also, this really shows how the incentives in "education" are deeply misaligned with the way we talk about it. At least in the US, the point of education seems to be mostly gating outcomes and sorting people. Learning is incidental and game theory suggests it's better to never take a class that's truly new material for you, because getting a bad grade can harm you, but learning something new isn't captured at all
• fhub 2y ago
  Greatest Educational Life Hack is getting your children to love going to school.
  • hnthrowaway0328 2y ago
    This.
  • javier123454321 2y ago
    Love learning, not necessarily love going to school.
  • euroderf 2y ago
    I always refer to my 4yo's daycare as "going to school". I want him to perceive continuity. Fingers crossed.
• secstate 2y ago
  EDIT: Nevermind, this whole thing is just an add for a tutoring service :( So, here's my hot take (which probably isn't terribly original): Compulsory school math should end before algebra, and the rest of the curriculum should be taught the same way (or better) to how we teach art or music. If you need advanced math for your career, teach advanced algebra or calculus as needed. At the very least this will force post-secondary schools to be honest about how prepared students are leaving secondary school. Right now, it "those people's fault" for how poorly prepared for advanced math most kids are. Basic math literacy is incredibly important. But being able to solve quadratics or discover geometric proofs is colossally unimportant to 98% of humanity and it's importance can usually be determined based on personal interest in a career. Let's be honest with ourselves that most people well and truly will never need advanced math. Exposed kids to it as a fun game or art form, not a tool that they will never use. Should learning to use a belt sander be an educational requirement to move from 9th to 10th grade? No, no it should not.
  • j2kun 2y ago
    Your argument applies to everything. Shakespeare? Biology? Chemistry? Physics? World history? Most careers don't need these either. If you limit an education to what people need for their careers, we should be have barista and tax filing classes. The only class I'd legitimately believe we should teach is labor organizing/union participation, since every career involves labor.
    • euroderf 2y ago
      Some kind of media awareness belongs in here too. Everyone 21st-century is drowning in information. Gotta sort it out. Some kind of DIY life ring.
• 1970-01-01 2y ago
  The greatest failure of our time is that there isn't a viral, ad-free website or app for children and teens to just go and learn math on their own. Everything worthwhile requires a credit card, user account, and monthly subscription. Children don't have credit cards, email addresses, and access to the latest iOS device. They do have time and at minimum sporadic Internet access. If we managed to create Wikipedia, we can manage to create a similar site for enjoying and learning math.
  • zozbot234 2y ago
    Khan Academy is close enough to what you describe, and it covers K-12 plus some college-level courses. If anything, it's a lot easier to achieve this wrt. math than many other school subjects.
    • Suppafly 2y ago
      This. Between Khan Academy and youtube, there isn't really anything stopping a motivated person from learning. Hell you can get graduate level instruction from some of the best university instructors around by using some of the open courseware materials. Granted some people need the rigor of having an instructor assign and grade assignments regularly, but there are no real barriers to the information itself.
  • jzebedee 2y ago
    Isn't this the whole premise of Khan Academy?
    • 1970-01-01 2y ago
      Khan Academy is limited to learning by boring examples (IMHO) in lecture format and does not virally engage a learner with play. It's analogous to a free virtual classroom.
  • spencerchubb 2y ago
    plenty of learning resources exist. kids just don't have the motivation or focus. i'm not saying the kids are at fault though. there are a thousand games/apps that are like nicotine.
• dmazin 2y ago
  I did this: I studied pure math in uni because “it could be used for anything.” I hugely regret this. 1. I didn’t find it that interesting, and so I don’t feel like I got much out of it. 2. I found later that I learn math much better when I can “hang” the ideas off practical examples. For example, I learned math for the sake of understanding deep learning far better than I ever understood math before. Ultimately, I think it’s far more important to study something that interests you, and to learn the tools you need as you go.
• factorymoo 2y ago
  I went to the most prestigious high school in France. The top 2 students in my maths class shared one thing in common: they would study the curriculum the summer before. I did it one summer, and while I was nowhere near as good as them - something magical happened: even though I hadn't understood all the concepts, my ability to understand the concepts during the class went way up. It was easier to follow what the teacher was saying since no concept was totally new to my mind.
  • raybb 2y ago
    Did that make it feel more or less boring?
    • factorymoo 2y ago
      To me less boring. I used to struggle to understand new concepts as they were presented. That year though, I was able to follow what the teacher was saying "live", ask interesting questions to deepen my knowledge.
    • exe34 2y ago
      It was like that with physics for me in high school. At ages 11-13 we learnt a bunch of stuff, which nobody except I paid any attention to, and then we had to do it all again, exactly the same stuff, for ages 14-15 to prepare for GCSEs. I was horribly bored, but at one point I was lucky enough that the teacher just gave me A-level and then early uni stuff to figure out, so that kept me busy. then first year of uni was horribly boring again, which led me to be over-confident, and didn't do much work in second year, but thankfully I managed to pick up the slack in 3rd and 4th year of uni.
    • djeastm 2y ago
      It'd be what you made it. I went back for a CS degree long after having coded for years and there were certainly things I would have had to sit around and wait for others to catch up on if I let it. But instead I always pushed myself to build much more sophisticated versions of the basic things we were learning and I also tutored, which is where it really becomes not boring, because you get to see how other people learn things in different ways, which broadens your own perspective, as well. So basically I'm just trying to say it's up to you to make things not boring
• alabhyajindal 2y ago
  I am currently learning maths independently. I'm using the book, Maths: A Student's Survival Guide by Jenny Olive. I'm towards the end of the first chapter and feeling confident with basic algebra now! I picked it up after seeing it recommended here.[1] The book explains a topic concisely and then gives exercises. Importantly, the exercises don't assume previous knowledge and you can solve them by applying previous explanations. Highly recommended! 1. https://news.ycombinator.com/item?id=39050972 https://news.ycombinator.com/item?id=39050972
• Joel_Mckay 2y ago
  The bimodal distribution of student entrance performance correlating to stratified fiscal castes has been observed for sometime: "Outliers: The Story of Success" ( Malcolm Gladwell, 2011 ) i.e. the curriculum lesson plans naturally evolve to exclude individuals that don't need introductory lessons, because they are on average 3 years ahead of their peers by the time they enter undergraduate programs. The kids that need to "catch-up" in introductory Math/English material are no longer failed/held-back a year in some municipalities, but rather given a remedial curriculum over the summer. If those kids parents can afford to put them through an early tutorial program, than excluding the "poor kids" from a seat at the more lucrative faculties is rather guaranteed. https://www.youtube.com/watch?v=qEJ4hkpQW8E https://www.youtube.com/watch?v=qEJ4hkpQW8E Mind you explaining to privileged kids why they _get_to_ attend additional instruction can be difficult. As social media normalizes lack of impulse control, and rewards group-think biases. Our little ingrates think they can con/hack their way through life, as some fool on the web is telling them to take the easy path. Some university kids that rely on student visa programs to access the US immigration process, will get desperate and try to outright cheat their way through a Bachelor of science degree. The real scandal is some folks get 50% of the final problems from $18.74 USD gray market course manuals out of HK, as many institutions must structure their exams this way for credit-transfer compatibility. The myth of natural talent deteriorates further with some fraternities also gaming the system to out-compete the rest of the student body when possible. Indeed, some people do hack/cheat their way to a better life using underhanded tactics, and are rarely held accountable. Some places are even removing the barrier where one needs to be fluent in English. You are probably still thinking this can't be right, and seats for becoming a physician/pharmacist/lawyer are open to anyone. Yet I can assure you that while the faculties will take your money, the probability of getting into a Masters/Doctorate level program quickly drops while you worked hard to catch up... Note your GPA took the hits along the way. People need to recognize there is a subtle yet important difference between intelligence and academic performance. No one ever claimed life was fair, but the hypocrisy of many meritocrats can be intolerable at times. Stealing Einsteins chalk does not make one Einstein... but does silence talent. Have a great day, =3
  • oglop 2y ago
    Best comment in the thread.
• vecter 2y ago
  This is simple but so effective. When I was 5 or 6 years old, my mom would sometimes give me one page of simple math problems. They were all basic arithmetic, things like 12+17 or 99+99 or 8x7, etc. I did them and got on with my life. They probably didn't take more than 15-20 minutes. They didn't feel like much because they really weren't. I think any 5 year-old can do them. I believe that whatever little "edge" that gave me in learning math in school compounded exponentially over the years. I always felt "ahead" of the standard school curriculum, and that created a virtuous feedback cycle of success, which bred confidence, which bred success, and so forth. Just a little nudge here or there at home can make a big difference.
• Bostonian 2y ago
  I remember having trouble in a electricity & magnetism course because I needed to learn some math concepts (divergence, gradient, curl) at the same time as the physics. It would have helped to have studied multivariate calculus before the E&M class.
• tptacek 2y ago
  This presumes an educational career that benefits from engineering math. It's interesting to me that even a lifetime in computer science doesn't necessarily reward this strategy (it might, it might not, depending on focus areas).
• matt3210 2y ago
  I had to lean match for writing programs at 12 and after just a few weeks of trying to make a game that had some higher math, I was leagues ahead of my classmates. Need is the key here in my opinion. Kids usually don't like math unless there is a need for math for something they do like.
• rqtwteye 2y ago
  Learning ahead definitely helps me a lot. For some reason I am not capable of learning things from scratch in one swoop. I always need to learn things a little, let them somehow settle in my brain for a while, and then go further. I always had trouble in school when things moved linearly.
• racl101 2y ago
  Tried teaching my young nephew about math. He just bashed me in the head with the abacus. Then started crying.
• proee 2y ago
  Perhaps I'm in the minority here, but I've wasted a ton of time in math classes working through way too many academic exercises that have little real world applications. For example, learning a bunch of tricks to solve a differential equation by hand feels like a circus act. Sure it can be done, but only with a limited set of "textbook" equations. When you get into the real world, you'll need to put those equations into a solver like matlab, etc. It would be nice IMHO to see a more hybrid approach at Universities to teach math and application at the same time. It's strange to send students through YEARS of math classes without strong application. It's like learning music theory without playing an instrument. Our academic system in general is still modeled after old-school institutions, based on textbook-style learning that all pretty much follow the same recipe. Is it not crazy that we have classrooms in this day and age with 300 students sitting in desks listening to a single professor? It's insane. We are ripe for an educational system that is truly disruptive - especially with the rise of AI systems.
  • sarora27 2y ago
    this was my biggest gripe w/ academic math. Whenever i'd ask my teachers how these concepts are applied in the real world, i'd get a non-answer that showed me a) the teachers themselves have no clue and b) they're hoping you'll just shut up and follow the curriculum. I agree that we are ripe for an educational system that is truly disruptive. Our current educators are so disconnected from the real world and have no idea how to apply what they teach.
• NoNameHaveI 2y ago
  One of the best, most cost effective ways to do this is by enrolling at your local community college. Faculty there are primarily focused on teaching, and WANT you to “get it”. In addition to math, I recommend you take ALL the STEM courses you can that you’ll touch in university. I took separate classes in Unix and C at community college before my university quickly introduced them in systems programming. Boy, that was time and money well spent.
• dambi0 2y ago
  Beyond the general idea that the more time you have to think about a problem the more likely it is you will do better at solving it. How does this translate into an ability to solve more emergent problems? Isn’t this “hack” somewhat similar to the idea of people who have never had to step up and learn to work harder. And in fact the hack gives a false sense of confidence in the ability to solve more typical real world problems when it matters.
• ivanche 2y ago
  I confirm this! My son is 10, finishing 4th class. We're constantly 6-9 months ahead of his class. I think he once in those 4 years got note 2 (one below highest), every other one was the highest. Vast majority of his math classes look like "oh I know that" or "oh I remember that, just need a 5 min refresher". Thanks to it, he has more time for other subjects. His stress level at school is close to zero.
• DowagerDave 2y ago
  The argument made here is there are risks learning math when everyone else does, so learn it earlier. Great, but how? Only the very few have the resources and environment to learn non-trivial math early. What does this displace? Is it more important for a kid to learn calculus, piano or a second language? Are younger people capable of learning math in a no-painful way? Why do they have patient, knowledgeable teachers at this level but not later? Math can be hard because of the required discipline and practice - are younger people better positioned to solve this, or worse? It seems insincere to frame this as math is important, and earlier > later without focusing on what this means, or the opportunity costs. Could we just do a global search & replace on 'math' with 'literature' and end up in the same place?
  • calf 2y ago
    I skimmed the article and don't see a section explaining how to properly accelerate for the typical student. Do you just give them good-quality math textbooks for them to work on in there spare time? Or do they mean hire an private tutor?
• dilap 2y ago
  Then there's the approach taken by my university's physics department, where they made it a point of pride to always have you using math before you'd learned it from the official math classes...
• DonsDiscountGas 2y ago
  Spending all of your time studying isn't a "hack". Not saying it's a bad idea, but it's a ton of work
• graycat 2y ago
  Yes, > The Greatest Educational Life Hack: Learning Math Ahead of Time (justinmath.com) worked for me, can work for a lot of people, and is a good idea. Partly: (1) One way to win a 100 yard dash is to start running half way to the finish line and have no one object. The US educational system will usually overlook something like that starting half way to the finish line. (2) Reasons: (a) The system assumes that their teaching is crucial and that no student really can learn on their own, i.e., the student didn't actually start half way to the finish line. (b) The system so wants more good students that they will overlook the evidence that the student was ahead at the start of the class. But, research in math mostly requires working alone directly from original papers, and working from a highly polished text is usually much easier -- so profs learn on their own, and students can too. (3) Generally in math, independent study can work well. Basically for each lesson, (a) study the text, (b) work most of the exercises, especially the more challenging ones, and check the answers in the back of the text (need a suitable text or just get the book for teachers), and (c) in a quiet room, lean back, relax, and think a little about what the value, purpose, content of the lesson was, say, be able to explain it to someone who never studied math. (3) So, take calculus in high school. And visit, call, whatever, and see what the popular college calculus texts are, get one or two of those (used can be a lot cheaper), and before college have worked hard on both the high school course and the college text(s). Then in college, right, take calculus, likely from a text have already done well in. So, will likely be one of the best students in the class. Then will get a good reputation that can be valuable. (4) Will be ahead, so continue this way and stay ahead. (5) Next math course, say, modern, abstract algebra, i.e., set theory, groups, fields, Galois theory, elementary number theory, maybe a start on linear algebra. Next, linear algebra, maybe the most important and useful course. Work through a popular text that is relatively easy. Then work carefully through one or two of the classics, e.g., Halmos, Finite Dimensional Vector Spaces. Likely next, "Baby Rudin", W. Rudin, Principles of Mathematical Analysis, calculus and somewhat more done with depth and precision. See the roles of open and closed sets, closed and bounded sets, i.e., compact sets, continuous functions, the powerful results of continuous functions on compact sets, Fourier series. Advanced calculus, i.e., partial derivatives and Stokes formula. Analysis, e.g., the real part of W. Rudin, Real and Complex Analysis, Lebesgue's alternate and nicer way to define integration (in short, partition on the Y axis instead of the X axis), the Fourier integral, Banach space, Hilbert space, the Radon-Nikodym theorem (can be used for grand approaches to information, Bayes Rule, the Neyman-Pearson result in best statistical hypothesis testing, and with von Neumann's proof based just on polynomials is charming, ...). More, e.g., differential equations, probability, statistics, stochastic processes, optimization, complex analysis, number theory, whatever. One consequence: Will learn how to write math. Too often people who don't know advertise that they don't know much math. At some point in business, some of that math might be valuable. E.g., current AI uses steepest descent via calculus and optimization, linear algebra, and hypothesis testing.
• saephanch 2y ago
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• greenhearth 2y ago
  "When a middle or high school teacher has a bright math student, and the teacher directs them towards competition math, it’s usually not because that’s the best option for the student. Rather, it’s the best option for the teacher. It gives the student something to do while creating minimal additional work for the teacher." Kind of a dick statement
  • skirmish 2y ago
    Agreed, my math high school teacher told a few of us "you don't need to take weekly tests, I know you will do well; instead here are more interesting competition problems you should try". It definitely kept us interested and motivated much better.
• oglop 2y ago
  Fuck this fucking article. You know one reason I know my math degree is bullshit? Because I figured out quickly my profs wouldn’t explain jack shit and I would have to “learn the math early” which meant just teach my self with other kids the god damned material. This isn’t a life hack. This is the sign of a failing system. Jesus fucking Christ.
  • teleforce 2y ago
    Calm down mate, don't be so worked up over a random article posted in HN. The OP is talking about taking pre-emptive maths course and accelerated learning not particularly taking a full course degree in math. Personally, I think engineering students will benefitted more if learning engineering maths in their pre-universities courses namely matriculation, A-Level or Baccalaureate, rather than spending few years learning the subjects during their main engineering degree. It helps the student focus and minimize the pre-requisites.
• beryilma 2y ago
  As a PSA for anybody who wants a very readable introduction to "real" math, check out Jay Cummings' two books: Proofs and Real Analysis at https://longformmath.com/ https://longformmath.com/ Each paperback book costs less than $20 on Amazon.