[HN Gopher] The Greatest Educational Life Hack: Learning Math Ah...
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The Greatest Educational Life Hack: Learning Math Ahead of Time
Author : harperlee
Score : 235 points
Date : 2024-07-17 08:46 UTC (14 hours ago)
(HTM) web link (www.justinmath.com)
(TXT) w3m dump (www.justinmath.com)
| bell-cot wrote:
| 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 wrote:
| > 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| You are not anywhere near the average in learning
| ability. Your experience is as an outlier.
| trte9343r4 wrote:
| 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 wrote:
| 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 wrote:
| >Academia wasted 5 years of my life.
|
| Nah, you wasted 5 years of your life.
| glitchc wrote:
| It definitely makes the first couple of years in university that
| much easier, although limited to the science and engineering
| disciplines.
| CrazyStat wrote:
| 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 wrote:
| 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 wrote:
| 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.
| bee_rider wrote:
| I actually did learn how to run before I learned how to walk.
| It caused my parents all sorts of stress. I guess, though,
| there's room to quibble about where controlled falling
| forward is really running.
|
| Anyway, it seems like a shame that there's a problem solving
| strategy beyond fundamentals for competitive math. What makes
| the puzzles in the game different from the sort of typical
| math somebody in STEM might do?
| zozbot234 wrote:
| Walking is just as much "controlled falling forward" as
| running is, it's just slower.
| qsort wrote:
| Conflict of interest since I was very much into competition
| math in high school, but I definitely agree that at the HS
| level it's just about the best thing you can do. It develops
| your mathematical maturity in ways that simply front-loading
| calculus or linear algebra won't. A LOT of competition alumni
| go on to become great academics or successful professionals.
|
| And just by the way: competition math is definitely "higher
| math" in a lot of cases. To be competitive at a decent level
| you have to know stuff like "real" algebra (groups, fields,
| etc., stuff like Burnside's lemma is pretty much table stakes),
| vectors, barycentric coordinates and so on for geometry
| problems, how to handle recursion for combinatorics, generating
| functions etc. It's by no means only silly tricks.
| zozbot234 wrote:
| > 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.
|
| And one of the best ways of developing that skill is...
| learning higher-level math. This can also include 'competition
| math' topics of course, but they should be approached as self-
| contained subjects of their own, not just as a bundle of
| disconnected "tricks" to be applied solely in a competition- or
| puzzle-solving context.
| CrazyStat wrote:
| Depending on how the course is set up, maybe. Most math
| courses are not set up to make students wrestle with problems
| for extended periods of time, even through University level.
|
| I took courses in topology and number theory in undergrad
| that _were_ set up this way--the professor did almost no
| lecturing; we were given a series of results to prove and
| expected to wrestle with them ourselves (mostly alone as
| homework). Once you thought you had a proof you presented it
| to the class. But this is very atypical. Your typical
| calculus or differential equations or linear algebra course
| does not develop this skill.
| conductr wrote:
| Good advice but not good general advice. This will benefit some
| but many more people will get frustrated and learn to dislike
| math.
| CrazyStat wrote:
| This is not my experience. If they see the task as "solving
| the problem is success and anything else is failure," like
| they might be used to from most school math classes, sure. If
| you set up the context properly my experience is that most
| kids enjoy working on hard math puzzles.
| conductr wrote:
| Perhaps on basic math with younger kids but I expect this
| will hit a wall at a certain level. Or, the audience of
| kids doing this is already a skewed/biased sample of kids
| that just love math (or it's parent driven)
| colonwqbang wrote:
| It seems that OP assumes you are already targeting a career
| where maths will be useful to you. If so, I disagree.
| Everything in school becomes much more fun when you
| understand what you're doing.
| insane_dreamer wrote:
| > Sitting with a problem that you don't know how to solve for
| __hours__
|
| my child is very good at math, able to grasp advanced concepts
| quickly, years ahead of his school curriculum, etc.
|
| there is __0%__ chance I could get him to do the above for
| __hours__
| twic wrote:
| Is there anything specific to mathematics about this?
| mamcx wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| > 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.
| fnord77 wrote:
| And there are places that have or are trying to ban algebra in
| Jr. High School (e.g. SFUSD)
| NotYourLawyer wrote:
| 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-mat...
| wnolens wrote:
| You've been downvoted, but the Seattle school system thinks
| math is racist
|
| https://www.edweek.org/teaching-learning/seattle-schools-
| lea...
| anthk wrote:
| >"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.
| lupire wrote:
| That makes it easier to learn ahead.
| litver wrote:
| The Even Superiorly Greatest and Lovely Educational Life Hack:
| Learning Latin Ahead of Time
| blowski wrote:
| Quicquid latine dictum sit, altum videtur.
|
| Learn Latin and you can fake your way through so many
| situations.
| euroderf wrote:
| It made French grammar a breeze. (Mostly.)
| rodolphoarruda wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| > 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.
| rtkwe wrote:
| They need English at home too, a lot happens in those early
| years where there's no schooling and it'd be way better to
| know English well going into school (what ever level that
| happens to be at) too.
| querez wrote:
| My daycare has a lot of non-native people who do not
| speak the local, native language with their child, at
| all. Still, all children (age 3, they're usually in
| daycare since age 1) speak the local language fluidly,
| thanks to how much they they spend in daycare.
| zarzavat wrote:
| No, it's not necessary to speak X at home if you live in
| an X speaking country, and it may even be harmful: often
| children will not pick up language Y if only one parent
| speaks it and the other parent speaks X.
|
| Bilingual children whose parents don't speak the language
| of the community at home may learn languages slightly
| slower but they quickly catch up once they make friends
| who only speak X.
| lbrito wrote:
| I would say the opposite; talk to your child only in your
| native language. Kids will learn English by themselves in
| school anyway, and if they don't learn your language from
| you, they for sure won't learn it elsewhere.
|
| Source: as a kid I was in that situation, at first my parent
| spoke only in English with me and I started to forget
| Portuguese. After my parents realized that they pivoted to
| speaking Portuguese. I learned English fine at school and
| never had problems with either languages. Now I'm a parent of
| a 2yo and 1yo and am speaking Portuguese with both.
| M4v3R wrote:
| > Kids will learn English by themselves in school anyway
|
| If you live in an English speaking country then sure. Over
| here it's almost impossible to learn English in school, you
| only get a few hours per week of English classes.
| paganel wrote:
| It depends on the kid and on the type of "immersion" (for
| lack of a better word). I grew up in Romania in the '90s,
| when we had 2 hours of English per week starting with the
| 5th grade. I turned up fine when it comes to
| speaking/writing/reading the language, of course that
| I'll always carry an accent when speaking it but I don't
| care.
|
| Looking back at it, after 3 decades, what helped me learn
| the language was that immersion I mentioned, i.e. I was
| watching English TV programs (Cartoon Network, Eurosport,
| MTV Europe) for a big part of the day, without that I
| wouldn't have been able to pick it up so easily.
| flyinglizard wrote:
| My experience is that it's very easy to expose kids to
| English in a non-English country - just let them consume
| all their entertainment (Netflix, games, books) in English
| right from the start. You don't need to do anything special
| other than that.
| rtkwe wrote:
| Do be mindful of the kid though. One of my wife's coworkers
| wanted to teach their kid multiple languages, I think the
| final count was 4 total (they wanted both the parent's native
| tongues, German which is where they were going to live after
| their visas expired in the US and of course English), while
| living in the US and it just made the kid confused and angry.
| Granted that's way more than just doing two but it could
| still back fire with the kid if it's too much.
| qsort wrote:
| As a non-native English speaker, this. Native English speakers
| are reluctant to give this advice, but it's the lingua franca
| of any field that matters. Not being able to communicate
| effectively will definitely be a blocker.
| smokel wrote:
| Using the term "lingua franca" for English demonstrates,
| twice, that this is only a temporary phenomenon.
| qsort wrote:
| Since Eve ate that apple pretty much everything is a
| "temporary phenomenon".
| ptmcc wrote:
| Ok, yes, and? English is the dominant language now and for
| the foreseeable future. Some day that may change but it
| won't be overnight.
| umanwizard wrote:
| English will almost surely still be the dominant world
| language for as long as any of us is alive.
| gwervc wrote:
| Heck no, I'd rather protect my (future) kids from a lot of
| ideas spreading in the English speaking sphere until they
| reached some given age. There's enough cultural, scientific and
| entertainment content in French and Chinese to fill one's mind
| until adolescence.
| rcbdev wrote:
| This.
|
| Most money is spent in manipulating English media. Only
| fractions for other languages. It makes a difference.
| runiq wrote:
| Another reason to learn English ASAP is because the orthography
| is pants-on-head stupid. Your young self will not have a
| reference system for just _how_ pants-on-head stupid it is and
| happily accept it without giving it a second thought.
|
| If you are learning English later in life, you _will_ struggle.
| rcbdev wrote:
| I'd argue some pants-on-head stupid declinations and
| arbitrary genders for every noun is a much more compelling
| reason to learn a language early than orthography.
|
| English is probably one of the dead simplest languages of use
| to learn later in life.
| dotnet00 wrote:
| It helps that since English is the lingua franca, people
| tend to be kind of used to interacting with those who don't
| speak it perfectly. Plus even those who don't functionally
| speak it likely know enough words to convey things in a
| pinch through either loan words or osmosis through media.
| saagarjha wrote:
| Nah, it sucks. Source: native speaker who also knows
| Spanish and Hindi
| euroderf wrote:
| Agreed. In some ways English is aggressively stupid and
| hostile to learners.
|
| In purely intellectual terms, know thy enemy.
| floatrock wrote:
| 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 wrote:
| > 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| >> 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 wrote:
| 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 wrote:
| 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.
| tptacek wrote:
| I put my kids through school (they're both out of college
| now) in an upper class Chicagoland suburb and this was
| definitely not the case.
|
| I'd be a little careful with venue effects on a discussion
| like this: this is a group of people that have, as a cohort,
| a particular fixation on academic and especially mathematics
| status signals.
| gjvc wrote:
| What is the preferred choice between Kumon and Russian School
| of Mathematics?
| dh2022 wrote:
| I sent my son to both of them and I prefer RSM by far. Kumon
| to me was rote learning - lots of very similar problems. My
| son did not last even the first semester.
|
| My son then attended RSM from first grade. RSM instruction
| started from problems like "there are 3 birds on a branch. 1
| bird leaves. how many birds are now on the branch" and
| progressed onward. By grade 7 he is learning logarithms and,
| at a very basic introductory level, abstract concepts such as
| function
|
| (by function I mean the real definition of a function, not
| the easy f(x) = 2 x + 1 -
| https://en.wikipedia.org/wiki/Function_(mathematics))
| alephnerd wrote:
| > any of the wealthy or upper-middle-class suburbs
|
| Working class too if you're Asian American.
|
| Asian American kids in SF public schools and the closest
| suburbs (eg. Daly City, SSF) skewed working class but the
| parents would also push their kids to attend Kumon or cram
| schools.
|
| Same story in working class Asian neighborhoods of SoCal and
| Boston like SGV or Quincy+Malden respectively.
| kjkjadksj wrote:
| True for college math too. I took calculus for the first time
| in my life in college. Half the class had it in high school,
| half of those students took AP calc. Exams were so brutal for
| those of us taking it for the first time especially. Nothing
| could have prepared me for them. The lecturer would schedule a
| two hour block outside of class and the exam was 7 very
| challenging questions. Most of us would not finish before the 2
| hours were up. Class averages were in the 50% range. I took my
| C and moved on with my life never needing to do calculus by
| hand ever again.
| rawgabbit wrote:
| My son did "Business Calculus" at a large state university. I
| have a masters in science and had taken many quite difficult
| math courses in my day. I looked at what he was asked to do
| and saw his exam papers. Needless to say "Business Calculus"
| had little to do with business and a lot to do with making
| math as difficult as possible. The class average was a C and
| I believe many of the students had taken AP calculus in high
| school. It was one of the courses whose purpose was not to
| teach but to prop up the university-industrial complex.
|
| EDIT. Below is an example (not from his instructor but the
| same material). Remember this is for "business calculus". It
| just seems like silly math tricks to me. https://people.tamu.
| edu/~jdkim/math142fall2019/math142week11...
| Acrobatic_Road wrote:
| just glancing over this pdf it doesn't seem so bad. The
| first couple of problems are just integrations with some
| very obvious u-substitutions.
| conductr wrote:
| Education is a part of culture. The American culture is one
| that doesn't actually value education. It's one of shortcuts
| and minimum effort and coasting by checking the boxes along the
| way to a decent enough paying job, or so we hope. We place
| value on our social lives much more so. Eg. popularity, sports,
| fraternities, "the college experience", etc
| DowagerDave wrote:
| Sure there are cases as you describe, but painting the entire
| American culture wrt education with your very wide brush is
| unfair and incorrect. It's also soundly refuted by the global
| demand for American education, and historic performance.
| sharadov wrote:
| I send my kids to Singapore Math, because the math curriculum
| and how they teach math is lacking - it's superficial, they
| gloss over the concepts. In schools my kids look at a worked
| example, then solve problems that very closely follow that
| example, repeating all the same steps with different numbers.
| In Singapore math, students must think through the concepts and
| apply them in new ways from the very start.
| hintymad wrote:
| > via Kumon or RSM or something else.
|
| My kids use Kumon and RSM too, only because what their school
| covers are pathetic. The content may be okay, but the teachers
| certainly didn't give good enough homework to help the kids
| deeply understand the math concepts and to get valuable
| problem-solving skills.
|
| That we rely on Kumon and RSM says a lot the abysmal state of
| the education quality in the US. Case in point, I would not
| need Kumon or RSM at all when I grew up, as my school covered
| way more and way deeper math. Note the US is still the best
| country for the top students and those who struggled with
| academics. It sucks only for the majority -- the students in
| the middle like me. They could've got trained hard, yet the
| school squandered the opportunity.
| markus_zhang wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| This is basically an ad
| lupire wrote:
| And an attack on the competitors -- opposing competition math
| because other vendors got their first and it has a narrower
| addressable market.
| WesleyLivesay wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Learning to read as an educational lifehack suffers from a
| couple issues with the target audience.
| CrazyStat wrote:
| The author works at a math education company, so the focus on
| math is understandable.
| yonaguska wrote:
| 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 wrote:
| 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....
| saagarjha wrote:
| This is generally because it stops being "reading" and starts
| becoming "literary analysis" which goes _very_ deep.
| grose wrote:
| 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 wrote:
| This is what DragonBox does too.
|
| Kids hate math because teachers and textbook writers hate math,
| who put no fun into it.
| ghostpepper wrote:
| 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?
| zozbot234 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Ahh, the very definition of isomorphism :)
| Syzygies wrote:
| 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 wrote:
| Love this quote.
| supertofu wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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.
| RealityVoid wrote:
| You learn math best by doing math. Sure, good explanations
| help, but sometimes dry rigorous ones are preferable since
| it asks you to grapple with the subject.
| moralestapia wrote:
| >sometimes dry rigorous ones are preferable
|
| My experience with the comments in this thread, the
| overwhelming majority of people I know IRL and the
| widespread sentiment that "Math is hard" does not seem to
| reflect that.
| grepLeigh wrote:
| Similar to the OP, I had a lot of anxiety around math and
| academic performance. I dropped out of college at 18 and the
| highest math class I took was in high school (pre-calc),
| which I almost failed.
|
| At age 33, I enrolled in community college and took Calc
| I-III, Linear Algebra, and Differential Equations. The
| community college hosts weekly "math jams" and offers free
| 1:1 tutoring.
|
| I'm currently taking a Discrete Math and Probability class at
| UC Berkeley for fun this summer (CS70), which would have
| seemed absurd just a few years ago. The community college
| system in California is extraordinary; I'm glad I got to
| experience it first-hand.
| Loughla wrote:
| Describe the math jams, if you would please. Is this just
| open tutoring labs for all areas of math? Or is it
| something different?
| nextos wrote:
| You can start simple. Read _Basic Mathematics_ by Serge Lang
| and do all exercises. Solutions are included. That book
| basically covers all mathematics up to junior high in a
| rigorous but approachable fashion. Serge Lang was a great
| mathematician. Then you move to logic, calculus, linear
| algebra and probability. Afterwards, focus on more specific
| areas that interest you.
|
| Springer Undergraduate Texts in Mathematics and Dover have
| lots of elegant and concise textbooks that can help you. At
| the beginning, the key is to move slowly and build some solid
| foundations.
| chongli wrote:
| I am rooting for you! I just completed a Bachelor's of
| Mathematics in December before my 40th birthday this year. I am
| so glad to hear about the effects you're feeling as you learn.
| I too experienced a deep sense of calm and confidence as I
| learned to write proofs. Surprisingly, none of my younger
| classmates agreed! So I chalked it up to being older and more
| mature in general.
|
| Now I feel vastly more mature than I did before I began my
| degree! I have that same belief and confidence that no problem
| I face is unsolvable. I've also discovered a much deeper love
| of learning itself, and a desire to continue studying long into
| the future, and that interest includes but is not limited to
| mathematics! I want to have many different hobbies and learn
| all about how the world works.
| kensai wrote:
| Thank you for this post. I am in my 40s and have a similar
| approach.
| bitwize wrote:
| Math anxiety... it's a real thing. My wife has a brilliant
| level of intelligence but refused to approach the higher levels
| of math. Not out of lack of capability... just fear. She says
| things like "Math should have numbers in it, but no letters.
| I'm not about the kind of math with letters in it." And for
| example, she never completed her psych degree because a
| statistics course was required to complete it and she didn't
| want to take it.
|
| It's like a fat person going to the gym for the first time. But
| once they start getting into the habit of working out and
| seeing the improvements, the anxiety goes away.
|
| Anyway, congrats on overcoming your math anxiety.
| ailtjalwiejr wrote:
| 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".
| hintymad wrote:
| > 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Greatest Educational Life Hack is getting your children to love
| going to school.
| hnthrowaway0328 wrote:
| This.
| javier123454321 wrote:
| Love learning, not necessarily love going to school.
| euroderf wrote:
| I always refer to my 4yo's daycare as "going to school". I want
| him to perceive continuity. Fingers crossed.
| secstate wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Isn't this the whole premise of Khan Academy?
| 1970-01-01 wrote:
| 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 wrote:
| 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.
| mensetmanusman wrote:
| Start a nonprofit to implement this. What you are suggesting is
| a lot of work, and it requires an institution to complete and
| maintain.
| JonChesterfield wrote:
| It's here https://us.metamath.org/
| dmazin wrote:
| 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 wrote:
| 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 wrote:
| Did that make it feel more or less boring?
| factorymoo wrote:
| 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 wrote:
| 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 wrote:
| 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
| petesergeant wrote:
| I did a Software Engineering Maths module at Oxford, having
| barely touched maths in several years. Working through the
| curriculum first was incredibly useful, because in the lectures
| everything just melded together, and my brain was already
| primed
| golergka wrote:
| I went to math high school which was the most prestigious one
| in Russia at the time. Most of math class graduates would go to
| study math at the uni, and for the first year would be far
| ahead of their coursemates -- but then would be hit by the
| sudden need to actually study the material and prepare for the
| exams like a wall of bricks.
| alabhyajindal wrote:
| 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
| Joel_Mckay wrote:
| 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
|
| 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
| vecter wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| Tried teaching my young nephew about math. He just bashed me in
| the head with the abacus. Then started crying.
| proee wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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?
| dilap wrote:
| 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...
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