Are Hackers Being Let Down In Education?

In my work for Hackaday over the years I have been privileged to interact with some of the most creative people I have ever met, I have travelled far more than I ever did when I toiled unseen in an office in Oxford, and I have been lucky enough to hang out in our community’s spaces, camps, and dives across Europe.

Among the huge diversity of skills and ideas though, it’s striking how many of us share similar experiences and histories that have caused us to find our people in rooms full of tools and 3D printers. One of these things I found surprising because I thought I was the only one; I never fit in with the other kids at school, I found much of the teaching incomprehensible and had to figure things out for myself. As an exercise recently I did a straw poll among some of my friends, and found that a significant majority had a similar experience. Clearly something must have gone badly wrong in the way we were being taught that so many of us could have been let down by our schooling, and maybe to understand the needs of our community it’s time to understand why.

School: How To Put A Child Off Learning For Life

Cross-section of a violin bridge
I didn’t come away from school music lessons with nothing, the interaction between bass bar, bridge, and sound post in a violin is pretty cool. Amitchell125 (CC BY-SA 4.0).

Where we go to school is not our own choice but one made for us by our parents — and often times that’s just a default of going to the school in nearest where you live. My parents were lucky enough to have some choice and I ended up through a scholarship at my local academic high-flyer’s school. It was a place that parents across my county rate as an Extremely Big Deal, so I found myself the only blacksmith’s kid at Hogwarts. In short, it was an exam factory where stuffing facts into your brain was the order of the day rather than necessarily being expected to understand those facts.

There are two sets of lessons from my school which stick in my brain, one because it spectacularly succeeded in teaching me what I needed to know, and the other in which it completely failed. The first was the physics curriculum, while the second was the music teaching which I gave up without a shred of regret after three years. In my physics class I gazed in wonderment as the beautifully ordered and interconnected thread of SI units fell into place and bound together an understanding of how the world really worked that still serves me today. In the music class I sat there as a teacher who evidently understood how it worked expected us to share his understanding simply by being told that it worked. I came away with a glossary of musical terms and oddly a knowledge of how a violin works (which is pretty cool), but I can’t honestly say I had a clue about any of the rest of it.

I think I’ve stumbled on the key to why this has gone so far wrong in my description of the music lessons. The mindset I share with so many of my friends in this community is one of requiring to understand something as part of learning it, in other words to merely tell us something is to then see it drift away in the maelstrom of other extraneous facts while to show us the reasoning behind that fact is to cement it in place. Thus I understood physics because I could spend a happy afternoon measuring the specific heat capacity of water and then see how those units could be defined in other terms, while the music passed me by because I was simply being told things without any frame of reference or meaningful means of investigating them.

I have since learned as a grown-up that there is a whole branch of musical learning referred to as musical theory, perhaps if I had been taught that in a similar way that I learned the structure of a BASIC program I could have understood some of it.

Every Kid Loves Music, Right?

A selection of harp guitars in a museum.
There are so many witty captions about user interfaces that could be applied to this picture. Lana, CC BY 2.0.

As an exercise over the last few weeks I’ve approached music again as a grown-up, to see how I could understand it with the benefit of an extra three decades. I now have the tools in the form of sequencers such as LMMS or environments such as Sonic Pi to cross that divide into understanding through practical investigation that was missing in my school days. Traditional musical instruments have complex and arcane user interfaces with a huge learning curve that leaves the experimenter none the wiser, something oddly akin to typical modern CAD packages. It’s hardly surprising that just as with CAD where I’ve found salvation in the coding interface of OpenSCAD, so I might find the same with its musical equivalents.

I was taught at school that there are seven notes in an octave, A through G which are the white notes on a piano. This I have found is of course a lie, because when you factor in all those black sharp and flat notes on the piano keyboard there are about twelve. The black notes we are told are half a note between the white notes, but just to seriously confuse matters there’s a pair of white notes that don’t have a black note between them, yet I understand are only half a note apart. I further read that the key of a piece of music is the note it starts on, which depending where on the keyboard it lies can be a major key which sounds happy, or a minor key which sounds sad. Musical timing is expressed in beats, which are grouped in fours to form bars, which I can see as the bits between the vertical lines on a sheet of printed music. Which is something like a primitive version of the waterfall plot from my SDR, a cross section of a frequency range over time.

The slightly humorous tone of the preceding few sentences conceals a serious point, which is that this relatively meaningless junk is how I understand that music works based upon how I was taught the subject, but which is completely useless when it comes to making any of the stuff. So let’s start again. I have twelve notes, they are my syllables. The number of beats per minute is my clock, and I can adjust that to match the speed of my chosen musical style. A bar is four beats and becomes something equivalent to a word, and some reading tells me four bars can become my sentence. I’m ready to make music!

Four Chords And An Attitude

the four chords in LMMS
I owe everything I know to the Axis of Awesome.

Except I’m not, because all I’ve done is define my canvas. If I could write a melody I could produce a simple tune, but it would come out in the manner of a nursery rhyme. I’m more interested in the structure of the everyday music I might hear, and for my first ray of understanding I’m indebted to the Aussie comedy rock band Axis of Awesome for their famous 4-chord song. The point they’re making is that the same four-chord progression underlies a significant proportion of popular music, but the trouble is that for the non-musical person it’s not explained just what that means.

I know what a chord is, several notes played at once, but this is where yet again my music teacher fell short. It’s left to more YouTube research and a kind explanation from a hacker friend to understand that this refers to the repeating pattern that underlies a song and holds it together. It’s played on the left hand on a piano an octave below the melody, or in a guitar rock band it’s the job of the bassist. Who knew! There are even formulae for those chords: a common one starts the first bar with a chord containing any note picked from the octave, the one six above it, and another six above that, then shifts the whole lot down by six notes in the second bar, up by two in the third, and down by 4 in the fourth. You then repeat these four bars ad infinitum, and immediately it starts to sound like a vaguely identifiable pop song you can’t quite put your finger on.

The rest of the composition comes from the melody — the lead guitar and singer, or the right hand on the piano — and the percussion as provided by a drummer. The melody simply starts with the same note you picked for the first chord in the previous paragraph but in the octave above, and then spins its tune around that. A musical ignoramus like me can create something passable after a while by messing about in a sequencer, but if that fails there’s even an open source database to mine. Finally the percussion is created by creating a repeating pattern of drum and other sounds in the same 4-bar unit as those chords. It’s only taken decades but finally I understand something about how the music I hear is assembled, and with a bit of absurdly easy work I can create a bit of generic sounding EDM that with the addition of some 1970s children’s TV samples might even have got me in the dance charts had I done it on my Amiga back in 1991. I’m a rock star!

The Real Problem With Not Learning Stuff

Of course, merely knowing a tiny bit about how a pop song is assembled does not make me a musical maestro, because while I may have learned something I am still almost entirely devoid of musical skill or talent. But the point I’m trying to make here is that by changing the way I learned it from the chalk-and-talk of my teacher to a hands-on breakdown of the music itself means I’ve learned far more about real music in a very short time than I ever did at school, and more to the point it’s stuck rather than drifted past me into the ether.

While my musical adventures are an entertaining diversion they served as a demonstration to me that I could have understood this stuff years ago if only the teaching style had matched my ability to learn. With the utmost respect to those who earn a living in music it’s clear that the subject was never going to form part of my career, but it’s certain that the same inadequate teaching style will have held me and my friends back in other subjects that could have been useful to us. It’s annoying at a personal level, but if teaching is failing so many people across our section of society then it also becomes an issue with a wider effect on society.

The worst part of all this is that we can see today’s kids like us showing up in hackerspaces with this educational damage pre-installed, and there’s nothing we can do to change an educational establishment that revolves only around stuffing in facts to be regurgitated on an exam paper. At least once they’re past that mandatory teenage purgatory we can help them learn some useful stuff.

Header image: Mænsard vokser, CC BY-SA 4.0.

62 thoughts on “Are Hackers Being Let Down In Education?

  1. My own musical non-education is very similar, but in addition I realised at about age 30 that other people could hear something in music that I could not: the beat, unless it is a thumping great obvious one. I could watch a musician tapping their foot, swaying etc to the music but I just didn’t experience it. Once I realised, I could learn to hear it, but I still have to concentrate on it where other people don’t seem to have to, and am easily thrown when the music changes or skips a beat. I’ve always put it down to just “not being musical”.

  2. Schooling methods have always been a problem because they need to teach to the average. It’s a scatter shot of information engineered to hit the most amount of targets within a specific time period. Because barring one-on-one tutoring that only the super wealthy can provide, no school has the time or budget to give multiple teaching styles within the alotted time. And hands-on people are generally outliers, meaning that most of the people and their compatriots that read this blog will have been missed.

    The other main issue is that schools don’t encourage problem solving or evaluating alternatives. They specifically encourage thinking and operating in one specific direction in everything. I did poorly in math class not because I got the answers wrong(the majority of the time, I had the correct answer), but specifically because I arrived at those answers through a different method than the teacher wanted me to, so I officially got the question wrong.

    1. Truth. And the stakes are even higher in this globalized world. The only thing I could quibble with it is use of the term “engineered”. I honestly think there is little long term thinking in educating educators.

      I am probably a good example of how students that don’t fit into the mold are poorly served. But there were a few teachers that helped me along the way – despite the onslaught of rote methods teaching that was the norm. My favorite was an 8th grade art teacher. I would never follow her instructions but for some reason she really liked what I did. A fellow student was complaining that I hadn’t followed directions for some project and she said in a very positive voice – “But I love to see what he comes up with, art doesn’t always follow the rules”. That has stuck with me – it allowed me to think outside the box with pride.

  3. This really ought be two posts, one on our educational system, the other on music.

    Yes indeed, “our” educational system is messed up — on both sides of the pond! This is a many faceted disaster. One aspect of this is tailoring education for the lowest common denominator. This leaves smart kids bored silly and looking for something interesting, somewhere, anywhere. There is some broken concept that all students are equally talented and given the same treatment will all rise to the same level. There were bright spots in my educational experience, but by and large I spent time in class eager to get home and do things in my “laboratory”.

    1. > There is some broken concept that all students are equally talented

      That’s an educational dogma coming from ideas of social determinism, which is the point where social sciences started back in the day, and how the educators are educated today because it’s no longer considered PC to classify and separate students according to their inherent strengths and weaknesses. The idea isn’t completely without merit, but people on the left end of the political spectrum tend to over-emphasize social determinism to the point of ignoring reality – with horrible results.

    2. At least in the British state school I attended not so long ago, the system didn’t seem to be designed for any sort of student. We were *all* desperately searching for something interesting, intelligent or not, because it’s a rare child that can engage with having the contents of a database spat at them. The main priority in designing the system seemed to have been to produce exams that would be easy/cheap to mark by flattening everything down to factoids and binary yes/no answers.

      It was a one-size-fits-all system that didn’t actually fit anybody. The non-intellectual kids were bored out of their minds because the headteacher, in line with the Minister for Education, decided that there is no value in anything that isn’t ‘intellectual’ and cut the funding (no Woodwork, no Design/Tech, nothing that could be considered ‘vocational’). The intellectual kids were bored out of their minds because the lessons were nothing but long strings of facts without thought or context.

      The idea of all kids being equal in ability was not present in my school: it was made abundantly clear that the thick kids in the lower sets would do worse than the higher sets whether they applied themselves or not. Every set below the highest two would sit exams where the marks were capped at “C”, and I remember being explicitly told by a teacher to not try too hard in one subject because “you can’t get above a C anyway”. Could be different elsewhere, of course.

  4. It’s interesting to consider what influenced your choices during your education. I was good at subjects I enjoyed out of school, but why those subjects. Was it the teacher? I don’t think so. There wasn’t much difference in the enjoyment level of a physics or chemistry lesson verses a history or art esson, but I never took anything away with me from hist/art lessons other than homework. Wheras with chem/phys I took home all kinds of plans for experiments and things to look up in the library. My school was a good UK 1970s school which was neither a joy nor a chore to attend. It was just something you did. As was university. And my career drew on almost nothing from what I learned through rote or glimmers of understanding. Two pieces of kit vied for my attention back the, a Vox AC30 and a Vax PDP11. The Vax won out and lives on as a replica on my shelf. Sorry, I digress. Thanks for the post though, Jenny.

  5. I do agree that conventional one-size-fits-all curriculum is problematic in many cases. A lot relies on rote memorization rather than understanding the underlying principles and relationships. An alternative approach may not be for everyone, but in my case in elementary school I genuinely felt I was mentally deficient in some way for being pretty bad at adding columns of numbers and don’t even get me started on division. I remember my mother in frustration at my poor scores in math but excellent ones in science had one night sat me down and went through the process of division very quickly. Then somehow I got the hang of it. It was a small epiphany to me — it wasn’t my mental deficiency, it was the ponderously slow rate at which things were being taught, and with a lack of ‘why’. Once past arithmetic mathematosis, I was newfoundedly good at algebra, geometry, and calculus.

    Similarly with things like SQL which I consider a life skill and am quite confident children can grasp it — at least from the standpoint of SELECT over existing datasets, if handwaving over database design itself.

    I do think those things can and should be taught at the elementary school level. Maybe not as a critical part of the curriculum, but at least as a means of priming the pump for those that can take it up. If you stimulate them, they will self-educate beyond the stock curriculum, and a habit of self-motivated research will be a boon that pays off one’s entire life.

    1. Exactly, that is the point here. Pump out mindless workers who are intelligent just enough to do their daily jobs, and nothing more. That is the solely goal of the education system across the whole Earth.

  6. In my school, funds for education were usually siphoned off to support the sports program.
    We never learned how to RIG weld, or how to use CAD software, or had extracurricular activities outside of drugs, but we had the state football championship 3 years in a row.
    Also, if you were on the team, you could abuse anyone as bad as you wanted and get away with it.
    Still kind of bitter over all of it.

  7. Why would they teach you an A minor scale as an example of an octave? The classic “all white keys” example is C to C, C major: C D E F G A B C.

    Your hacker friend told you some wrong stuff about music as well.

    1. You’re looking at the Meyers Briggs personality scale. This has been shown to have zero predictive value, in the sense that the personality types do not predict variance in various life measures.

      The Big-5 model has good selectivity and predicts about 30% of the variance in life measures (the rest of the variance due to intelligence and environment). There’s a theory currently being tested that the Big-5 measures plus fluid intelligence are a complete description of personality, in the sense that it covers everything and no other measure will give you more information.

      1. The big five also have some serious issues, such as pitching opposite pairs that are not opposite. (e.g. friendly/compassionate vs. critical/rational)

        People can be both in different contexts and intentionally.

  8. When I went to our local option Purdue Onionversity I could have taught half of the courses I had and they couldn’t teach me the other half. I dropped out when calculus came up in the 3rd year. It took half a century for me to learn some people can’t handle numbers but can manage complex relationships in electronics and physics.

    I was over 30 when I finally understood that those Seven notes wouldn’t fit into a split even-odd left right symmetrical harp. The “ninth wonder of the world” was a self-played a violin and a piano which was symmetrical to stay in tune better than any normal scale instrument. Weights on the violin strings kept tune there also. It’d stay in tune as a coin operated jukebox in bars.

    Only then did I realize why I gave up at standard notation. It tries to be a graphic system with a prime number which doesn’t fit into any scheme. We call it 12 tone music but the octave note isn’t counted this time. No thirteenove, no such word. I’ve never heard 7 tone as a term either, just diatonic which refers to the 2 pairs of intervals in a major scale, which counts redundantly again.. This led to the addition of first b-flat and then f-sharp to modulate without being modal.

    Play with harmonics on a single string or an organ pipe flute and it will be apparent where and why notes are what they are. Only in the west in the past do you stop at the 8th harmonic, and the 7th is the blues note. Prof at Purdue years ago said the 7th, “that’s a wild card we’ll throw that one out”. Nope that’s the blues barbershop bluegrass and most of Africa. Minor scale richer, major less so. Six or seven modes not just minor and major, and that’s just in the west. Arabic and Turkish scales get it going thicker than just those 2 scales.

    1. It is all about the physics. Some things we want aesthetically just can’t be done. The circle of fifths can not exactly match the octave and thus there are the various temperings of the scale to get close. Personally I think the reason a great choral can sound so good is because singers can “temper on the fly” so that everything sounds perfect.

    2. “I’ve never heard 7 tone as a term either”
      “Heptatonic” is a very common term. You’re lifting your skirt and showing your seat. So much wrong stuff….

  9. This piece made me wonder. Most hackerspaces I know focus on computers and electronics on one side and woodworking and making on the other side. Some also do a little work on chemistry or biochemistry. But are any hackerspaces equipped for working with music? Band practice spaces can offer you a room and equipment, but no theory, and might not have (or appreciate) the hacker approach. Judging by the hackaday articles there are quite a few hackers that play with music and/or musical instruments. So is this a new frontier? Let’s boldly go then!

    1. Well, not just “the autistic” (in some cases, formerly known as “Asperger’s Syndrome”, but whatever). It also fails for various learning “disabilities”. To be clear, some really are disabilities and some are just plain old differences. And there are some unusual ones, not just the blanket “dyslexia”, but also things like “hears fine but can’t tell where sounds are coming from” and all sorts of really unusual stuff. Dyslexic AF in their native language, reads a second language just fine. All kinds of wild stuff. I’ve got a pretty odd one myself, didn’t know it until I was a senior in high school, and we can debate if it should be classified LD or just some odd little neuro thing. Either that or I had a stroke when I was a kid, which seems awfully far fetched.

      And then there are the folks who just “do stuff differently”. I had a student in a class that just couldn’t “get” calculus and seemed to barely understand algebra at all. Smart one, really good programmer. On a hunch I showed how Recursive Descent interpreters work and how computer algebra systems use them. On seeing how computer algebra systems worked, algebra and elementary calculus was obvious. Which, coincidentally, is why I didn’t understand basic algebra until my first year in college. Yes, I could “do” it, but I was essentially doing macro substitutions instead of extracting any semantics from the problem. No relation to my little neuro thing, as far as I can imagine.

      Yes, I know (some of) the limits of recursive descent approaches in computer-assisted mathematics, and I know modern systems don’t really use this at all for integration, for instance. The techniques are probably toxic for math majors, but they’re good enough for almost all of “engineering student math”. Just memorize the transcendentals and the differential equations of degree 2 like everyone else and get on with it. :-) OK, computer science students really need to understand discrete math in a very intimate way, and that’s a different beast entirely, but around here it’s taken in the junior year after enough CS classes that it’s one of those things that’s obvious in retrospect.

      Some mathematician is going to punish me for saying this, but honestly if a qualitative understanding of calculus and one page out of the CRC integral table isn’t good enough, you’re probably going to lose your engineering license anyway.

    1. I was thiinking of a Feynman Story as I was reading Jenny’s article. He was in Brazil I think, talking to some students. They could recite Snells law (angle of incidence equals ….) but had not idea how to relate it to the world around them or explain anything using it. I think they looked out the window at a sunset and Feynman discussed how physics could explain the spectacle before their eyes. He was frustrated.

  10. “Never fit in” – I remember a card from a woman when I was an undergrad at U.C. Davis – her note: You certainly march to a cifferent drummer!”
    My learning style: Listen with all possible concentration, don’t take notes (interferes with listening and it’s well established that humans don’t “multi-task” cognitively). Finally, if I could put my hands on any aspect, that was a win – I loved every lab I ever took, be it Organic Chem, Biochem, numerous Micro classes, and when in Nursing school, disection was deeply interesting.
    Being the odd one out is still a challenge, but I’ve found that joining other groups of makers and tech-oriented people has worked OK.

  11. Now you know why I home educate my tribe of kids, with Hacker style STEM based education too, yeah they also do art but that is totally informal and undisciplined, just background activity to everything else that they do, as it should be if you want to foster pure unconstrained creativity and expression. I have been subject to so much abuse from people, near and far, about the choices my wife and I made as to how to let our children grow so as to maximise their potential but recent times have proven us right. My kids are happy and they keep doing stuff that just blows us away, they are years ahead of where we were at the same age.

    1. A considerable part of group education is socialization. How to interact with people of all sorts. Given a choice of two comparably smart people where one went to public school and one was home-schooled, I’d hire the one who went to public school. Being jobless does not maximize potential. Being self employed is often a very rough road. Being smart is only a part of the equation.

      1. Two of my colleagues were home schooled, and they are almost indistinguishably sociable compared to my other colleagues. However, their love of education and self-directed practice is significantly stronger than anyone else I’ve ever met. Not to generalise, but I don’t think we should weigh home schooling any differently to regular schooling if we’re assessing someone’s skill and talent in a technical or artistic field.

        Interacting and working with adults is vastly different to operating in a school-yard, and I’d have to assume that they would be doing that far more often from a young age when home-schooling than when attending a school.

      2. To be completely fair, Homeschooling != unsocialized.
        It definitely wasn’t for me.
        I’m in college atm, and most people I know have no idea I was homeschooled untill I mention it months after we’ve known each other.

        Is it possible to homeschool wrong? Yes.
        Is it possible to public school wrong? Yes.

        I’d personaly rather have the responsibility of doing it right fall on myself, rather than on the local pub school, so chances are my (future) kids will be homeschooled also.

      3. But going to school is not the only way to get social learning time. There are many ways to do that, and with enough children at home some of that will happen there too.

        There really shouldn’t be any hire based on schooling choice, though like everything humans do to each other bias creeps in, or the conscious decision to try and not look biased does – what should matter is the qualifications and interview.

        I would also suggest that being home schooled by parents with enough (which wouldn’t need to be mega-rich – just not broke, barely able to live) money means you are more likely to have better qualifications – in public schools you might learn about x, home schooling you may well have built/done/tested x or some scale representation etc – so you have a body of work that proves you really understand some things rather than just know what the book says and how the exam question will be worded.

      4. I always find it amusing when this argument is brought against homeschooling. Mainly since it’s really the only argument that’s ever brought up. The people who bring this up as an argument always fail to remember that there are unsocialized people in homeschooling and there are unsocialized people in public schools and unsocialized people in private schools. You didn’t mention public or private, you said “group education”, but many homeschoolers are part of large families or homeschooling co-ops, which for many people would qualify as “group education.”

        My experience has been that most homeschooled kids know how to interact with adults more thoughtfully and respectfully than the majority (not all, but the majority) of public schooled kids. YMMV.

        Bob, if you prefer to hire only kids that meet your definition of “group educated”, please hire only them. They need a chance as many employers are finding that a lot of them are not prepared for jobs so I appreciate your willingness to take the time to bring some (not all) of those kids up to speed. I also know of employers that will only hire homeschooled kids because of their willingness to learn and their work ethic, so your efforts have been offset by other employers for years.

        [] [], keep up the good work, your kids will thank you when they start college, or their career. I know this from experience.

  12. Actually Jenny, you’re right as usual. Over here the school systems are still trying to catch up from the shock of when Sputnik happened, and that was well over fifty years ago. Never mind supporting our current efforts it seems.

  13. Jenny you are perhaps my all time favorite Hackaday writer. Today however I think you rose to hero status.

    You describe exactly my experience with CAD software. I first got my 3D printer and a “brick” was my first item designed via CAD test case. Then I wanted to put a hole in the brick. No, I couldn’t just specify the center location and diameter, some obscure trickery was required. Then I discovered OpenSCAD and I shouted for joy.

    I still do intend to learn to play the banjo however.

  14. just 2 things that didnt get a mention so far. as i understand it, each note (both the white and black keys) are frequencies (the twelfth root of two) apart, so after stepping 12 notes you are exactly one octave up or down and that is exactly half or double the frequency, (dont know how they arrived at the black and white notes though, maybe artistic rather than logical). secondly i learned from “James May’s Man Lab” about tuning a guitar to an “open fifth” which makes it easy for a non musical person to play a few chords as it doesnt require the complex finger patterns. google, tune guitar man lab.

    1. Several days late here, but…

      As you go up the scale, each of the 12 notes of an octave go up in frequency as (compared to the first note) a factor of 2 ^ (1/12), 2 ^ (2/12), 2 ^ (3/12) … 2 ^ (12/12). On a “just intonation” tuned instrument, anyway. On modern, temperament tunings, they actually use a sort-of close approximation. The advantage is having an instrument that can play in any key. The disadvantage is that most notes sound a bit “off”, especially in a space big enough to have echos.

      And yes, open tunings are fun. You can get a good and nasty blues sound that way. :-)

  15. I felt deficient because I need to learn how things work in practice rather than accepting things by rote. My high school (ages 11 to 15) was an early adopter of “Nuffield” science, which is heavy on “discovery learning” rather than predominantly theory. It’s interesting to imagine how many students learned Nuffield science to qualification who might have rejected science altogether without the hands-on learning.

  16. i have spent most of my life trying to understand music to some degree. and i’m not sure i actually agree with the critiques here of what sounds like a pretty standard introductory classical music education. what has made the biggest difference for me has simply been *doing*. absorbing enough technical trivia to be able to read sheet music and perform it myself on the piano has made the music theory i learned come to life. that is, introductory formal education enabled playing, which then enabled an understanding of the more advanced formal education. i understood the symbolic manipulation of music theory ‘well enough’, i suppose, but it didn’t *mean anything* to me until i’d learned a few bach or chopin pieces.

    but i’ve approached it from a lot of different angles over the years. for example i recently (a couple years ago now) had kind of a breakthrough in how i think about things from learning basic rhythm guitar technique, which is very different from how i thought about things on the piano. i think the most important thing, and maybe this was missing from your formal education, is to find an *enjoyable* practice. i was lucky to learn sheet music in a middle school band program that progressed very rapidly to actually playing the instrument, and of course the director always struggled to find works that would be easy enough for us but would also simply be fun to play. you won’t get a ton of insight from playing a bach piece if you aren’t able to enjoy playing it.

    what i’m trying to say is that for most people music is a very hard thing to break into and a really thorough exploration will require going through a bunch of phases where the progress isn’t really apparent or fun. you will be exposed to material that is a turn off, you will struggle to self-educate, and you will struggle to find other instructors or inspirations that remedy these weaknesses. that’s how it is, and that isn’t a failure of any of the parts of this whole.

    but anyways i learned this core fact of music theory that i think demystifies the scale. the core lemma from which most music theory derives is this one formula: 1.5^12 =~ 2^7. to move up one octave, you multiply the frequency by 2 (so 2^7 would be seven octaves up). to move up a “perfect fifth” (which is actually 7 notes up), you multiply the frequency by 2^(7/12) =~ 1.5. and then one other detail, if you sound a note on most instruments then there is a rich series of harmonic overtones and the strongest one is at the octave, is at 2x the base tone. so basically, at the perfect fifth, the overtones overlap with the overtones of an octave. that’s why the perfect fifth is special (it’s the third note in most simple chords), and it’s a big part of why you can divide the octave into 12 tones. there are other relationships that are basically the same in form, for example a “major third” is an interval of 4 notes, or 2^(4/12) =~ 1.25 times the frequency of the original note.

    the fact that all the numbers above are approximate is also why people used to use tempered scales more often (where in some keys, the relationships were exact, at the cost of in other keys the relationships were wildly out of balance).

    if you start from nothing, i doubt any of that made any sense, but if you’ve (like me) been exposed to a bunch of theory before without really gaining much understanding, then something like that is real eye-opening. that’s an example of what i mean, there’s simply no substitute from going through the exercises that make you feel stupid or bored in music, because they prepare you for the future moment where it ‘just clicks’. there doesn’t seem to be a good way to get it to click on the first telling.

    1. Fostering creativity and curiosity in the children means sometimes just letting them play (and I would say that still applies to adults – experimentation, curiosity and having fun mean you want to learn new stuff on your own). With an instrument that can lead to them learning, and learning far more than if you push them into lessons – they play around figure out simple chords, melodies, even repeat whole songs they know by ear – stuff they like the sound of and will then want to play that song they like and can’t quite figure out, or write their tune down like the ones you have played from etc.

      You don’t actually need any formal musical learning to play music, where that learning comes in is being able to collaborate and discuss music with others. But its not even needed there – show don’t tell still works. Also much of music as its taught is kind of bollocks anyway – limited in the permitted sounds, timings and what is ‘allowed’ by the system – things like a theremin, or much ‘World’ music can’t really be properly represented and won’t be ‘correct’ to the rules of western music. Might sound awful in your opinion (on some ‘World’ music I’d even agree, and I have pretty broad tastes – its just so odd and I don’t have the right cultural context that even after a few listens it just sounds wrong – can’t find the logic and order, the ‘story’ in the ‘noise’) but it is still music…

      How things are taught can matter – and matter hugely to your ability to understand or remember it! Not everyone thinks or learns in the same fashion, and some folks have a great memory while others don’t – and even that isn’t universal – I have a great memory for how stuff works, all the axiom, constants and formula contents stick, but what they are called almost never does – so most of the marks I dropped in exams were questions along the lines of “Use x on y” with no context to know what the relationship between them is supposed to be and thus what they actually want. Where one of the guys I went to school with was pretty smart, but mostly just remembered everything – so I’d probably figure out how to solve the problem faster, but wouldn’t be able to write down the useful lines of ‘by x leads to’ to really show the working neatly and in detail as easily.

      Same thing with languages for me, new vocabulary is a challenge, now at least, but the grammar and ‘rules’ of the other languages stick better – though learning new vocabulary isn’t actually impossible, its very much how it was taught on that one, it just doesn’t engage with my brain correctly to sink in long term for me (or get repeated depressingly often to get stuck anyway, I’m sure that would work eventually…).

  17. Re: music – I get Jenny’s idea of using music as an example of how she didn’t get a grasp of it for the lack of theory at school – and I (floating point round errors included) 101% agree on that.
    Her summary of music theory is lacking, necessarily so, as she still isn’t “into it”. If Jenny wanted to dig a bit deeper and, maybe, find some “understanding in the beauty of the craft”, I highly recommend Robert Greenberg’s courses, especially the older “big ones” about “how music evolved”. He starts before the beginnings and gives more than a bird’s eye perspective on why we “use” musical theory (today) we do. He also steps into “non-standard” systems and explains why they exist and what they bring into the “mix” (pun intended).

    Re: education – I agree with those who say that education caters for the masses. That said, it doesn’t capture the whole picture. UK teachers just last year were astonished to learn that home schooling was GOOD for the “bad” pupils (who had problems understanding things and now were allowed to watch lessons over and over again and actually benefitg from it) and “good” pupils (who could skim over a topic and be done with it), but that the “masses” fell behind, as they now missed their “personal note” and suddenly didn’t fit in any longer. So, the system is built “for the masses”, which is never the right approach for anything except for Amazon. Progress needs exceptions, you cannot expect solutions to the world’s problems from “the masses”. You need someone who is “bad” at most topics but excels at her SPECIFIC thing – or someone who is exceptionally clever or … you get the picture. The educational system (in Western Europe) is broken, at best, and has been for many decades.

    Re: “understanding things” instead of learning to accept them – this, I think, is more a matter of family context than of school context. I do believe that schools (in Western Europe) play a vital role in social education for their most part, but it’s the family context that lays grounds for how children “learn how to learn”. If your parents are musically interested – good for you. If your parents accept your destructive investigation hobby: What better could you have. If your parents are “the masses” who are being educated by TV shows … you’re lost and the best you can hope for is to one day be allowed to vote for a new president-with-orange-guinea-pig-on-head.

    1. I make no claims about the comprehensiveness of my new-found grasp of music, as you say it’s an example rather than a primer.

      Home schooling, in my experience it’s more often something done for the wrong reasons: “little Tarquin is too special to go to a normal school”, or “I don’t like (my slightly warped perception of the ‘politics’ of) the school so I’m going to keep the kid at home and indoctrinate them with my (somewhat nutty) worldview”. Sadly too often it ends up with isolated and messed up kids.

      1. No disagreement on home schooling “in general”. I was merely referring to the (very special) experiences gathered from “mass-home-schooling-with-some-top-down-control-approach”, not the classic (probably more US-style) “home schooling for special kids”.
        I think – with many years of “parents-work” in the school sector – that the education system here in “the old world” hasn’t evolved enough to cope with modern technology (and I am NOT a fan of “give that kid a tablet and be free”) AND changes in society AND changes in science AND changes in “globalness”.

        And, because, maybe I didn’t make that clear enough, I fully agree with your overall statement that some of us haven’t had the best experiences in school or university. I could write more than a book about that (and maybe I will) but … it’s a self-serving system. Here in Germany, people still, even after 40 years that I witnessed it knowingly, say that “if you fail at university, you can always switch to teaching”. Which, in this country, refers to school-teachers being academics to begin with (read: don’t have no real life experience and never will have, since they stay in their bubbles, only talking with and to other academic teachers). The system is rotten fundamentally.

      2. Jenny,
        You said:
        “Sadly too often it ends up with isolated and messed up kids.”

        Given how many people are homeschooled vs how many are in public education, I think your statement much more often applies to public schooled kids. Especially when public schooled kids feel isolated due to poor teaching, thinking they may be the only ones who don’t understand the topic or the course. With homeschooling, there is a much higher chance that the child can get one-on-one time with the instructor to understand things better. Often times in American public schools the teachers just don’t have the time, whether they are a great teacher or not, don’t take my word on this, ask a teacher.

  18. So much positive feedback :( Anecdotes is not data!

    So one more anecdote: I went to a public school where we were filtered into four grades almost from the get go. Some classes I got, some teachers were better than others – for *me* -, nothing was ever tailored specifically to me but I made the effort to absorb and assimilate it anyway. And though I don’t use s parameters in my day job, I am still glad I was taught them.

    And if my parents had tried to home-school me they would have failed miserably.

    1. Former teacher here.

      I am really glad to hear that you’re “still glad you were taught them!” Yep, some of the things you learn won’t be applicable to your day job, and that’s feature, not a bug. Have we lost the ideal of a “rounded” education? Jaded Hobo will be able to meet new people and have interesting conversations with them, thanks in part to having had an education that was more than just the things that he/she absolutely NEEDED to know.

      The other really pleasing comment was “Some classes I got, some teachers were better than others – for *me* -, nothing was ever tailored specifically to me but I made the effort to absorb and assimilate it anyway.” Sure, the quickest way to learn a specific concept or skill would be to have a private tutor, but being able to learn as a group, or from a teacher who doesn’t “get” how you learn, is a skill all in itself. When people graduate, they will also have to learn in groups, or from ineffectual educators. And if you want to be REALLY good at something, you might still need private lessons. We don’t expect athletes to get to the Olympics based on what they do in P.E. at school, so why should we expect students to be advanced academics after a few years of generic education? The P.E lessons were still valuable, even if they didn’t produce Olympic athletes. The maths classes were still useful, even if they didn’t produce Fields medal winners.

      I see some rants elsewhere on this thread about “school just being a bunch of facts.” Two things leap out at me here. Some facts are GOOD to know. A rough idea of geography and history will help prevent you looking like an idiot. There are so many adults who don’t know that the sun rises in the east, or can’t find China on a map, or identify the places where their military is at war! If these adults hadn’t been too special to learn some “boring facts” at school, I propose that the world would be a better place. Oh and if these people are so smart, maybe they should be taking these “facts” and looking for patterns in what they are learning.

      I agree 100% that not all teachers are great. But I also submit the old cliche that you get out of education, what you put into education. Even the dumbest teacher will have _something_ to contribute. Just because the teacher has bad breath, or suck at teaching calculus, or have different political beliefs, maybe they will be the one to show you the difference between a major and a minor key in music!

      Homeschooling has its ups and downs, just like “normal” schooling. Oh and remember that school classes are what? 30 hours a week? 35? You don’t need to pull your kid out of their school, just use a bit of the other 130+ hours to learn things with them! Play some music, build a model aeroplane, get a cheap microscope and look at pond water… or if they need arithmetic practice, why not teach them to play blackjack or count cards?

      For what it’s worth, I got pretty decent reviews from both my students and my supervisors when I was a teacher… but I will leave the rant about how we measure teacher performance for another time :-)

      Thanks for the thought provoking article Jenny, and Jaded Hobo et al for the comments. FWIW, I still don’t know the difference between major and minor keys in music either. It HAS to be more scientific than “happy” and “sad” sounds. Was I let down by my music teacher? Or did I just not ask the right questions? I bet if I’d asked if they knew a good book explaining major vs. minor key, they could have made some suggestions.

  19. “In short, it was an exam factory where stuffing facts into your brain was the order of the day rather than necessarily being expected to understand those facts.”

    THIS! This is what is utterly wrong with our (USA) education system! I had the same experience in math classes from 2nd grade and beyond; they would try to teach the short cuts, but NOT HOW THEY GOT THERE! They would explain how something works, BUT NOT WHY IT WORKED! This last one, in particular, infuriated me.

    It wasn’t until well after I graduated high school and watched some YouTube videos with great explanations that I truly started to understand the things that baffled me in math class. Not that I’ll ever use them…

    To this day, the only use I ever found for Algebra II was helping someone else with their Algebra II homework! I recently asked a math teacher what practical use the quadratic formula (the focus of that class) had, and she replied “projectile motion”.

    Everything clicked into place: THAT was the primary use of computers that were invented back in WWII (calculating artillery trajectory tables which were done by hand in WWI)! –

  20. Sorry, but I think you missed the point, and being insulting is not called for.
    This article is about education methods. The methods often used in formal education do not work for many people.

    As an aside, B flat is certinally a note. Whether it is a note in the octave depends on what key is being used.

  21. Music is generally taught for the purpose of human regurgitation of a score written by somebody else, rather than understanding the mechanics so that you can create your own music.
    As such, it is taught in a way that is incredibly boring.
    The concepts are really surprisingly simple.
    It’s called “playing music”, not “working music”.
    Folks should stop trying to turn it into work.

  22. The education system all around the world is fundamentally flawed. It is an outdated system created way back in the time of the industrial revolution, when expertise and quality work were replaced with number-focused mass production. Master craftsmen and tradesmen were no longer needed, instead there was a sudden demand for relatively low-skilled and easily trainable workers. Needless to say, the world wars did not improve this situation.

    Ever since then, the main goal of the education system is to train mindless workers who are intelligent enough to do their designated job properly, but not too intelligent, so they don’t have individual thoughts. Knowledge is power, and the people in power do not want rivals.

    Take a look at what you learn in school: individual work, following orders, repeating pre-defined methods, memorizing facts and numbers, etc.
    What you don’t learn: teamwork, critical thinking, creative problem solving, understanding problems, etc.
    Shut up, listen, and do your job.

    It is sad and infuriating. But it’s not going to change, because those who could change it do not want to. They want it just like this.
    All in all, you’re just another brick in the wall.

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