One of the things you figure out is that some kids aren't interested. And if your kid isn't interested in thinking about prime numbers, you're going to be hard pressed to change that. Conversely they will have interests that you don't share, and it's going to be harder for you to participate meaningfully in that beyond being generally supportive. They are individuals that way.
I ask him to tell me about what he is learning, and he patiently tries to explain it to me, but I just nod along because I have no idea what he's talking about.
Most everything beyond is attaching labels to the frequencies and combos. Just as we have names for frequencies of light (red, yellow, blue) and patterns (gradient, checkerboard) there are names for frequencies of sound (A, C#, E) and their combinations (major, minor). There are also more esoteric terms (chiaroscuro in painting, neapolitan flat 9 in music) for people who've spent so much time on a subject that the basics have become boring.
Oh, and there's also divisions of and patterns for time in music theory. E.g., "hold this note for twice as many milliseconds as the previous one".
There have been some good resources here on HN: https://hn.algolia.com/?query=music%20theory&sort=byPopulari...
@jimbokun: It might be easier for your son to express what he's learning if you can catch while he's got e.g., a piano or guitar at hand. Humans have a hard time generating compound musical waveforms using just their vocal folds (though it can be done to a limited extent as in Mongolian throat singing). Explaining it while playing it will probably also help cement the concepts in his understanding ;) .
There are 12 unique notes in an Octave (yes, octave means 8; ignore this for now). On the 13th note, the octave repeats itself (counting is 1-indexed). But of these 12 notes, only specific subsets are combined into specific scales.
The most popular scale is the Major Scale which follows the pattern "Tonic Major_2nd Major_3rd Perfect_4th Perfect_5th Major_6th Major_7th" (there exist other notations). The Major Scale imparts a generically-happy mood. But there's other scales, including: the Chromatic Scale; the Major Scale; 3 varieties of Minor Scales; 7 varieties of Diatonic Modes (including Major and Natural Minor); the Pentatonic Scales; etc. E.g. Smoke on the Water, Sunshine of your Love, and Fight for your Right (to Party) all sound similar because they use the Blues Scale.
Once you familiarize yourself with the intervals, scales, and their various notations (which is its own feat), you can jump into the meat & potatoes of Music Theory. Which mostly consists of analyzing Chord Progressions and Key Signatures in order to find commonalities in mood. Chord Progressions and Key Signatures determine a song's general mood. It's too complicated for me to summarize quickly. But it's where all the interesting stuff happens.
N.B. I've deliberately omitted various details for the sake of brevity. E.g. I could have mentioned Time Signatures, Rhythms, Tempo, Dynamics, etc.
Is there a good YouTube video introducing some of these concepts using popular songs?
Another thing to keep in mind is that musical patterns accrete into genres. And there's a wide variety of genres. So it's difficult for any single video to cover everything in detail. I think it's more common for videos to cover the patterns of a particular genre. E.g. if you're interested in Blues, consider searching for videos about Blues.
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https://www.youtube.com/watch?v=xm4LO22-cyY I remember the above Vox video highlights a unique chord which sounds "melty" and is often used in holiday music. The chord is known as a "minor_7th, diminished_5th" aka "m7d5".
https://www.youtube.com/watch?v=5pidokakU4I This video is about the infamous "4-chord pop progression". It's ubiquitous on the radio. Elitists and connoisseurs tend to look down on it for appealing to casuals. The progression is "I V vi IV" (capital denotes major chords, lowercase denotes minor chords).
https://www.youtube.com/watch?v=kfjXp4KTTY8 When I think of the "12-Bar Blues (Chord Progression)", I think of Stevie Ray Vaughn's "Pride and Joy". But there's tons of educational videos on this. It's very popular in not only Blues, but Rock & Roll. It's "I I I I; IV IV I I; V IV I I". But things get interesting here because musicians often substitue "jazzy" chords like Dominant_7th's (aka V^7). For bonus points, look up "tritone" (N.B. Rock is truly the devil's music).
https://www.youtube.com/watch?v=dISEg1ydQoM I'm not actually sure what song I'm thinking of, but there's a particular trope often used in Hollywood films to denote a bullfight. It's based off the Phrygian Mode, which tends to sound very "spanish-y". In lieu, I've linked the the first bullfight track I found.
https://www.youtube.com/watch?v=X4fa44_sq2E A genre I'm particularly fond of is House. Which is often characterized by its "Four on the Floor" drum beat. It's very simple, just continuous quarternotes of kicks. The rhythm is sometimes denoted "1 2 3 4" (where the structure of a single bar is "1 e & a 2 e & a 3 e & a 4 e & a"). The above video is Daft Punk's "Superheros".
And then there's Jazz. Which is hard to explain, because it's the genre where anything goes. And besides jazz, there's lots of other techniques and obscure genres that I can't possibly cover in a single post.
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In any case, I'd suggest looking up a particular genre you like and studying it. If you're a musician, learn scales. 90% of pop music these days uses either Major or Natural Minor. But you can really expand your horizons by learning other scales. It's boring, but it builds a strong foundation. Like how a basketball player will run laps rather than shoot freethrows all day.
Guess what... A perfect fifth is a 3:2 ratio/interval of frequencies (+/- a small allowance for the historical/mechanical constraints that lead to well/equal tempering unless we're talking modern micro-tonalism in which case no adjustments are necessary). The inverse, 2:3, is a perfect fourth.
The example frequencies I gave correspond to concert-A, then E and D. I took a very simple/short path from intervals to harmonic function/progression to try to give a taste of the meat and potatoes before providing a link to additional sources.
I avoided music theory terms because that would've been a circular definition for any readers who had no understanding of even the basics.
In light of your post, I should've added a sentence or two about mood (major = happy, diminished = tense/scary) and compared that to how you can make a 'warm' picture using reds, oranges and yellows or a sombre picture with darker colors, etc.
See my other comment.
Similarly, it seems like studying the frequencies and their relationships illuminates at least a portion of what music theory covers.
It is mostly a descriptive theory in that it studies musical patterns (rhythm, melody, harmony, intervals, scales, modes, chords and chord progressions) but it can also be prescriptive (for e.g. - don't use certain note intervals in a guitar solo if you are using certain chords in your song)
None of this has anything to do with Physics. Music Theory is completely abstracted from the physical world.
Already learned some things, thanks!
If you can provide a better overview or point out how it's anything more than a bunch of terms/shorthand for sonic patterns, I'd love to be informed.
It might be easier for your son to express what he's learning if you can catch him while he's got e.g., a piano or guitar at hand. Humans have a hard time generating compound musical waveforms using just their bodies/vocal-folds (though it can be done to a limited extent as in Mongolian throat singing). Having him play the sounds as he explains them will probably also help cement the concepts in his own understanding ;) .
You can't start telling your child about maths if they're busy doing something else. All you can do is wait for a moment when their curiosity spots something and try to feed that.
Even when you catch their interest it's easy to break it if you can't explain it, so los of kudos to Brent for navigating it perfectly.
That is the most depressing thing I've read in a good while.
If it feels better though, as the youngest of three children, I find I was allowed to wander a bit more, and that has actually proved useful.
I grew up in a family with 7 kids and my youngest sibling is just 12 years old. I remember when my younger set of siblings were born, I was thinking "I'm going to teach them EVERYTHING I've learned at a young age, and they will be way ahead of their peers." I failed to grasp just how much of their personality is ingrained in them from their DNA and that they might not have all the same interests as me. It was a great learning experience though -- when I do have kids, I'm not going to try and shove my interests down their throat. I'm going to pay attention to what they are drawn to and give them as many resources as I can so they can pursue that interest as much as they desire.
Is this really true? I hope not!
Interests can be encouraged because there's some flexibility in someone's natural tendencies. It's the old "nature vs nurture" discussion, about which one dominates the other.
Perhaps the above poster's sibling looked for other interests because the poster had already 'taken' whatever interests they were sharing. But perhaps not - it's hard (impossible?) to know.
If I had a strict clock-in/clock-out job, and only had limited time to run errands, I'd have a lot less patience for waiting for my kid to do stuff or answering her questions.
I consider myself very lucky that I have that privilege and can pass that on to my kids.
Also the 33 point on the post tell me at least 33 more people found it interesting than did not.
I'm sure we can both agree, though, that the gold standard for statistical significance is 30 Helens. 33 HN users is nowhere close to 30 Helens.
It's great. But I think we missed the balance a little - there are so many life experiences that are out of reach that we parents experienced when we were kids. Yes being tight with our kids is awesome - but when they get old enough to spread their wings a little, and when they're inquisitive about new things, then supporting that is exceedingly difficult when you're of low means.
School skiing trip? Not a chance, way out of our price bracket. Holiday abroad? Same, the interest is there, they're keen to learn geography/languages/culture. Piano lessons? Same, we've got a keyboard, one child is really keen and show some ability but we don't have means to support him in that and let him find fulfilment through that creativity.
But I do get to talk Fibonacci series; build fires in the woods; teach them about how aliens with 0, 4, 16 fingers count; but buy an up to date globe, or take them for a train ride, or go on a boat, or have a pet, or visit a mountain, ...
My problem is not time so much, nor fostering inquisition, but resources to develop the questioning in to solid foundations. Our kids are not the free-spirits of knowledge-hunger we anticipated because we instead have to follow economics.
A good friend of mine was the grandson of a couple that ran a school for gifted children. When they retired, there was a video produced about their careers and, at one point, they were both asked what they liked best about their jobs. His grandfather answered, "Getting to speak to the children every day." His grandmother answered, "Getting to listen to the children every day. I always liked her answer better than his.
Because if it's the former, I'm impressed you have even one second to be on HN!
Which sounds totally plausible and correct, 'cept it'll take you awhile to get up to that sort of economy of scale :P
Did you know older siblings don't even get paid for the work they do?
The transition from zero to one is of course world-changing. But at one child, 100% of the connections in the sociogram connect to a given parent: zero economy of scale.
At two children they have each other, but that is only 1/3 of the children's connections when one parent is present.
At three, we're up to 50% of the connections that are child-to-child. At this point the sociogram is rich enough to become interesting.
Four => 60%. Eight => 77.8%.
But the family is poor enough to become boring!
(I can't resist a good pun.)
Anyway, kids aren't raised in isolation with their parents. Our two year old tot already has two kids that I would consider her friends; she mentions them when she's home, and she prefers spending time with them to spending time with other kids.
Yours is not the only worldview.
And with birth rates plunging worldwide, many now trending below sustainable levels, who will provide you with healthcare and other services in old age?
Maybe we need to look at our priorities.
I worry that if you try to dumb down things for kids, they might become interested in dumb things. :)
Also, as the OP mentions, it can be a fun "pedagogical challenge" to try to explain free theorems or turing completeness or MySQL sharding to a young child. And you may find a clever way to describe it, that they can easily understand, which is satisfying for both of you.
Do challenge your kids intellectually beyond their years and you might be pleasantly surprised. My daughter heads to CERN in two weeks to study anti-matter, and I have no doubt that our brief intro to algebra at a Home Depot has a small role to play in that journey. Maybe Star Trek did too :)
I got stuck thinking in integers, and quite quickly left the exercise as an oversight in writing the post (since X + y = even, X - y = odd is impossible for integers)
3 seconds into the first coffee of the day the realisation of my stupidity hit me in the face.
I feel like I’m missing something entirely, though...
x and y are more commmonly used to represent real numbers.
She spent her teens trying to get away from dad, why spend her working life there? :)
People don't give children enough credit for what they can really understand.
I remember distinctly teaching my oldest daughter how to do a basic cipher - like direct substitution and she got it immediately. I also taught my son how to do pin bumping and pin counting/picking on locks with my lockpick set. I even bought him a transparent set of master locks to practice on and he would sit for an hour at the age of 4 picking those locks. The obvious downside now is that he knows how to get into everything!
Very cool to watch what are basic principals being applied at the very basic level.
Then yesterday she asked: "Why couldn't you call gramps when we were on the plane?" I told her that the mobile phone wasn't close enough to the receivers on the ground.
It amazed me that obviously some facts had been stewing for a week in that tiny head. And out comes another question.
One of my biggest failings as a parent has been to assume that my children will learn things somehow without me teaching it to them. If anybody learned 1/3 of what my mother taught them in detail, they learned a lot.
I have not read this, but it's from the same person who helped create "anchor modeling" and I find that quite interesting.
On a serious note, you may be right in that it's a simple call for attention, but at least with my kids those are the opportunities for the best instruction, because the kid is usually bored, curious, and wants attention. If you give said attention, and answer questions in a way that they can think through and reason about, they will grok stuff you never expected.
And much more likely: who's to say that the overstimulated little monster that asked 15 questions in 5 minutes doesn't need a little dose of adult life to encourage some self-play?
Explaining things to them and seeing the dawn of understanding in their eyes in easily my greatest joy in life. As a parent, I basically get to relive this xkcd[0], over and over, every day.
We take it to an extreme - we unschool[1]. We do our best to treat our daughters as any other member of the family, expecting to act as adults to the extent that they're able to do so. My nine-year-old spends much of her days right now playing Roblox and Star Stable, but even that is punctuated by her coming to us with random questions about things she's interested in. If I'm not head-down on a project I take the time to explain as best I can. If I'm otherwise occupied I always at least take the time to say "Go search for <insert keywords>" and follow up with once I'm free.
The results have, so far, been incredible. Our oldest was a late reader by the standards of the testing done in government schools, but once she ran into something she wanted to do that could only be accomplished by reading, she achieved fluency more quickly than I would have ever expected. For what it's worth, that "something" was an online RPG where she had to do quests to progress. In order to do that, she had to be able to read the quest text.
These days she's engrossed in the "Pegasus" series by Kate O'Hearn, and devouring them at a rate of ~1k pages per week. She'll have finished the series by the end of this week and I'm hoping she'll pick up Asimov's "Norby" series next. If not, she'll find something else that interests her and continue reading well into the wee hours of the morning I'm sure.
0: https://www.xkcd.com/1053/ 1: https://en.wikipedia.org/wiki/Unschooling
Virginia requires a Notice of Intent to be filed with the local school district and periodic standardized testing - there are some way around each of these things, but that's the course that the vast majority of homeschoolers take. It's annoying but not onerous.
Arkansas basically requires nothing at all.
It’d be nice if traditional school had a better balance where personal interests could be explored in a structured and formally accepted way.
In my experience as an unschooled child who was in constant contact with the parents of other unschooled children, and other unschooled children, if a child isn't interested in something, that almost always changes over time. One example was where one kid did not wish to learn to read, until about the age of seven where he taught himself to read, without much struggle (and without parental intervention -- the parent found out about it because the kid kept the books under his pillow!), simply because he found a topic he was so interested in that he wanted to learn more about it.
I also know someone else who did not learn to read until the age of 6 or 7, after which he rapidly caught up, and at the age of 9 or 10 he sped through all three of the Lord of the Rings series, and was an avid reader. These are only two examples of something that was typical within unschooling circles.
One fundamental idea behind unschooling is that children develop at different rates, and thus in some cases, trying to force them to learn something before they are ready to learn can actually cause damage -- in a lot of cases this damage isn't visible, but that doesn't mean that it isn't there. I experienced this first hand, with a primary school maths teacher. This mathematics teacher misexplained things, and would constantly pile on the stress. It took me 6 years of unschooling to de-stress enough with regards to mathematics enough to simply add up efficiently (it felt like punching through a mental brick wall, I was completely unable to manipulate the numbers, despite being able to see them). Now at the age of 20 I am still filling in gaps in my mathematics education, through the right aids.
Something I would add is that most people learn the skills that are required for them in day-to-day life, so even if a child is not interested in mathematics, they tend to learn the basics just by helping out their parents with shopping. The most important thing that a child needs in their life is the willingness to learn, which is a skill that school rips out of our children.
And then I was royally screwed. I always had enough grades for teachers to pass me on almost all subjects, but in my last year of high school I was really stressed out about what I wanted to do at university, and stopped making an effort for a lot of subjects at high school that were suddenly going at a pace I couldn't follow in "zero interest mode". It took me two years and a detour via a central government exam to get my degree.
Then I was screwed again in my final year of university college (software development). While I did great in the actual software development courses, I couldn't get myself focused on subjects I didn't care about (because I never had to, so I had absolutely no study methods for things that don't interest me). So of course after three years when I should've had my degree, I had nothing. Even though I had been to all classes and seen everything, on some subjects I just didn't pass because they didn't interest me at all.
So I just quit and started working, which was absolutely fine. I found enough at work that interested me and I became a pretty decent developer in no time. 26 now and I'm still coding cool stuff, so I'd say it ended well.
Based on how my education went I'd say unschooling would've been a great fit, but I really wonder if an unschooled kid would be more or less likely to encounter the same problems I have. While for programming you can easily get your professional life going without a sign of a degree, for many fields that's not a possibility and you will have to study (a lot). If you've never _really_ had to just process and memorize things that don't interest you, that might get really hard. I fear that being unschooled might be great at the start, but there's a point where (for most fields) you have no choice besides going into a classic education system, and you'd be less prepared than other students...
Not trying to be snarky, but genuinely interested.
Did the "inability" to focus on things you're not interested in impede you later in life, e.g. with taxes, social life, exercise etc?
Taxes and administration: not that complex in Belgium so I can't say much about that, but I value correctness a lot and that makes my administration easy to do (I never ever postpone doing my taxes, paying bills, ...). I usually find a way to make things interesting too, by keeping my administration as digital as I can. I'm always an early adopter.
Exercise: I struggle with this. Once I get going it usually goes quite well (but always have to combine it with something that does interest me, for example running with "Zombies, Run!", a sort of interactive audiobook/running trainer combination), but tend to stop completely if I hit roadblocks.
Social life: maybe. I have a great core group of friends that I've known since high school but that's about it, and I am not great at forming deep bonds. I have some work friends, but not at the level that I'd invite them over for dinner on a random week night. It's not at all at a problematic level though. I don't really know. I tend to be extremely honest and open about basically everything, and that scares / freaks out a lot of people, so it's not easy to make new good friends.
If you want to chat more, feel free to message me on whatever messaging platform you like. My username is always Ambroos or AmbroosV.
This is very interesting to me. I come from the UK, and the government's attitude to education is contrary to all of the pilot schemes, studies, and research I've seen. Namely they seem to have warmed their heads with the idea that the only way to advance learning is to put the student into the education system earlier and earlier. Rather than waiting until later (when they are ready), and improving material concerns so that good nutritional health from birth onwards is available to everyone.
I was initially concerned about this as well, but my experience so far is that it's not really an issue. We test regularly, both formally and informally, which I feel is very important so my wife and I have a good understanding of where she is relative to her peers. With the exception of the "sight words" portion of language testing in K-3, she has continues to be far ahead of them.
"Child-directed" doesn't mean "no parental involvement". Where a traditional school manages the things that she would be taught, we manage the things that she's interested in. We take care to do things as a family that expose her to skills that we think she needs to know.
If that sounds time-intensive... well, it is. My wife doesn't work outside the home and I work remotely. It's substantially less time-intensive than building a traditional curriculum and teaching it daily, though.