Very poor take. The author clearly has very limited experience with raising kids. Most kids won't do difficult things if you don't push them. Playing music, learning to spell correctly, doing mathematics, and so on. A very small minority of kids will do all of that easily and for the fun, but you can't rely on it. If you don't push your kid to do their 20 minutes of piano every day, they will half-ass it and will stop after 1 year and conclude they are not good at music. Same for sport. Same for reading books. Same for maths. And you know what? It's your fault. You chose to be lazy and complacent and didn't push them because it's hard to be a good parent. And now you expect me to validate your laziness? Nah.
A friend of mine taught remedial math at UW to incoming freshmen. She would write:
x + 2 = 5
on the blackboard and ask a student "what is the value of x?" The student would see the x, and immediately respond with x means algebra, algebra is hard, I cannot do algebra.
So she started writing:
_ + 2 = 5
and ask the student to fill in the blank. "Oh, it's 3!"
The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'.
People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.
I’ve always found that an indictment of math education — and spent many, many hours discussing it.
When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?”
There is a game called dragonbox algebra which I'm currently working through with my son and is an absolutely fantastic approach to this problem. Sadly its now part of a horrendous subscription service and is hard to access. I find it really sad that we've had computers for decades and there are so few good maths games like this.
One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones.
Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter.
So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.
She loves it. It uses a ‘?’ for basic algebra style problems and after a few days of playing (if/when she wants to, we don’t make her play it), she was already much better and faster at those problems. It made me think that schools should be giving kids games like these.
There are two sides to this. The system or method might be bad but also a determined person can go all the way and perform at a decent level if they put in enough time.
Even if the system was better the person still has to be able to motivate themselves and put in the time.
I tell my kid that math is a language. You learn to speak it, just like you learn to speak any other language, slowly, by listening, understanding, speaking, intuitively recognizing patterns, rules and exceptions. When you start to become fluent you translate problems into math and solve them. At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris and learns how to say "where's the bathroom", "hello", "would you like to sleep with me", "thank you", "goodbye", etc.
If you are a physicist or an economist, you may be using mathematics as a language in the sense that you are using a mathematical description to convey an understanding of the natural world or the economy to your colleagues. But if you are a mathematician, you are interested in the mathematical objects for their own sake.
There is also a difference between the purpose of learning language and learning math. The goal of learning language is (often) to be fluent in it. In other words, the goal is to reach a level of proficiency which would allow you to not have to think about language and focus on the content of the conversation instead. On the other hand, the goal of learning mathematics is usually to be able to solve mathematical problems. Being able to do math without "thinking about it" is not usually a requirement.
"At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris…."
Like learning dozens of trig identities without any explanation about why one would need them. As I've mentioned elsewhere learning math for the sake of it isn't enough. For most of us math has to have relevance, and for that we have to link it to things in the real world.
I'm damed sure I'd be much worse at math if I'd not been pushed in a formal environment such as a school classroom.
I liked math—especially calculus as it made sense to me—but parts became a drudgery when I could see no reason for studying them.
Right, there's always the kid in class who excels at math like a mini Euler and gets bored because the rest can't keep up but the majority of us aren't like that—doing Bessel functions and Fourier stuff as abstract mathematics without any seeming purpose can seem pointless and our only interest in them was to pass exams. (Teaching may be better these days but my textbooks never discussed the value of learning these aspects of mathematics.)
Later whilst studying elec eng/electronics it became very obvious to me how important these aspects of mathematics were. If I'd been given some practical examples of why this math was useful then I'd have been much more enthusiastic.
Same goes for the history of mathematics, I'm old enough to have had a small textbook full of log and trig tables yet if someone had asked me at highschool who John Napier was I wouldn't have had a clue. In hindsight, that was terrible.
Mathematics is often taught as if the student was going to become a mathematician à la Hardy or Ramanujan and I'm firmly of the belief this is not the best approach for the average student let alone those with few math skills.
Mathematics ought to be taught with the real world in mind for ease of understanding. For example, it's dead easy to represent AC power as a sine wave and from there use that mathematical fact to solve power problems. (Perhaps maths and physics texts should be written in tandem and synced to show relevance.)
Teachers need to take time to explain that math isn't just abstract concepts but that it's very relevant to everyday life and that tying up mathematical functions to things in the real world is actually interesting and enjoyable.
Compare learning math to learning to bicycle. There is some some sweat and struggle that needs to be put in, before one "gets it". After this it can become enjoyable. I encouraged my daughter with practice exercises from a young age, but tried to avoid making it a drudge. She built up confidence and did well with it. She is also very hands on creative. She decided to study engineering and is working towards her PhD.
Those aren't nearly comparable. Riding a bike is one simple skill and as long as you're not racing that's enough for most people. Meanwhile learning maths is a years-long effort at best. I learned how to ride a bike within an hour by myself when I finally had a good reason to learn it. I can't say the same about maths.
The key element here is nurturing curiosity.
Since then i and my 10yr old have been sitting through a virtual math circle led by Aylean McDonald on parallel.org.uk an organization run by Simon Singh
Forcing is kind of hopeless. So is logic, and reasoning.
How children learn (they can't rely on a fully formed prefrontal cortex like adults) is very different than how adults learn (no fully developed prefrontal cortex until 25-26), learning about this can help a lot.
Learning more about the Reggio Emelia approach might help parents curious about this, it has been quite surprising how much is possible naturally. One of the best things to do is to relentlessly read to and with your kids.
Showing kids the math in every day things, especially things they already love is a helpful way of making it approachable, or at least aware.
Also, linking a topic to their interest's radar, encouraging curiosity, play in general, and letting them potentially discover it can go a long away.
When they've got something they want, teaching math and savings is a great thing. Understanding life is a lot harder without knowing a basic bit of math, and can be made a bit easier when doing it younger.
I had a math teacher that once made it clear, some stuff can just click, others is just about doing a lot of examples to learn the patterns. Doing math is very different than being creative with being comfortable to find it.
Today, I'd probably setup a good prompt to find a way for the child to share their mine to discover how they like to learn, and how they might like to learn faster and easier by taking some shortcuts through math directly or on navigating an ontology/taxonomy perspective.
> One of the best things to do is to relentlessly read to and with your kids.
My mom would bring us into the clubhouse in the backyard and read to us, which I found really boring. Ended up not liking books because of it, and I'm pretty sure the same happened to both of my brothers. For years I'd only read the bare minimum required for school.
Years later I happened to see an neat book cover in the impulse-buy section of a store and begged for the book. That one book was what actually got me set on reading, and from then on I'd always have something with me.
She never realized this and still thinks I like reading because she read to us. I can't help but wonder how many of the anecdotes here are also parents not realizing what's actually going through their kids' minds.
When I was 8, I went to the library in our town a lot. My parents went there sometime to return their books. At some point I just stayed there when they would go home. First I was in the children/teenager section and soon in the general library, where I would read about programming and computers. I learned C by age of nine.
The "undeveloped PFC" argument is shallow, unspecific and usually just used to infantilize younger people. It may be useful if the child is under 6 years old, but at the time someone is 17 or older, it becomes essentially useless.
My learning process was always, and still is fueled by curiosity.
As a counterpoint, look at how the Polgar sisters were raised.
Yes, Lazlo and his wife were both education professionals, and spent an inordinate amount of time dedicated to developing the girls. But look how it turned out.
On a different note, I used to hate sport when my parents forced me to play it. I liked screwing around on the computer or playing video games. However, when I found tennis naturally around 12 or 13, I couldn't get enough of it, and vastly improved on my own because I had a lot more fun playing than most of my peers did, who were forced into it by their parents. Most of them don't even play for fun anymore with friends, and I'm in my mid 30s and still play frequently.
It's not about forcing your kids to "do math", but to excel at important skills far before the benefits of being good at that skill matter.
The amount of homework/study per day that maximizes math scores on tests is significant, 1+ hours/school day by the time they're in middle school, with it helping even more for those who are starting out poor at math[0]. You'll note the referenced study doesn't even max out progress for any group - meaning most could have studied more and improved more.
I don't know any kids that voluntarily did an hour or more of solely math study per day. I know plenty that were forced, and ended up loving math or other technical fields as adults.
As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.
As someone who just finished school, I’m trying to figure out how to get genuinely interested in mathematics. I’ve never been particularly strong at it, yet I’m planning to enter a university program that demands a high level of math. The problem is, it’s hard to motivate myself to study math for its own sake. For example, I loved learning programming because it’s hands‑on—I can build something and immediately see the results. In everyday life, though, I rarely need more than basic arithmetic or simple sin/cos/tan trigonometry.
How do you develop a lasting interest in math when it doesn’t feel immediately useful?
Make it practical! Graphics programming involves linear algebra. Databases involve relational algebra. Machine learning involves requires calculus. You’ll naturally encounter hands-on tasks with tangible goals that involve learning new math.
One of my undergrad degrees is in math. As you study it, you learn to identify your assumptions (axioms), find or build interesting abstractions, prove properties about them (theorems), and then map all sorts of other things into those abstractions by figuring out that they're really the same thing. It's even more interesting when you start to find things that are different or question things you always took for granted.
Math gives you the ability to leverage the very structure and relationships of pure abstraction. It's quite the super power.
None of the specific things you learn studying math will be nearly as useful as the ability to think mathematically.
N=1 datapoint here.
I studied physics in university and before I started I was not aware that physics is basically just math where the results sometimes relate to reality. The pure math courses I took were the most difficult and in the beginning I loathed them, because it felt so unattainable to get any intuition, let alone real proper comprehension for all the concepts they threw at us. For a long time I felt like I was just hanging on by threads and especially if I compared myself to those who had some innate interest in math or generally some really good intuition on the abstract concepts (or even prior knowledge) it was really demotivating. But I also felt like I had no choice but to continue and as time went on the I grew fond of it. And the feeling of being overwhelmed changed - that is to say I still was completely lost every time a new topic was breached and I could not understand even half of the proofs in class - but I did not feel so defeated about it. And I grew to like the feeling of actually completing the work sheets they gave us every week. The process of solving them was often excruciating but if you did the sense of accomplishment is real. I think for most people higher math is really difficult and that is part of why it is interesting. Another aspect I had to accept over time is that even though you can state a mathematical fact or conjecture in just a hand full of symbols or a plain sentence it does not mean that truly understand it, its implications or how you got there can be understood the same way that other prose can be. Sometimes you have to stare at, contemplate and scribble around one equation for days until you understand whats up.
If there was any advice I would give, then it's probably similar advice on how to stop procrastinating on anything that is difficult. Establish a routine first - find a spot that you will only use for studying this (like a spot in a library), start small, divide and conquer, accept that you will not understand most things easily, reward yourself for the small wins along the way, find an accountability partner or someone to study with if that's your thing, make a regular schedule with regular times where this is what you do - consistency is key, even if its just for 5 minutes, stack it onto other habits, see yourself as a scholar of math - it is what you do, lean into the discomfort, as enduring that is a valuable skill in itself.
Don't study it for usefulness, study it for beauty. Look for amazing insights.
Yes, you need some practical math as well. I did engineering, there's a lot of inelegant stuff there.
But that stuff actually tends to be right next to some very interesting things.
Here are three things you can find out.
First, there's more than one kind of infinity. You can't make a map from natural numbers like 1, 2, 3 etc to real numbers like e, 0.632268, sqrt(2) etc. Look for Cantor diagonalization.
Second, a random walk like a heads vs tails comes back to zero almost certainly. It also does so in two dimensions, like walking randomly in Manhattan. In three dimensions, it does not, and so for higher dimensions. Look for Polya.
Third. There is a way for you and me to communicate secretly, despite everyone in HN being able to see our entire exchange. Look for Diffie Helmann.
These days, there's a whole industry of people doing math videos with interesting stuff.
I didn't particularly find (at the time) calculus, multivariable calculus, physics, etc. interesting as I didn't find the applications interesting at the time. I find these subjects representative of what you traditionally learn at school.
When I entered uni I discovered my passion for discrete math, algebra (groups, rings, fields, etc.), number theory, cryptography, theory of computation, etc. as they have a lot of application in CS.
That's really what did it for me - and also I had great uni lecturers. I wish they would have taught the subjects I like in highschool - the difficulty level is about the same.
> Kids are born explorers. They naturally want to discover new things, including math.
That's true only until their senses are not shut off and attention is not fixated on screens. Exploration happens only when you have unused attention, sensory capabilities and need for a bit of hard work and risk-taking. Curiosity is less of a biological feature. It is a product of the need and the available resources (senses etc). All of these are missing now.
There is no need or motivation. And there are no available resources (senses, attention). There is no justification for exploration and hard thinking.
When I was having trouble learning multiplication my father made up a payment system. He made flash cards and I got a payment for every one I mastered (I had to get it right some number of times, not just once). I ended up with maybe $25 or $50 which was a lot for a kid in the 1970s.
My mother tried to give me $5 for every book of the Bible I read. I never took her up on it even though I knew about the basically freebies like Jude. I wasn't opposed to it, but it felt like –on the one hand– I didn't want to half-ass it and read a few books –and on the other– I really didn't want to read the entire Bible. So I guess that a completionist attitude prevented me from getting $30!
For elementary school age kids, maybe even middle school, try getting them started with the app "Euclidea".
They won't think of it as math. It's gamified geometric constructions. Starts simple, "how do you bisect an angle" with a compass and a straight edge. It goes to a very high level that will challenge anyone.
30 minutes of play per 3 days is such a brutal reality to acknowledge. One of the most wonderful experiences in all of life so drastically limited by the society we’ve constructed.
> One of the most wonderful experiences in all of life so drastically limited by the society we’ve constructed.
I could understand if someone was forced to work two full-time jobs (as my grandfather was), but I find it much harder to blame ‘society’ when so many of these situations are self-imposed.
It’s possible that I’m jaded from hearing a subset of parents complain about not having enough time with their kids but then get stuck scrolling their phone while kids want to play. I also know some parents who insist on having a spotlessly clean house every day and then complain that there is enough time to spend with their kids.
I’ve gravitated toward peer parents who have similar priorities in life which has indirectly made me happier. Seeing all of the parents in my friend circles prioritize spending time with their kids and being honest with themselves about their priorities has been unexpectedly helpful for my own sanity.
Again, nothing against parents who are really forced to allocate time elsewhere, but I’m tired of seeing self-inflicted problems of prioritization and time management be externalized as blaming society.
In some ways yes, but men have always been the ones to go hunt/farm for long hours and provide for the family, leaving the children home under the care of the mother/village for days or weeks at a time.
I would go so far as to say modern society actually enables us to be more involved in our children’s lives, especially those for whom remote work and home schooling are options.
Something I've been thinking a lot about is "stealth edutainment" games.
When I was a kid, I remember "edutainment" games that were basically like normal computer games, except every so often a homework problem pops up.
I think that doesn't work super well. Better is a game which has you learning naturally, in order to play the game more effectively. For example, I've been enjoying the computer game Slay the Spire recently, and there is a great deal of mental math which is inherent to the game. If I had a kid, I think I might give them that game as a method to motivate them to learn arithmetic.
ChatGPT makes it so easy to build a lesson/workbook for something your kid is interested in. I've used it to build workbooks on special relativity, tsolkovsky's rocket equation (including euler integration to build a scratch program), triangulation, logic gates, probabilities of simple dice games, etc. My pro-tip is to tell the LLM to format the document in LaTeX, so you get beautiful math typesetting.
You don't even have to get through the workbook. Get to a part that they need to understand better and make a detailed workbook on that part (for example, triangulation -> solving a system of linear equations).
Maybe find an application of the subject that they might find interesting. I suppose if you can't find anything that interests them, then it's much harder to teach it.
For instance, perspective drawing might provide a nice application of 3D projective space, its subspaces, and perspectivities between those subspaces. Some of the theory of conic sections might be relevant too.
Computer graphics provides a nice application of coordinate geometry. This covers elementary algebra, Pythagoras's theorem, etc.
Even eating pizza can provide an application of differential geometry.
I tell my kids they can have letter cookies if they pick a word that starts with the letter, and can have 5 treats if they ask for 4 but know what "plus one means" or can have 4 if they recite "2 plus 2 equals ... ".
They're 3, so I don't expect that to scale, but I'm hoping it's normal reward-for-knowledge by the time we get report cards.
Something we don't pay enough attention to is that while calculators have solved everyday math to the point we downplay it as a required skill, people are not pulling out their calculator at the grocery store to make better purchase decisions, even though we all have one in our pocket now.
So we handwave the importance of being able to do everyday math in our heads, while also not taking advantage of the tool that's a substitute for it. We're less educated but also less effective than we would be if we'd never invented automated calculation and were forced to be sharp about it.
Is there a name for this phenomenon?
And what's it going to look like a decade after AI has caused people to stop using their brain for general thinking like it's stopped them from doing math?
(I'm sure you, the reader, are very good at math and are an exception to this still-apt generalization.)
Oddly enough I found a great 'trick' for this. Kids hate doing math tests, but turn it into a competition and game and suddenly they love it. Print out a bunch of remedial problems, perhaps 50. And then give them 1 or 2 minutes to do as many as they can. It's just a contest to improve against your own scores over time, with prizes for the kids who score the highest after a month or whatever.
It's still literally just a math test/quiz, but somehow the context changes everything and even kids who really aren't into math were loving it, and also improving rapidly because the repetition helps instill intuition.
I imagine the part of a test people dislike is failing, and the consequences from failing. Framing it as a game without those emotional stakes fixes that.
If the teaching environment was set up to encourage learning rather than punish not having learnt yet we might not need these tricks, but that culture is slow to change
[+] [-] laurent_du|10 months ago|reply
[+] [-] WalterBright|10 months ago|reply
A friend of mine taught remedial math at UW to incoming freshmen. She would write:
on the blackboard and ask a student "what is the value of x?" The student would see the x, and immediately respond with x means algebra, algebra is hard, I cannot do algebra.So she started writing:
and ask the student to fill in the blank. "Oh, it's 3!"[+] [-] sublinear|10 months ago|reply
People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.
[+] [-] zmgsabst|10 months ago|reply
When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?”
Pedagogy is hard.
[+] [-] RobinL|10 months ago|reply
[+] [-] jand|10 months ago|reply
One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones.
Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter.
So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.
[+] [-] unknown|10 months ago|reply
[deleted]
[+] [-] danenania|10 months ago|reply
She loves it. It uses a ‘?’ for basic algebra style problems and after a few days of playing (if/when she wants to, we don’t make her play it), she was already much better and faster at those problems. It made me think that schools should be giving kids games like these.
[+] [-] ozgrakkurt|10 months ago|reply
Even if the system was better the person still has to be able to motivate themselves and put in the time.
[+] [-] unknown|10 months ago|reply
[deleted]
[+] [-] hahamaster|10 months ago|reply
[+] [-] chasely|10 months ago|reply
Quite a story condensed into those five phrases.
[+] [-] agnishom|10 months ago|reply
I think there are some differences
If you are a physicist or an economist, you may be using mathematics as a language in the sense that you are using a mathematical description to convey an understanding of the natural world or the economy to your colleagues. But if you are a mathematician, you are interested in the mathematical objects for their own sake.
There is also a difference between the purpose of learning language and learning math. The goal of learning language is (often) to be fluent in it. In other words, the goal is to reach a level of proficiency which would allow you to not have to think about language and focus on the content of the conversation instead. On the other hand, the goal of learning mathematics is usually to be able to solve mathematical problems. Being able to do math without "thinking about it" is not usually a requirement.
[+] [-] hilbert42|10 months ago|reply
Like learning dozens of trig identities without any explanation about why one would need them. As I've mentioned elsewhere learning math for the sake of it isn't enough. For most of us math has to have relevance, and for that we have to link it to things in the real world.
[+] [-] hilbert42|10 months ago|reply
I liked math—especially calculus as it made sense to me—but parts became a drudgery when I could see no reason for studying them.
Right, there's always the kid in class who excels at math like a mini Euler and gets bored because the rest can't keep up but the majority of us aren't like that—doing Bessel functions and Fourier stuff as abstract mathematics without any seeming purpose can seem pointless and our only interest in them was to pass exams. (Teaching may be better these days but my textbooks never discussed the value of learning these aspects of mathematics.)
Later whilst studying elec eng/electronics it became very obvious to me how important these aspects of mathematics were. If I'd been given some practical examples of why this math was useful then I'd have been much more enthusiastic.
Same goes for the history of mathematics, I'm old enough to have had a small textbook full of log and trig tables yet if someone had asked me at highschool who John Napier was I wouldn't have had a clue. In hindsight, that was terrible.
Mathematics is often taught as if the student was going to become a mathematician à la Hardy or Ramanujan and I'm firmly of the belief this is not the best approach for the average student let alone those with few math skills.
Mathematics ought to be taught with the real world in mind for ease of understanding. For example, it's dead easy to represent AC power as a sine wave and from there use that mathematical fact to solve power problems. (Perhaps maths and physics texts should be written in tandem and synced to show relevance.)
Teachers need to take time to explain that math isn't just abstract concepts but that it's very relevant to everyday life and that tying up mathematical functions to things in the real world is actually interesting and enjoyable.
[+] [-] CommenterPerson|10 months ago|reply
[+] [-] alpaca128|10 months ago|reply
[+] [-] imtringued|10 months ago|reply
[+] [-] smath|10 months ago|reply
The key element here is nurturing curiosity. Since then i and my 10yr old have been sitting through a virtual math circle led by Aylean McDonald on parallel.org.uk an organization run by Simon Singh
[+] [-] j45|10 months ago|reply
How children learn (they can't rely on a fully formed prefrontal cortex like adults) is very different than how adults learn (no fully developed prefrontal cortex until 25-26), learning about this can help a lot.
Learning more about the Reggio Emelia approach might help parents curious about this, it has been quite surprising how much is possible naturally. One of the best things to do is to relentlessly read to and with your kids.
Showing kids the math in every day things, especially things they already love is a helpful way of making it approachable, or at least aware.
Also, linking a topic to their interest's radar, encouraging curiosity, play in general, and letting them potentially discover it can go a long away.
When they've got something they want, teaching math and savings is a great thing. Understanding life is a lot harder without knowing a basic bit of math, and can be made a bit easier when doing it younger.
I had a math teacher that once made it clear, some stuff can just click, others is just about doing a lot of examples to learn the patterns. Doing math is very different than being creative with being comfortable to find it.
Today, I'd probably setup a good prompt to find a way for the child to share their mine to discover how they like to learn, and how they might like to learn faster and easier by taking some shortcuts through math directly or on navigating an ontology/taxonomy perspective.
[+] [-] Izkata|10 months ago|reply
My mom would bring us into the clubhouse in the backyard and read to us, which I found really boring. Ended up not liking books because of it, and I'm pretty sure the same happened to both of my brothers. For years I'd only read the bare minimum required for school.
Years later I happened to see an neat book cover in the impulse-buy section of a store and begged for the book. That one book was what actually got me set on reading, and from then on I'd always have something with me.
She never realized this and still thinks I like reading because she read to us. I can't help but wonder how many of the anecdotes here are also parents not realizing what's actually going through their kids' minds.
[+] [-] fleshmonad|10 months ago|reply
The "undeveloped PFC" argument is shallow, unspecific and usually just used to infantilize younger people. It may be useful if the child is under 6 years old, but at the time someone is 17 or older, it becomes essentially useless.
My learning process was always, and still is fueled by curiosity.
[+] [-] NickC25|10 months ago|reply
Yes, Lazlo and his wife were both education professionals, and spent an inordinate amount of time dedicated to developing the girls. But look how it turned out.
On a different note, I used to hate sport when my parents forced me to play it. I liked screwing around on the computer or playing video games. However, when I found tennis naturally around 12 or 13, I couldn't get enough of it, and vastly improved on my own because I had a lot more fun playing than most of my peers did, who were forced into it by their parents. Most of them don't even play for fun anymore with friends, and I'm in my mid 30s and still play frequently.
[+] [-] globular-toast|10 months ago|reply
[+] [-] codemac|10 months ago|reply
The amount of homework/study per day that maximizes math scores on tests is significant, 1+ hours/school day by the time they're in middle school, with it helping even more for those who are starting out poor at math[0]. You'll note the referenced study doesn't even max out progress for any group - meaning most could have studied more and improved more.
I don't know any kids that voluntarily did an hour or more of solely math study per day. I know plenty that were forced, and ended up loving math or other technical fields as adults.
As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.
[0]: https://pmc.ncbi.nlm.nih.gov/articles/PMC8025066/
[+] [-] jamesy0ung|10 months ago|reply
How do you develop a lasting interest in math when it doesn’t feel immediately useful?
[+] [-] jakelazaroff|10 months ago|reply
[+] [-] jodoherty|10 months ago|reply
Math gives you the ability to leverage the very structure and relationships of pure abstraction. It's quite the super power.
None of the specific things you learn studying math will be nearly as useful as the ability to think mathematically.
[+] [-] Escapado|10 months ago|reply
If there was any advice I would give, then it's probably similar advice on how to stop procrastinating on anything that is difficult. Establish a routine first - find a spot that you will only use for studying this (like a spot in a library), start small, divide and conquer, accept that you will not understand most things easily, reward yourself for the small wins along the way, find an accountability partner or someone to study with if that's your thing, make a regular schedule with regular times where this is what you do - consistency is key, even if its just for 5 minutes, stack it onto other habits, see yourself as a scholar of math - it is what you do, lean into the discomfort, as enduring that is a valuable skill in itself.
[+] [-] lordnacho|10 months ago|reply
Yes, you need some practical math as well. I did engineering, there's a lot of inelegant stuff there.
But that stuff actually tends to be right next to some very interesting things.
Here are three things you can find out.
First, there's more than one kind of infinity. You can't make a map from natural numbers like 1, 2, 3 etc to real numbers like e, 0.632268, sqrt(2) etc. Look for Cantor diagonalization.
Second, a random walk like a heads vs tails comes back to zero almost certainly. It also does so in two dimensions, like walking randomly in Manhattan. In three dimensions, it does not, and so for higher dimensions. Look for Polya.
Third. There is a way for you and me to communicate secretly, despite everyone in HN being able to see our entire exchange. Look for Diffie Helmann.
These days, there's a whole industry of people doing math videos with interesting stuff.
[+] [-] commandersaki|10 months ago|reply
I didn't particularly find (at the time) calculus, multivariable calculus, physics, etc. interesting as I didn't find the applications interesting at the time. I find these subjects representative of what you traditionally learn at school.
When I entered uni I discovered my passion for discrete math, algebra (groups, rings, fields, etc.), number theory, cryptography, theory of computation, etc. as they have a lot of application in CS.
That's really what did it for me - and also I had great uni lecturers. I wish they would have taught the subjects I like in highschool - the difficulty level is about the same.
[+] [-] zkmon|10 months ago|reply
That's true only until their senses are not shut off and attention is not fixated on screens. Exploration happens only when you have unused attention, sensory capabilities and need for a bit of hard work and risk-taking. Curiosity is less of a biological feature. It is a product of the need and the available resources (senses etc). All of these are missing now.
There is no need or motivation. And there are no available resources (senses, attention). There is no justification for exploration and hard thinking.
[+] [-] SoftTalker|10 months ago|reply
[+] [-] Rendello|10 months ago|reply
[+] [-] r58lf|10 months ago|reply
They won't think of it as math. It's gamified geometric constructions. Starts simple, "how do you bisect an angle" with a compass and a straight edge. It goes to a very high level that will challenge anyone.
[+] [-] grepLeigh|10 months ago|reply
> I have an internal KPI: if in the last three days I haven’t spent at least 30 minutes playing with my kid, there’s something seriously wrong
I think I'm interpreting this ungenerously, because my knee-jerk reaction was to wonder about who is handling the other 12+ waking hours a day.
[+] [-] sdrothrock|10 months ago|reply
[+] [-] raymondgh|10 months ago|reply
[+] [-] Aurornis|10 months ago|reply
I could understand if someone was forced to work two full-time jobs (as my grandfather was), but I find it much harder to blame ‘society’ when so many of these situations are self-imposed.
It’s possible that I’m jaded from hearing a subset of parents complain about not having enough time with their kids but then get stuck scrolling their phone while kids want to play. I also know some parents who insist on having a spotlessly clean house every day and then complain that there is enough time to spend with their kids.
I’ve gravitated toward peer parents who have similar priorities in life which has indirectly made me happier. Seeing all of the parents in my friend circles prioritize spending time with their kids and being honest with themselves about their priorities has been unexpectedly helpful for my own sanity.
Again, nothing against parents who are really forced to allocate time elsewhere, but I’m tired of seeing self-inflicted problems of prioritization and time management be externalized as blaming society.
[+] [-] twodave|10 months ago|reply
I would go so far as to say modern society actually enables us to be more involved in our children’s lives, especially those for whom remote work and home schooling are options.
[+] [-] 0xDEAFBEAD|10 months ago|reply
When I was a kid, I remember "edutainment" games that were basically like normal computer games, except every so often a homework problem pops up.
I think that doesn't work super well. Better is a game which has you learning naturally, in order to play the game more effectively. For example, I've been enjoying the computer game Slay the Spire recently, and there is a great deal of mental math which is inherent to the game. If I had a kid, I think I might give them that game as a method to motivate them to learn arithmetic.
[+] [-] jerkstate|10 months ago|reply
You don't even have to get through the workbook. Get to a part that they need to understand better and make a detailed workbook on that part (for example, triangulation -> solving a system of linear equations).
[+] [-] le-mark|10 months ago|reply
[+] [-] ogogmad|10 months ago|reply
For instance, perspective drawing might provide a nice application of 3D projective space, its subspaces, and perspectivities between those subspaces. Some of the theory of conic sections might be relevant too.
Computer graphics provides a nice application of coordinate geometry. This covers elementary algebra, Pythagoras's theorem, etc.
Even eating pizza can provide an application of differential geometry.
[+] [-] jvanderbot|10 months ago|reply
They're 3, so I don't expect that to scale, but I'm hoping it's normal reward-for-knowledge by the time we get report cards.
[+] [-] CBLT|10 months ago|reply
[+] [-] add-sub-mul-div|10 months ago|reply
So we handwave the importance of being able to do everyday math in our heads, while also not taking advantage of the tool that's a substitute for it. We're less educated but also less effective than we would be if we'd never invented automated calculation and were forced to be sharp about it.
Is there a name for this phenomenon?
And what's it going to look like a decade after AI has caused people to stop using their brain for general thinking like it's stopped them from doing math?
(I'm sure you, the reader, are very good at math and are an exception to this still-apt generalization.)
[+] [-] somenameforme|10 months ago|reply
It's still literally just a math test/quiz, but somehow the context changes everything and even kids who really aren't into math were loving it, and also improving rapidly because the repetition helps instill intuition.
[+] [-] greggsy|10 months ago|reply
Imagine having to move a round thing around some other people to get that thing into a square frame. Then, imagine that you can only use your feet!
[+] [-] procaryote|10 months ago|reply
I imagine the part of a test people dislike is failing, and the consequences from failing. Framing it as a game without those emotional stakes fixes that.
If the teaching environment was set up to encourage learning rather than punish not having learnt yet we might not need these tricks, but that culture is slow to change