Another article where someone thinks being a parent means they understand all children. I have 4 kids, and 2 of them definitely would never do math, even basic math, for fun, ever. Their brains lack whatever pathways most people utilize to learn math, so I now have a 15 year old who has to work nearly as hard at arithmetic as she did when she first learned it. No amount of drilling, change of curriculum, buckling down or backing off has had any impact. She has absolutely no interest in math. But the kid reads faster than I do, which is not slow at all.
The only thing I know about kids after having adopted 4 of them is that none of them are alike. The only time when you can really train them to do anything consistently is when they are babies. As a result all 4 have great sleep habits :)
I read it (as a non-child), and a lot of my certainties about what young brains are and are not capable of got joyfully exploded. I'm not linking it to you proscriptively, or with a specific suggestion or riposte in mind whatsoever - you just might be interested in it.
School is very successful at convincing kids (and former kids) of two things: firstly, that the academic subjects they purport to teach are actually delineated by the school textbooks and curricula. And secondly, that the reaction people have to specific subjects within these school structures are the actual unchangeable nature of the person's relationship with the subject.
I hope one day our societies move past these two egregious and immeasurably damaging beliefs.
I haven’t read the book, but we have 100% had the “you don’t have to graduate if you don’t want to” talk with this one haha. She doesn’t want to drop out, but definitely isn’t interested in college. We want to keep that door open for her if we can, so we just remind her that staying in school requires doing some things she doesn’t like.
But yeah, at 15 it gets a little hairy. You have a kid who wants to be an adult, but in a lot of ways they are not prepared to make adult decisions still. Eventually she will have to make them, ready or not. But we have a few years left to help her, so the focus becomes how to best do that.
I as a child, a teen, and a young adult thought I hated math, I got bad grades and it bored me. I dropped out of school. I later went to college and took remedial algebra twice.
Math in school was purposeless and rigid, a rote procedure to be followed by command because that's what kids have to do.
Now, I have grown older, and my curiosity drove me to learn because I wanted to make things, machines and software and probabilistic strategies. Things that necessitate math. If you can't rotate a vector, your guy walks faster diagonally. If you can't think mathematically and you want to lift a 2 jointed robot arm that weighs several tons, you're going to tip it over, and possibly die in the process. You can do it without trig but you can't do it without thinking about math.
Once I found purpose, I began to appreciate the beauty of the more elegant solutions. I kind of fell in love with math as an adult. Now I watch numberphile with my kids and make complicated machinery and software at work.
I think a lot more people love math than realize it, because they're conflating math itself and what school calls math, which is worksheets and demands, not beauty and creation.
Yes. And it's the same when the kids come from the same parents too. We have one kid that's willing to go very deep on math. The only does what can be figured out in 3 seconds or less. Same genetic parents, same school system.
The original concept in the article of exploration is great. Some kids want to explore math, some science, some music, and some Starcraft.
I think you’re rationalizing. I don’t know a single asian American immigrant kid who isn’t pretty good at math. You may mot be willing to take the measures their parents did to force them to engage with math. But those methods do seem to work on virtually any kid of average or above intelligence.
I don’t personally see how one person’s experience with children other than my own has any connection to my own children. That was the point I was attempting to make, though. Just because you have anecdotes to share doesn’t mean you’ve stumbled upon some universal truth. They can be helpful to share but NOT if used to dismiss other people’s experience.
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.
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.
2. A love of subversives and cheating the system. Basically, the guys writing leetcode cheating software are saints in my book. All subversions of the attempt to turn society into a meritocracy (a term which was originally supposed to be a slur/negative connotation - https://en.m.wikipedia.org/wiki/The_Rise_of_the_Meritocracy) is extremely good.
3. An advanced knowledge of TI basic, so I could cheat hard on every single school assignment I could get away with. AP Chemistry? I’ve got a symbolic stoichometry solver app! Calculus? CAS system in the palm of my hand!
Play stupid games with children, win stupid prizes. Maybe don’t force them to work like little slaves in their early life, and they won’t strike back at your society systems.
I had similar conclusions, but the other way around: absolutely no guidance. Fortunately by the time I programmed and sold the basic ti math exam solvers to by classmates for 2 euros a pop I had everything memorized.
Nothing like cheating the system to know the system
Raising kids is hard. Sad. And what do I know about it? Regardless, parents do need to get involved in their children's education. For instance, they should help their children prepare for entry exams into secondary school. This shouldn't take their child 4 hours a day. Maybe 10 minutes on some days, and 1 hour on others.
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!
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
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).
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.
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.
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.
My daughter and loads of kids watched number blocks from around two or three up, I think it made quite a big difference- she's far ahead of where I was now, years later.
Kids do not understand the concept of "importance". At least no kid I've met. That part of their brain doesn't work. They'll trade effort for privileges or toys tho, and are little mimicry machines so they follow you if you use it.
yeah, I recoiled when the author of the post says "no bribing" - bribery is one of the most useful tools a parent has. I guess you could call it "incentive" or something, but really, it's quid pro quo.
Honestly it's so close to how the world works I can't believe 1. Avoiding loss of privilege and 2. Gaining new things as reward isn't the top two parenting tips.
But probably zeroth, most important, is modelling good behavior. Kids are mirrors.
I'm fortunate enough that my daughter has an admirable interest (and talent) for Math since very early age. She even won a medal at a renowned nationwide Math competition when she was in Grade 5... competing in the Grade 10 category.
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.)
But the reality is that's usually almost a false trade - I'm not buying one item in the grocery store I'm buying easily a dozen or more. The best way to do this would be toss the online inventory into a solver to calculate "best value" for me, but in reality it would be a waste of time because if they're out of something, or the quality looks suspect, then that blows that calculation completely. And then am I going to do this for every single item, where every minute in the store is multiplying through the rest of my day? How much is the time shopping trading off against extremely sparse leisure time?
And then there's intangibles - something being slightly cheaper doesn't necessarily mean I'm making a good trade off by buying it for my overall quality of life.
In Australia at least this whole problem was perfectly adequately solved by mandating bulk price labeling on all items in the supermarket. Products in comparable categories have per volume/weight prices listed alongside item prices.
Another article where someone thinks being a parent means they understand all children. I have 4 kids, and 2 of them definitely would never do math, even basic math, for fun, ever. Their brains lack whatever pathways most people utilize to learn math, so I now have a 15 year old who has to work nearly as hard at arithmetic as she did when she first learned it. No amount of drilling, change of curriculum, buckling down or backing off has had any impact. She has absolutely no interest in math. But the kid reads faster than I do, which is not slow at all.
The only thing I know about kids after having adopted 4 of them is that none of them are alike. The only time when you can really train them to do anything consistently is when they are babies. As a result all 4 have great sleep habits :)
Have you come across https://en.wikipedia.org/wiki/The_Teenage_Liberation_Handboo...
I read it (as a non-child), and a lot of my certainties about what young brains are and are not capable of got joyfully exploded. I'm not linking it to you proscriptively, or with a specific suggestion or riposte in mind whatsoever - you just might be interested in it.
School is very successful at convincing kids (and former kids) of two things: firstly, that the academic subjects they purport to teach are actually delineated by the school textbooks and curricula. And secondly, that the reaction people have to specific subjects within these school structures are the actual unchangeable nature of the person's relationship with the subject.
I hope one day our societies move past these two egregious and immeasurably damaging beliefs.
I haven’t read the book, but we have 100% had the “you don’t have to graduate if you don’t want to” talk with this one haha. She doesn’t want to drop out, but definitely isn’t interested in college. We want to keep that door open for her if we can, so we just remind her that staying in school requires doing some things she doesn’t like.
But yeah, at 15 it gets a little hairy. You have a kid who wants to be an adult, but in a lot of ways they are not prepared to make adult decisions still. Eventually she will have to make them, ready or not. But we have a few years left to help her, so the focus becomes how to best do that.
I as a child, a teen, and a young adult thought I hated math, I got bad grades and it bored me. I dropped out of school. I later went to college and took remedial algebra twice.
Math in school was purposeless and rigid, a rote procedure to be followed by command because that's what kids have to do.
Now, I have grown older, and my curiosity drove me to learn because I wanted to make things, machines and software and probabilistic strategies. Things that necessitate math. If you can't rotate a vector, your guy walks faster diagonally. If you can't think mathematically and you want to lift a 2 jointed robot arm that weighs several tons, you're going to tip it over, and possibly die in the process. You can do it without trig but you can't do it without thinking about math.
Once I found purpose, I began to appreciate the beauty of the more elegant solutions. I kind of fell in love with math as an adult. Now I watch numberphile with my kids and make complicated machinery and software at work.
I think a lot more people love math than realize it, because they're conflating math itself and what school calls math, which is worksheets and demands, not beauty and creation.
Best advice I ever received is: You have to parent the kid you have - not the kid you want
I have 5 and can say that this is the way.
This 100%
Yes. And it's the same when the kids come from the same parents too. We have one kid that's willing to go very deep on math. The only does what can be figured out in 3 seconds or less. Same genetic parents, same school system.
The original concept in the article of exploration is great. Some kids want to explore math, some science, some music, and some Starcraft.
I think you’re rationalizing. I don’t know a single asian American immigrant kid who isn’t pretty good at math. You may mot be willing to take the measures their parents did to force them to engage with math. But those methods do seem to work on virtually any kid of average or above intelligence.
I don’t personally see how one person’s experience with children other than my own has any connection to my own children. That was the point I was attempting to make, though. Just because you have anecdotes to share doesn’t mean you’ve stumbled upon some universal truth. They can be helpful to share but NOT if used to dismiss other people’s experience.
> The only time when you can really train them to do anything consistently is when they are babies.
This is really stupid.
If you can’t recognize a little tongue-in-cheek humor then maybe you’re the stupid one ;)
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.
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.
[0]: https://pmc.ncbi.nlm.nih.gov/articles/PMC8025066/
Me being forced to do tons of horrible math by my abusive grandfather at a young age for literally 4+ hours at a time gave me a few things.
1. A true hatred of work, make work, and a strong desire to defend laziness as a concept (note that Bertrand Russel agrees hard with me here!) -https://en.m.wikipedia.org/wiki/In_Praise_of_Idleness_and_Ot...
2. A love of subversives and cheating the system. Basically, the guys writing leetcode cheating software are saints in my book. All subversions of the attempt to turn society into a meritocracy (a term which was originally supposed to be a slur/negative connotation - https://en.m.wikipedia.org/wiki/The_Rise_of_the_Meritocracy) is extremely good.
3. An advanced knowledge of TI basic, so I could cheat hard on every single school assignment I could get away with. AP Chemistry? I’ve got a symbolic stoichometry solver app! Calculus? CAS system in the palm of my hand!
Play stupid games with children, win stupid prizes. Maybe don’t force them to work like little slaves in their early life, and they won’t strike back at your society systems.
I had similar conclusions, but the other way around: absolutely no guidance. Fortunately by the time I programmed and sold the basic ti math exam solvers to by classmates for 2 euros a pop I had everything memorized.
Nothing like cheating the system to know the system
Raising kids is hard. Sad. And what do I know about it? Regardless, parents do need to get involved in their children's education. For instance, they should help their children prepare for entry exams into secondary school. This shouldn't take their child 4 hours a day. Maybe 10 minutes on some days, and 1 hour on others.
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!
About a year ago I came across the concept of ‘math circles’, here on HN. It was this longish but very interesting article: https://www.thepsmiths.com/p/review-math-from-three-to-seven...
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
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).
Where can one learn more about this? I want to get some activities for my kids this summer…
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.
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.
Have them play a game like math maze 2!
They will force themselves to play... and do math in the process.
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.
My daughter and loads of kids watched number blocks from around two or three up, I think it made quite a big difference- she's far ahead of where I was now, years later.
Teach kids to do math by have them make mods for their favourite games.
Perhaps make them aware how important it is with examples from nature? https://duckduckgo.com/?t=lm&q=fibonacci+in+nature+examples&...
Something occurring in nature doesn’t necessarily make it important to their lives.
Kids do not understand the concept of "importance". At least no kid I've met. That part of their brain doesn't work. They'll trade effort for privileges or toys tho, and are little mimicry machines so they follow you if you use it.
yeah, I recoiled when the author of the post says "no bribing" - bribery is one of the most useful tools a parent has. I guess you could call it "incentive" or something, but really, it's quid pro quo.
Honestly it's so close to how the world works I can't believe 1. Avoiding loss of privilege and 2. Gaining new things as reward isn't the top two parenting tips.
But probably zeroth, most important, is modelling good behavior. Kids are mirrors.
I'm fortunate enough that my daughter has an admirable interest (and talent) for Math since very early age. She even won a medal at a renowned nationwide Math competition when she was in Grade 5... competing in the Grade 10 category.
That kid's name? Alberta Einstein.
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 that might work for getting your kids interested in modular arithmetic: The Chicken McNugget Theorem.
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.)
But the reality is that's usually almost a false trade - I'm not buying one item in the grocery store I'm buying easily a dozen or more. The best way to do this would be toss the online inventory into a solver to calculate "best value" for me, but in reality it would be a waste of time because if they're out of something, or the quality looks suspect, then that blows that calculation completely. And then am I going to do this for every single item, where every minute in the store is multiplying through the rest of my day? How much is the time shopping trading off against extremely sparse leisure time?
And then there's intangibles - something being slightly cheaper doesn't necessarily mean I'm making a good trade off by buying it for my overall quality of life.
In Australia at least this whole problem was perfectly adequately solved by mandating bulk price labeling on all items in the supermarket. Products in comparable categories have per volume/weight prices listed alongside item prices.