Don't force your kids to do math
> Without realizing it, he was doing algebra.
A friend of mine taught remedial math at UW to incoming freshmen. She would write:
x + 2 = 5
So she started writing:
_ + 2 = 5
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.
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.
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
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.
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?
> 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.
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.
I adored this post right up until:
> 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.
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.
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.
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.
My claims are as follows: - most math programs in the US schools are behind where children’s math abilities are - most school math programs do an abysmal job connecting math with real life - you can completely turn off a child to a subject/sport/activity by pushing it too hard -being numerate is a real long term advantage in life
It’s balancing these things that’s hard, if your children are above “pace” math wise, see the value of math in their everyday life, and are on track to be numerate, yes don’t push, otherwise not pushing is the disservice
I think this isn't quite the same thing, never the less: I have dyscalculia on extreme mode (/dyslexia/autism), and I was forced to do math in the 90s in the UK, rote style. I don't know if they didn't know about dyscalculia, didn't care, or whatever, but holy hell I wish I'd never been forced to do that, it's still today a fairly painful memory and I'm in my 40s now. If you're gonna force kids into math, at least make sure they're not unable to process it correctly.
Related to what the article mentions, about playing cards, I tried to get my kids into doing basic arithmetic by playing "scopa"[0] with them.
Turns out, the one who didn't like math didn't like the game either, and the one who did like math liked the game too.
So I'm not totally convinced you can just "trick" kids into liking maths, tho for sure it's a way to get them to exercise.
[0] Scopa: https://en.m.wikipedia.org/wiki/Scopa
Is there any knowledge that is recommended to be forced to kids?
Forcing is kind of hopeless. So is logic, and reasoning.
How children learn (rely on the prefrontal cortex of their 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.
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.
Must add i had struggles with mathematics. It can be interesting, but little did i understand as a pupil. Later in life, i discovered it, i became a car mechanic, then it-guy, then non-destructive tester. English is my first and only second language, its enough to lurk here, read books and serve customers on a professional level. I think i dont need french, nobody around me speaks it, i am not interested going to france..at all. All the math i was thaught, was do to the job and that filled my fridge. Its okay to push kids to university so they can use that math knowledge, but who foresees what the kid wants to work? School is not the end of the road, one can always attend courses, getting autodidactic knowledge later in life. Today we dont need 10 architects while having only 1 roof tyler.....
I'm reminded of another HN comment on learning math, more pitched at advanced maths but probably still applicable
>...recommendation is a metaprinciple: enjoy mathematics. Benjamin Finegold said similarly that the secret to chess is to enjoy every move. https://news.ycombinator.com/item?id=42290996
Since then I've watched a few times Ben's beginners chess advice aimed at kids and feel it can apply to other things, math or in my case I'm trying to apply it to trading. It's been quite good. The basic idea, enjoy doing the thing and do it repeatedly so you build pattern recognition https://youtu.be/B5bCfwCyo18
I don't get why people take it so negatively when a parent mandating kids to do/learn things they don't like.
But the entire notion of public education is rested upon mandating that kids wake up and go to school, sit down and learn things they don't necessarily like. I am pretty sure there isnt a single student who loved/found joy in all the subjects all the time.
Yet when a parent does it, there is backlash?
Humans respond to carrot and stick, and so do kids. To excel at anything, requires healthy mix of enjoyment, love, discipline and motivation. Some of these come intrinsically, others extrinsic.
taps the Case Against Algebra II sign
And then your kids and their same generation would be replaced by their peer kids from hard working boys and girls from India and China. Unfortunately curiosity only works with brilliant minds. Normal minds plus curiosity is useless.
Teach kids to do math by have them make mods for their favourite games.
A lot of people hope there is a magical way of making learning fun. The argument generally goes "young kids love exploring nature, experimenting, etc, so we are all inborn scientists. If only school did not extinguish the fire from us".
A huge problem is that giants of education such as Jean Piaget and Seymour Papert make a strong case for this. Unfortunately they generalized their own experience as kids to all others. They did not understand that they were exceptional cases, and what applies to them does not necessarily apply to 99.999% of the rest of the world.
But their message was so cool, somewhat similar to "we can all love each others", or "world peace", that it was embraced with abandon.
I was fortunate to have a great math educator in college (i.e. a guy who was teaching us, math majors, how to tech moth to kids). He told us bluntly "math is hard".
I think education would progress if one simply accepted this truth "math is hard". Stop the delusion that there is a way to make all math fun.
Still, once you accept that math is hard, you realize that the mission is the same: try to find ways so that learning math is less hard and more fun. But accept that the default state is that math is hard. There is no "royal road" to math. Aristotle was onto something.
And by the way, the fact that "math is hard" is not all bad news. The goal in school is not only to learn math, but also to learn how to work hard. There are kids for whom math feels like swimming for a dolphin. Up to a point. There will inevitably be a point where they will hit the phase of "math is hard". And it's going to come as a rude shock. It's better for this realization to come a bit early in life and a bit less shocking.
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.
I believe that the most important thing I can show my kids is how I pursue the things I enjoy. That I make time for myself and that I handle setbacks and dips in motivation. So that they will know that when you do find something that interests you, that is how you pursue it in the long run. I show them how to not quit.
I'm not great at maths, my daughters good though, I think her binge watching number blocks when small helped a lot - felt my own arithmetic getting a bit better watching it, the songs were very catchy.
Everybody is different. Some should be forced to learn and others not. Quit trying to measure fish on a tree climbing test.
There is no template for how to raise kids. Expose them to as many things as you can, figure out what interests them and feed it. Keep doing this as they grow up because they change as they grow up.
The same can be said of music, art, sports and a zillion other things.
Perhaps make them aware how important it is with examples from nature? https://duckduckgo.com/?t=lm&q=fibonacci+in+nature+examples&...
Know what, brother? I tell you that studying the humanities in high school is more important than mathematics — mathematics is too sharp an instrument, no good for kids.
Stephan Banach quoted by Steinhaus in Through a reporter’s eyes, Roman Kaluza, 1995
Have them play a game like math maze 2!
They will force themselves to play... and do math in the process.
I do agree with the overall premise of encouraging children's creativity and the things that they enjoy doing. You don't want math to become a chore.
On the other hand, some things require study and practice to be really good at, and that is "work", and many kids don't want to do the work.
Our boy, who just turned 9, is very good at math (his school's standardized tests put him at 99th percentile in the US for his grade level, though 1) I don't put a lot of stock in those standardized tests, and 2) the US doesn't exactly rank high in math skills, so this is less impressive than it sounds). He's not a genius, but he grasps concepts quickly and fairly intuitively. He's curious about the world, asks lots of questions, and is capable of understanding and retaining many scientific concepts that kids older than him would struggle with. (Example: two days ago, he was asking me about quantum computers and I mentioned that they need to be kept very cold, he asked whether they use oxygen, because oxygen turns to liquid at -173C. I thought he just made that up, but when I checked (I didn't know myself), he was pretty close (the actual number is -183C.) So he has the innate talent to work with.
But despite his gifts, he still needs practice for the math concepts to take root, and without that he makes a fair share of basic mistakes; and he still needs to improve his logic reasoning skills. So he has daily math homework after school (because math instruction in elementary schools in the US is low). We use Singapore Math workbooks (I've tried various apps and online programs, and honestly, paper workbooks are just better--but that's another topic).
He knows he's good at math and wants to continue to excel at it. (Just like a talented basketball player doesn't reach his full potential without working at it, something I repeatedly emphasize to him.) BUT he still struggles every single day to do his homework, because he prefers to play video games, shoot hoops, etc. (loves basketball, football, soccer, but has a lifelong physical disability that will prevent him from ever playing a team sport, to his great chagrin). I have to push him every single day or he would simply not do it. He actually wants to do math, and when we talk about it, he'll confirm that, but when it comes time to actually do it, he just doesn't have the willpower. (I mean, what kid prefers to practice math problems instead of play video games?). Hopefully he'll get the willpower at some point when he's older. But that day has not yet come.
That was a long reply to say: it sometimes does take a lot of pushing.
This article has all the tells of being AI generated with random bolding and constant emdashes.
This is all fun and games until your kid has school assignments with deadlines
I expected way more than a personal opinion coated in some moralization.
Humans are more terrible at teaching math than any other concept. I remember being taught algebra by a teacher that had terrible idiosyncrasies. She would sometimes write numbers and variables differently, and this caused major problems trying to understand how and why the variable was to be written differently due to new context. But she would just go on writing it differently, just because she was weird. For example, she would sometimes write 'x' using two curves that didn't touch ')(' and expected you to continue with the algebra equation as if nothing was strange. My point is that teachers still don't understand how to correctly teach math to students. They reinforce using their old methods that are overall sloppy shorthand in a space where rigor, both visually and conceptually, must be maintained. When young minds are this fresh, you cannot have this slop and idiosyncrasy in your lessons and expect students to become enlightened. So no, forcing them to do some math is not harmful. Poor teaching in a very hard space definitely is harmful.
Surprised no one here has mentioned Kumon. Hated it but it works
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.
Every kid is different. We can’t generalize the approach.
Get a set of dominoes. Make up games with them.
Learning is pain, knowing is pleasure...
math circles are good for this. i’d suggest it if there is one nearby
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 :)
At some point you have to force them for the sake of homework, just saying.
But yeah, you're better off in math if you can make it make sense on a philosophical level. That I agree with.
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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.