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.
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 :)
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
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.
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.
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!
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).
Perhaps make them aware how important it is with examples from nature? https://duckduckgo.com/?t=lm&q=fibonacci+in+nature+examples&...
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.
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'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 that might work for getting your kids interested in modular arithmetic: The Chicken McNugget Theorem.