But probably zeroth, most important, is modelling good behavior. Kids are mirrors.
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.
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.
Nothing like cheating the system to know the system
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).
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 :)
The original concept in the article of exploration is great. Some kids want to explore math, some science, some music, and some Starcraft.
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.
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.
Well, and thirdly, that your worth as a person is determined by your results in graded examinations, and by extension, your salary or some other numerical rating decided by someone else.
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.
This is really stupid.
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
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.
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.)
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.
Some things aren't optional, and if they are seen as such, it's going to force the child to learn later in life what they couldn't earlier on.
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.
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.
They will force themselves to play... and do math in the process.
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.
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.
ogogmad•5h ago
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•5h ago
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•5h ago