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Communicating Advanced Mathematics to Kids

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Re: Communicating Advanced Mathematics to Kids

#41

Post by threatofrain »

colomon wrote: post #17
DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

I've actually been trying to explain that exact concept (algebra variables) to some advanced third graders. It's been surprisingly hard to get them to grasp it.

Have you tried analogous approaches, such as showing kids an empty box, a question mark, multiple metaphors, etc?

I find that visual approaches work well, but when you write an English letter which has already been used for other purposes, it's a little less clear.

Re: Communicating Advanced Mathematics to Kids

#42

Post by kirillzubovsky »

Honestly, this is a fantastic idea. As a dad of a toddler I am starting to look for more math-oriented materials, and this will definitely be on the reading list.

I especially love the "How to write for this audience" section. It says: be concise, convey the excitement, say exactly what is important and why, and draw the reader in.

This is how most concept should be explained, to adults or kids, doesn't matter. As someone who's gone through an engineering degree, so much of it was written/presented in convoluted "this is going to be difficult" format, instead of this playful "here, try something tasty" one. Wish more educators would adopt this kid-friendly way for older kids too :)

Edit: Do you know any dads who have been very successful teaching kids math at home, better than they are taught in schools? I'd love interview them for my podcast.

Re: Communicating Advanced Mathematics to Kids

#43

Post by iak8god »

DoreenMichele wrote: post #38
iak8god wrote: post #35

Earlier quoted context omitted.

> A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. I don't see any reason to restrict this to those homeschooling for nonreligious reasons. There are plenty of bright homeschooled kids interested in advanced subjects regardless of their parents' primary motivation for homeschooling.

I am in no way restricting it, merely suggesting fertile ground to find enthusiastic early adopters who can help it flourish.

I am suggesting that the broader homeschooling community may be equally fertile ground to find enthusiastic early adopters.

Re: Communicating Advanced Mathematics to Kids

#44

Post by mncharity »

I'm interested in insightful descriptions of the physical world for young kids.

For illustration, what might it mean to teach friction well? Is it memorize-and-regurgitate of bogus definitions in late primary? Or plug-and-chug of Arrhenius's law of large objects sliding on pig fat in high-school? Or instead, could we talk about sock nubbies in K-3? Their similarity to cleats and crampons and klister. How to avoid slipping and falling. Sliding and slipping and sticking - pervasively surrounding us. Nanoscale origins connecting nicely with macroscale behavior. And for the numerate, a feel for reasonable order-of-magnitude values. So physics, but coming from sort of an engineering perspective - hands-on, pragmatic, rough quantitative.

Could we approach math similarly? What might it mean to teach category theory to young kids? Perhaps math as a vocabulary for describing similarities among everyday things? "Oh, you missed the square, but you can get it the next time you go around the board":"It's almost one o'clock now, so we'll wait for lunch-time tomorrow":"Missed the parking space, so we'll drive around the block". Movement around short loops is a theme of everyday experience. Could it be taught? Now, or with future AR/VR tech?

In preK-1, learning to describe physical properties is a thing. Rough, smooth, etc. But instead of drawing on well designed vocabularies from industrial design or material science, it's left to dysfunctional ad hoceries. Similarly, K-12 physics education leaves students having seen almost no physics. What about math?

Could math be taught not as a random fun thing to do, like crossword puzzles and fashion magazines, but as a deeply insightful and broadly illuminating vocabulary for describing everyday experiences?

Re: Communicating Advanced Mathematics to Kids

#45

Post by rb808 »

laderach wrote: post #20

My son is now 4 years old, he has been showing a great deal of interest in playing with numbers and puzzles, so I have been thinking quite a bit about this lately. The other day I ran across an issue of Scientific American from the late 70s ( http://flowcytometry.sysbio.med.harvard.edu/files/flowcytome... ) and I was super impressed by the quality and educational value of the content. Much superior to its current ver…

Scientific American looks awesome. Love the ads too,

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Re: Communicating Advanced Mathematics to Kids

#46

Post by dbcurtis »

DoreenMichele wrote: post #37
dbcurtis wrote: post #31

Earlier quoted context omitted.

I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks. A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books…

My son is actually math challenged and also a science nerd. This is a whole other mind-boggling challenge. I bought math books full of words off the bargain table for as little as a dollar and, after sorting things out with his father, just gave my son the stack of books to read. No tests. No written work. No problem solving. Just read these books. That finally worked and he has a good grounding in math, though he ca…

I hear you. Math isn't arithmetic. Exploring math from the discrete math and geometry side often is a good approach for those kinds of kids.

Re: Communicating Advanced Mathematics to Kids

#47

Post by normaluser_ »

dbcurtis wrote: post #31
DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks. A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books…

It sounds like you are an upper middle or upper class family. There are gifted children in the US that aren't identified as such that come from lower class families who are deprived of their education. I checked the AoPs site and if you get the pre-algebra -> calculus textbooks + solution guides it's over $200. This may not sound like a lot to you (as you suggested) because it is due to your class. This is something some poor families cannot do. Even if they want to buy those books. Sending your middle schooler or high schooler to take college level classes is another sign of class status. I believe we should have schools like AoPs and the Proof School targeted not at the wealthy gifted children, but poor gifted children. I also think these schools shouldn't filter applicants out by SAT scores (since mostly gifted children from well off families seem to do better than gifted children without access to education). It seems like most places ignorantly assume the gifted only come from well-off places and put cultural barriers (such as exams) to identify them. This class advantage carries over into university admissions when the well-off students have 30-60+ credit hours from colleges coming in, as opposed to the gifted kids from poor families with 0 college credits. The former are admitted to elite schools, while the latter are denied. If you look around, these elite prep schools and elite colleges tend to lack economic diversity. Teaching advance math to gifted children of the elite, while excluding the gifted children of the poor (due to barriers of entry) do a disservice to our society as a whole.

Re: Communicating Advanced Mathematics to Kids

#48

Post by DoreenMichele »

dbcurtis wrote: post #46
DoreenMichele wrote: post #37

Earlier quoted context omitted.

My son is actually math challenged and also a science nerd. This is a whole other mind-boggling challenge. I bought math books full of words off the bargain table for as little as a dollar and, after sorting things out with his father, just gave my son the stack of books to read. No tests. No written work. No problem solving. Just read these books. That finally worked and he has a good grounding in math, though he ca…

I hear you. Math isn't arithmetic. Exploring math from the discrete math and geometry side often is a good approach for those kinds of kids.

We pursued a statistics track.

Re: Communicating Advanced Mathematics to Kids

#49

Post by [deleted] »

normaluser_ wrote: post #47
dbcurtis wrote: post #31

Earlier quoted context omitted.

I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks. A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books…

It sounds like you are an upper middle or upper class family. There are gifted children in the US that aren't identified as such that come from lower class families who are deprived of their education. I checked the AoPs site and if you get the pre-algebra -> calculus textbooks + solution guides it's over $200. This may not sound like a lot to you (as you suggested) because it is due to your class. This is something…

[deleted]

Re: Communicating Advanced Mathematics to Kids

#50

Post by dbcurtis »

normaluser_ wrote: post #47
dbcurtis wrote: post #31

Earlier quoted context omitted.

I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks. A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books…

It sounds like you are an upper middle or upper class family. There are gifted children in the US that aren't identified as such that come from lower class families who are deprived of their education. I checked the AoPs site and if you get the pre-algebra -> calculus textbooks + solution guides it's over $200. This may not sound like a lot to you (as you suggested) because it is due to your class. This is something…

I'm not sure why you were downvoted, as you are absolutely correct. I've lived both sides of that.

I grew up in rural fly-over land, and my little farm country high school with a very high proportion of kids on the lunch subsidy didn't prepare me very well for engineering school. Maybe one kid every other year would attempt engineering school. My pig farmer father died when I was 5, but my mother managed to stuff enough money away even in the lean years that I had money for a cheap land-grant university.

As I mentioned, I wasn't all that well prepared. I remember one night when DiffEQ homework was kicking my butt, and said to my self: "Ether get this stuff under your belt, or go home an clean hog barns for the rest of your life." I chose option A. My wife's parents were dairy farmers. She was the guru of scholarship application essays... that paid for her undergrad degree.

So, I get what you are saying. I've lived it. My wife lived it. But between us we've accumulated 5 degrees, made some good investments, been in a couple of situations where stock options were pleasantly large, and yes, work is optional right now, even living at Silicon Valley prices. Pardon me if I don't appologize for accompishing what YC and HN are all about.

So your post is a little short on actionable solutions to the problems we both see as clear as day. Here is a suggestion: MathPath has a need-tested scholarship fund so that kids that can't afford the camp can go. Tax deductable donations gladly accepted. Join me in donating. Then spread the word about MathPath -- anybody can apply.

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