Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Communicating Advanced Mathematics to Kids

blogs.ams.org

Post reply on HN
Print view View original

11–20 of 58 posts

Re: Communicating Advanced Mathematics to Kids

#11

Post by skadamat »

So many things I could say about this, but I"ll let Alan Kay speak for me - https://youtu.be/p2LZLYcu_JY Alan talks about how ideas in Calculus could be manifested from an early age and a richness in understanding built up as they aged up:

- at very young ages, kids really respond well through "doing" / the enactive channel. When asked to draw a circle, kids in Papert's group would first emulate what a LOGO turtle would do by rotating their body in a circle (making tiny increments in x and y).

- as they got a bit older, the visual / iconic channel was more developed and they could understand the abstraction of a circle on pencil/paper and how the concepts carried over there

- closer to early teens, symbols were much easier to grasp and relate to, etc.

With this context in mind, there have been some cool efforts to mix the second and third channels I just mentioned to communicate advanced math concepts. Vi Hart and Grant Sanderson's youtube channels come to mind. Here are my favorite videos by Grant:

- "What does it feel like to invent math": https://www.youtube.com/watch?v=XFDM1ip5HdU

- On the visual intuition behind a hard problem on the Putnam exam - "The hardest problem on the hardest test": https://www.youtube.com/watch?v=OkmNXy7er84

- From vectors to matrices to vector spaces to higher-level ideas like the link between linear algebra and calculus: "Essence of linear algebra" series: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

What I especially like about Grant's videos, is that he often walks through what a mathematician would do, the questions she would ask, etc.

Re: Communicating Advanced Mathematics to Kids

#12

Post by dboreham »

Unfortunately if you follow the link to the proposed site for publishing kid-friendly mathematics articles, then search with a filter for mathematics, you get zero results :(

fwiw I have made some attempts to get my own children interested in 'advanced' mathematics. I found the TV series "Story of Maths" by Marcus du Sautoy to be helpful. I've also had some positive results watching lectures from Harvard's E-222 class[2] with my older son (14).

[1] https://www.netflix.com/title/80093836 [2] http://matterhorn.dce.harvard.edu/engage/ui/index.html#/1999...

Re: Communicating Advanced Mathematics to Kids

#13

Post by vog »

jonnybgood wrote: post #3
vog wrote: post #2

This strongly reminds me of the various math magazines we have here in Germany. (I know that other countries have similar magazines, but I only grew up with the German ones, except for one Canadian one.) The most popular seems to be "Wurzel" [1] (translated: "root"). The target audience of the magazines are students (pupils) at school, as well as young students at university. The articles explain advanced math topics…

You reminded me of Chalkdust [0]. I would love to see more publications along these lines. [0] http://chalkdustmagazine.com

Very nice site! Too bad they don't offer an RSS feed, so it's hard for me to keep in touch with that site.

Re: Communicating Advanced Mathematics to Kids

#14

Post by DoreenMichele »

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 blank space in an equation as X so you can more easily move the blank space around.

He had been doing algebra in his head for years to infer stats in games while simultaneously feeling baffled and intimidated by formal math, like the concept of algebra. He had assumed all variables were like E=mc^2 where letters stood for specific concepts, not for floating "=___".

Re: Communicating Advanced Mathematics to Kids

#15

Post by ColinWright »

vog wrote: post #13
jonnybgood wrote: post #3

Earlier quoted context omitted.

You reminded me of Chalkdust [0]. I would love to see more publications along these lines. [0] http://chalkdustmagazine.com

Very nice site! Too bad they don't offer an RSS feed, so it's hard for me to keep in touch with that site.

Doesn't this work?

http://chalkdustmagazine.com/feed/

Re: Communicating Advanced Mathematics to Kids

#16

Post by montecarl »

vog wrote: post #2

This strongly reminds me of the various math magazines we have here in Germany. (I know that other countries have similar magazines, but I only grew up with the German ones, except for one Canadian one.) The most popular seems to be "Wurzel" [1] (translated: "root"). The target audience of the magazines are students (pupils) at school, as well as young students at university. The articles explain advanced math topics…

This reminded me of a math professor during my undergrad. He would print out copies a math problem from some journal that published these kinds of interesting problems that are pretty hard and a little different from what you normally see in class. He would then put the copies in the halls of the math building. If you could bring him your solution and explain it to him he would give you $20 and mail in your answer to the journal, who would then send you back a little certificate and publish your name in the next edition.

It was by solving one of these problems (using math that was above the course I was currently taking) that I started to interact more with the math department and decided to take more advanced classes!

Re: Communicating Advanced Mathematics to Kids

#17

Post by colomon »

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.

Re: Communicating Advanced Mathematics to Kids

#18

Post by mkesper »

vog wrote: post #2

This strongly reminds me of the various math magazines we have here in Germany. (I know that other countries have similar magazines, but I only grew up with the German ones, except for one Canadian one.) The most popular seems to be "Wurzel" [1] (translated: "root"). The target audience of the magazines are students (pupils) at school, as well as young students at university. The articles explain advanced math topics…

I was reminded of the book 'The number devil' (Zahlenteufel) which showed me you can reason with children about math if only you do away with intimidating language: https://en.m.wikipedia.org/wiki/The_Number_Devil

Re: Communicating Advanced Mathematics to Kids

#19

Post by opportune »

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.

When I was a child, the first thing that made sense to me was that "x is the number that makes the statement true". That is, 100 = 100, so if 25 * x = 100, you need to figure out what value of x multiplied by 25 gives you 100. I didn't even understand the manipulations or how you would really solve for x at first, but I did understand that you were trying to figure out the number that would do that. I would just phrase it like a puzzle, like "what plus 9 equals 14" or "3 times what equals 42"?

For some reason, one of my earliest memories I have is from when I would try to show off to older kids that I understood algebra.

Re: Communicating Advanced Mathematics to Kids

#20

Post by laderach »

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 version. They have a ton of super interesting "mini" papers about all sorts of topics. In that issue alone I learned about:

- The metabolism of alcohol

- The meteorology of Jupiter

- Simpson's paradox

Take a look at it. I think you might be impressed too.

The other site I have fallen in love with recently is Fermat's Library (https://fermatslibrary.com). They essentially publish an annotated paper every week (usually physics, cs, math). Reading their papers is now a part of my weekly routine.

Post reply on HN