
Communicating Advanced Mathematics to Kids - ColinWright
https://blogs.ams.org/matheducation/2017/12/11/communicating-advanced-mathematics-to-kids/
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vog
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.
Not too advanced, of course, but still far outside what they see in school.
The articles use formalisms only where they make things more clear. They build
on common school knowledge. Advanced formalisms are only okay if they are
introduced in the article. And the articles aren't too long. The goal is that
everything can be understood by students, if they are interested.

Also, the magazines usually contain reports about math olympiads and similar
activities, usually written by participants (i.e. by students, not teachers).

Finally, these contain math exercises. But don't think of school exercises.
Think of math olympiad, just that you have more time to solve them. Students
send their solutions in and it is published in the magazine which students
solved which exercise successfully.

The latter one should not be underestimated - it is more or less how all these
magazines started: You have math competition, the students go back to school,
and you want to keep in touch with them, so you offer them so solche math
puzzles in their free time, give them feedback to their solutions, and do
everything they don't feel alone with their mathematical interests. You can do
that individually only with so many students, so you start a magazine for a
more efficient communication.

[1] [http://wurzel.org/](http://wurzel.org/)

~~~
mathgenius
> far outside what they see in school

There's so much cool mathematics out there that school kids can understand
given a good enough teacher. It's really disappointing to me the crud that
gets taught in school, but then i remember that a big part of this is the
teachers just aren't that inspired. All it takes is one or two good teachers
to really change a kids outlook on mathematics.

~~~
briandear
You also have the problem (at least in public schools,) that teachers are
obliged to “stick to the curriculum” and much of a teacher’s time is spent
catering to the lowest common denominator lest the test scores fall to an
unacceptable level.

I might argue that kids should get a double period for math, especially
earlier in their school careers — one class to teach the fundamentals, another
class to simply explore. The benefit being that critical thinking is enhanced
in all academic areas and not just the obvious in mathematics.

~~~
mathgenius
I hated learning the multiplication table when I was 5. Basically, I boycotted
the whole thing. It occured to me recently, why don't they talk about the
holes in the multiplication table? These are the prime numbers! So easy to
mention this and may have inspired my 5 year old self to dig a bit deeper.

My first real mathematical experience was in second grade. My teacher had some
hoops on the floor, and was putting coloured shapes inside. Red shapes in one
hoop, and triangles in another hoop. But then the problem arose: what to do
with the red triangles? It was total magic when she dragged one hoop to
overlap with another hoop and placed the red triangle in the overlap. Venn
diagrams for six year olds.

And I still can't multiply six times eight! I have to work it out every
time...

~~~
vog
_> And I still can't multiply six times eight! I have to work it out every
time..._

No offense intended, but if that still bothers you, it's time to learn it.

Either by accepting the offer you got with 5 (that is, memorizing the
multiplication table - BTW, it is more fun to do this with 15x15 or 20x20
rather than 10x10).

Or by playing mental calculation games and trying to get high scores in speed.

(Essentially, this is the same as with learning vocabularies for a foreign
language. The word "4x3" is translated to the other word "12".)

Maybe your teachers failed to make it interesting to your 5-year-old self. But
your current self does seem to be interested, so that can't be the issue
anymore.

You can critize your teachers that they didn't make your learn it at 5, but
you can't critize them for still not having it learned later as an adult.

------
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...](http://flowcytometry.sysbio.med.harvard.edu/files/flowcytometryhms/files/herzenbergfacshistory.pdf))
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](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.

~~~
todd8
I grew up in an inner city Detroit neighborhood. The junior high school that I
attended was pretty rough so, to avoid the gangs that formed after school, I
quickly ran over to the near by public library and stayed there until it was
safe to walk home around dinner time.

A friend showed me a magazine at the library; it was Scientific American and
it completely hooked me. This was 1963 and SA was then a great magazine. I
read every current issue and then read the bound volumes of past issues. My
favorite monthly columns were Martin Gardner's Mathematical Games and the
Amateur Scientist. I read every one of those two columns ever published.

The schools I attended were not very good, but I learned a lot of math and
science during those years at the library. I went on to score very high in
math and science, got into great colleges and ended up with a very successful
career.

~~~
laderach
Thank you for sharing your story! I am going to google Martin Gardner's
Mathematical Games later this afternoon!

~~~
nileshtrivedi
A book that is based on many of Martin's articles is: "Symmetry, Shape &
Space".

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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 "=___".

~~~
colomon
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.

~~~
burp3141
I've always translated "x" to "?" (the value to be discovered) as a mental
shortcut. The "?" symbol might be easier to interpret for third graders.

~~~
colomon
I think they are used to seeing empty boxes for mystery values.

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skadamat
So many things I could say about this, but I"ll let Alan Kay speak for me -
[https://youtu.be/p2LZLYcu_JY](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](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](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...](https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)

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.

------
CurtMonash
The great teachers of math to kids in the US are of course the Ross Program
folks. (When last I checked in I thought Boston University's Promys was
actually livelier than the original Ross Program at Ohio State.) They
basically take very smart kids and help the rediscover much of abstract
algebra and basic number theory.

Decades later, I probably couldn't state quadratic reciprocity any more, let
alone prove it. But proving the Two Squares Theorem is still one of the best
ways to clear my mind of less pleasant thoughts, should I need such a device.
It's just a whole lot of fun, even if you go in assuming next to nothing. (I
start by proving that the Gaussian Integers are a Euclidean Domain and that
all Euclidean Domains are Principal Ideal Domains, and proceed from there. It
doesn't take long.)

------
mathgenius
Quantum journal is also doing a version of this:

[https://quantum-journal.org/call-for-papers-good-popular-
sci...](https://quantum-journal.org/call-for-papers-good-popular-science/)

~~~
ivan_ah
Wow nice, thanks for posting this.

------
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?

------
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](https://www.netflix.com/title/80093836)
[2]
[http://matterhorn.dce.harvard.edu/engage/ui/index.html#/1999...](http://matterhorn.dce.harvard.edu/engage/ui/index.html#/1999/01/82345)

------
sitkack
Tangentially, I think wikipedia should really focus on increasing the depth
and depth(ha) of
[https://simple.wikipedia.org/wiki/Main_Page](https://simple.wikipedia.org/wiki/Main_Page)

We need advanced concepts explained in simple clear language so that students
have enough context to anchor the knowledge.

------
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.

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beagle3
Tangentially related, this looks amazing, and I wish there were more schools
like this

[http://www.proofschool.org/](http://www.proofschool.org/)

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perseusprime11
What about Art? Are there any good sites for parents and kids to get really
deep into art such as drawing, painting, etc?

