
Math for eight-year-olds: graph theory for kids - AllTalk
http://jdh.hamkins.org/math-for-eight-year-olds
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j2kun
I'm very surprised that we don't teach basic graph theory in <= high school
education. It has such a nice, gradual slope from puzzles and pictures to
proofs, algorithms, and all sorts of science. I've done activities/lectures on
the topic to all levels of high school (some with notes [1]), and it is
routine to see amazement and engagement. And Hamkins shows it can go all the
way down to eight-year-olds. It seems like a win-win to include it in every
math teacher's repertoire. It can go as deep as the students want it to go.

[1]: [http://jeremykun.com/2011/06/26/teaching-mathematics-
graph-t...](http://jeremykun.com/2011/06/26/teaching-mathematics-graph-
theory/)

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primitivesuave
I found your site through HN a while back, and since then I've sent a link to
your site to pretty much every math/STEM teacher I meet (and I encounter quite
a lot of them). Many of them have specifically mentioned to me what a great
resource you've created for teachers and how you got their kids excited about
math. I hope you know that your work is having a tremendous impact on math
education and that impact will grow exponentially.

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j2kun
Wow, I really appreciate that, thank you.

I just wish I had more opportunities (and time, money) to try more things in
classrooms.

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davyjones
Your write up on EC and tensors, I enjoyed it a lot. Thanks for the excellent
effort!

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_dark_matter_
This is very interesting. I was recently looking over Leslie Lamport's
writings[0] and noticed that his first publication was in high school, and was
actually about graph theory. Similar to another comment on here he was
interested in braids, a branch of graph theory.

Obviously he is a prodigy compared to the general populace. But perhaps an
earlier introduction to some of these mathematical concepts led to the man we
know today? If so, one would hope that a similar interest would motivate young
students to take a different path, one where mathematics isn't quite so scary.

[0] [http://research.microsoft.com/en-
us/um/people/lamport/pubs/p...](http://research.microsoft.com/en-
us/um/people/lamport/pubs/pubs.html#bxscience)

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raffi
When I was in high school and early on in college--I didn't enjoy math. I
always thought of math as the drone of memorizing formulas and plug+chug.

I later took a class that used a textbook, Laboratories in Mathematical
Experimentation. The book and that class were the first time math became play
for me. A big part of that class was digging into graph theory.

Really fun stuff.

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kaitai
That's a great book. It's got a lot of number theory and dynamical systems as
well, and the topics covered fit really well with experimentation using a
computer.

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melling
Cached:
[http://webcache.googleusercontent.com/search?q=cache:9kOKiXL...](http://webcache.googleusercontent.com/search?q=cache:9kOKiXLAQXIJ:jdh.hamkins.org/math-
for-eight-year-olds/+&cd=1&hl=en&ct=clnk&gl=us&client=safari)

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eridius
This is very cool. I actually learned something from this even though I'm much
older than the kids being taught :) Are there any resources for learning graph
theory that present it in a fashion like this?

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jnotarstefano
I apologize for the self promotion, but some people told me they immediately
grasped the Havel-Hakimi Algorithm by solving this puzzle I made:
[http://jacquerie.github.io/hh/](http://jacquerie.github.io/hh/)

~~~
eridius
No need to apologize! I haven't heard of the Havel-Hakimi Algorithm before,
and I don't have the time to actually try and solve your puzzle right now, but
I appreciate the link and will check it out later.

Although just reading the description, I do have one question: What is a
"degree sequence"? I going to go ahead and assume that it's
[https://en.wikipedia.org/wiki/Degree_(graph_theory)#Degree_s...](https://en.wikipedia.org/wiki/Degree_\(graph_theory\)#Degree_sequence).
If that's correct, I'd encourage you to add a hyperlink to the term "degree
sequence" with that URL, for people like me with zero background in graph
theory.

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jnotarstefano
Yes, that's what I meant with "degree sequence". Thanks for the suggestion!
That description is more succinct than it needs to be.

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fred256
I wonder if instead of V-E+R it would be more intuitive to use V+R-E so there
are no intermediate negative numbers in the calculation.

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j2kun
So it turns out that this formula generalizes to an alternating sum over many
dimensions [1] (although it can be stated more simply than Wikipedia does).
From that perspective, it makes more sense to put the minus sign in the
middle.

In either case, I don't think it is that big of a conceptual stumbling block
to have a minus sign in the middle...

[1]:
[http://en.wikipedia.org/wiki/Euler_characteristic#Generaliza...](http://en.wikipedia.org/wiki/Euler_characteristic#Generalizations)

~~~
jonsen
But it is an operational stumbling block when subtraction gives negative
results. It may lead to calculation errors otherwise avoided. In a pedagogical
setting like this one error sources should be minimized.

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learnstats2
But the students are at exactly the stage where calculating with negative
numbers has been introduced and needs practice and precision, so this works
out _very_ nicely with the curriculum.

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afterstep13
Also see, [http://csunplugged.org/](http://csunplugged.org/)

From the webpage:

CS Unplugged is a collection of free learning activities that teach Computer
Science through engaging games and puzzles that use cards, string, crayons and
lots of running around.

The activities introduce students to underlying concepts such as binary
numbers, algorithms and data compression, separated from the distractions and
technical details we usually see with computers.

CS Unplugged is suitable for people of all ages, from elementary school to
seniors, and from many countries and backgrounds. Unplugged has been used
around the world for over twenty years, in classrooms, science centers, homes,
and even for holiday events in a park!

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bambax
There was a truly fantastic post a few years ago about how to teach binary
notation to eight-year-olds.

Children are very capable of understanding basic or even not-so-basic math;
only when they learn that «maths are for nerds» do they decide it's not for
them.

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j2kun
I believe it was this article:
[http://www.garlikov.com/Soc_Meth.html](http://www.garlikov.com/Soc_Meth.html)

One of the shining ideas in this lesson is the difference between an object
and its representation, a nail which I think the author hits squarely on the
head.

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bambax
Yes, it was! Thanks!

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raldu
There is much emphasis on teaching kids computer and math related subjects
these days. Although it is exciting to see educational initiatives like these,
they might actually be motivated by economical and institutional needs rather
than taking into account individual interests of children. A shortage of
computer programmers emerges and there is instantly an interest to teach
children graph theory...

Math is not the only thing that is interesting. Why not have, "critical
thinking for kids", or "composition for kids", "cinema for kids", "creativity
for kids", or something else? A great deal of other skills and literacies are
left out just for the sake of meeting the industrial "demand".

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marincounty
No, I think math is very important. There are a few subjects I wish I was
taught in high school though.

1.The scientific method(I can see young eyes rolling already though) 2\. The
Placebo effect 3\. Basic statistics(with an emphasis on how adults often use
statistics to deceive) 4\. Basic course in Psychology(I don't recall if my
high school had any psychology courses. In College, I had a great Psychology
instructor. His course covered every thing I listed. When I look back at
college, I can honestly state he changed the way I viewed to world. I remember
thinking, I wish I had this information in HS. He was a great teacher.)

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octatoan
And that correlation does not imply causation.

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ufo
Why are all the kids girls?

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smorrow
Probably a girls' school.

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trialstartup
Cached:
[http://hn.premii.com/#/article/9354597/](http://hn.premii.com/#/article/9354597/)

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ChrisArgyle
Heroic. This is exactly the kind of thing America needs to get over the
bizarre general notion that "math is dumb".

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fit2rule
I will try this on my 7-year old. I'm fairly certain that he's going to enjoy
this.

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kelukelugames
looks like it's down already.

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AllTalk
Screenshot of the site:
[http://i.imgur.com/yFfyjN0.png](http://i.imgur.com/yFfyjN0.png)

