Math for eight-year-olds: graph theory for kids

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.

Agree, This applies to pretty much every topic. If you make it relevant, interesting and create a safe environment where mistakes are ok a lot can be taught to kids.

I was fascinated as a kid from various types of sailor knots. I was in the air modelling, then computer club, and our neighbours were the young sailors, but I've never got into it.

But I know kids around me were fascinated by them too (it could be that we were after all living in a fishing/sea town with lots of big ships, etc.).

But then even for girls (knitting, or other activities) - there is something about graph theory to be found there. Just wondering...

>I'm very surprised that we don't teach basic graph theory in <= high school education

Not US, but I learned graph theory in HS, so it is done in some countries (CS class though, not maths)

> And Hamkins shows it can go all the way down to eight-year-olds.

At the bottom he mentions his previous visit - Math for seven-year-olds: graph coloring, chromatic numbers, and Eulerian paths and circuits http://jdh.hamkins.org/math-for-seven-year-olds-graph-colori...

I had like one grade where it was taught, but I mean, it would've been so much cooler to talk of things in Matrix-algebra land in terms of graphs.

I think Bourbakian formalism should be kept where it belongs : > upper undergrad. Math should be about pictures and things. Also see, http://pauli.uni-muenster.de/~munsteg/arnold.html

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.

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/

The V-E+R follows the pattern of zero-dimensional, one-dimensional, two-dimensional, and this alternating sum formulation continues for the Euler characteristic in higher dimensions. So that is one reason to keep V-E+R.

Another reason, however, is that although some negative numbers show up, the numbers are all very small, and this could be a good opportunity to introduce some exposure to negative numbers.

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...

I believe it was this article: 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.

That's a bit cynical. I think at least a large portion of it is that people tend to believe that whatever skill sets they have are important.

So a plumber thinks that basic plumbing knowledge is something everyone should have. Chefs think that everyone should be able to cook the basics. Programmers think that programming is valuable knowledge that everyone should have some familiarity with.

If confronted with this, all of them will be able to rattle out perfectly rational arguments in defense of their positions. They aren't wrong. It is just that what they prioritize or think about most often is influenced by what they know and do. Basic plumbing knowledge is useful for anyone who owns a home (or just uses a toilet, sink, or shower), but how often do you see chefs advocating for that sort of practical education? Being able to cook a nice meal for friends or family is a great skill with a lot of social value, and cooking your own food can be very economical, but how often do plumbers advocate for that?

We see a lot of people advocating for tech education and extolling the virtues of tech knowledge because we surround ourselves with people who are already in this field.

This said, I think there is some truth in what you say. I get pretty suspicious when I see national campaigns for tech education being pushed by the elite. Business leaders or politicians; people who have made something other than programming their profession. Maybe there is a plumbing equivalent of things like code.org, but if so I am not aware of it.

Graph theory is not a subject taught solely for computer science. In fact, graph theory has a rich mathematical history independent of computer science, even through today.

The reason graph theory (and mathematics in general) is nice to teach is that it includes "critical thinking" and "composition" and "creativity," it's arguably the most efficient, direct way to teach these skills, and all you need is the knowledge to teach it and a writing utensil.

Graph Theory is pretty widely applicable. It's been a core course in my undergraduate program for years (I think since the beginning of the program). For example, you can apply it to a number of different domains in physics. It can be used to analyze electrical circuits, pipe flow, and mechanics. It's at the core of a number of packages related to these topics. The circuit simulator SPICE uses graph theory as does Modelica and MapleSim. That's only the physics applications. I've read papers that use graph theory in a lot of domains. There was a good book I used as reference when I looked at using graph theory for CAD (as part of an undergrad project), but I don't recall it as that was years ago.

I very likely would have done a graduate degree under a professor studying graph theory (he was my 4th year project supervisor), but he died over New Year's that year and I had to change supervisors for my last four months. But, he was the reason I decided to go to grad school in the first place.

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.)

Probably a girls' school.

Screenshot of the site: http://i.imgur.com/yFfyjN0.png