I just wish I had more opportunities (and time, money) to try more things in classrooms.
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...
Not US, but I learned graph theory in HS, so it is done in some countries (CS class though, not maths)
I faintly remember that we did `use` graph theory in our HS assignments, but haven't actually touched hypothesis or proofs, that I now associate with it.
I remember we wrote programs to higlight a graphs skelet, find shortest path, search for components, e.t.c.
Discussions on correctness and efficiency were informal.
At the bottom he mentions his previous visit -
Math for seven-year-olds: graph coloring, chromatic numbers, and Eulerian paths and circuits
I think Bourbakian formalism should be kept where it belongs : > upper undergrad. Math should be about pictures and things. Also see,
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.
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.
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.... 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.
That challenge is always to prove for definite that it will always work. The proof is in, well, the proof.
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.
In either case, I don't think it is that big of a conceptual stumbling block to have a minus sign in the middle...
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!
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.
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.
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".
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.
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.
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.
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.)