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Math for seven-year-olds

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Re: Math for seven-year-olds

#51

Post by j2kun »

kaitai wrote: post #39
j2kun wrote: post #35

Earlier quoted context omitted.

At a high level you're right, Common Core philosophy does encourage this sort of lesson. The unfortunate part is that Common Core still is largely a list of facts that students need to know, and when they need to know them. This is why graph theory is not "compatible" with the standards, because in the huge list of topics they pretend these things don't exist. And since the Common Core is really a document for non-te…

I'd disagree that it's a list of facts; the high school modeling standards are skills. I've read some good discussions of whether the earlier-year standards are useful for their age groups and am not sure (I think they're pretty reasonable). The high school modeling and geometry components are great. But what does Common Core have to do with graph theory not being taught in elementary school? It never has been, and n…

The modeling standard is, I feel, the most honest part of the standards. I'm arguing that if someone tried to teach graph theory as part of, say, modeling (which it is by all means), then they would see blowback from the people that make sure teachers are working toward meeting the standards.

Re: Math for seven-year-olds

#52

Post by j2kun »

gohrt wrote: post #47
j2kun wrote: post #35

Earlier quoted context omitted.

At a high level you're right, Common Core philosophy does encourage this sort of lesson. The unfortunate part is that Common Core still is largely a list of facts that students need to know, and when they need to know them. This is why graph theory is not "compatible" with the standards, because in the huge list of topics they pretend these things don't exist. And since the Common Core is really a document for non-te…

There are so many hours in the day. Either you argue that graph theory is more important than the other topics (which?) or you acknowledge that graph theory is an enrichment topic for some students who learn the core material faster or devote more time to math study. It is true that Common Core lacks "enrichment" -- by defining a minimum standard, it doesn't specify what to do with student with more capacity to learn…

I don't want to argue that graph theory is more important (though I could list which topics I think it's more important than). Rather I want to argue that, partially because primary and secondary school educators don't have so many years of preconceptions about the right way to teach the subject, it can do a better job building the underlying skills we want to teach students in teaching them math. We don't teach math because we want students to know facts (the correct answer to "What's the derivative of arccsc(x^2)?" is almost always "who cares?").

I certainly don't think that basic graph theory should be reserved for "advanced students." This second grade experiment shows that it's accessible to everyone.

Re: Math for seven-year-olds

#53

Post by j2kun »

pbhjpbhj wrote: post #49
j2kun wrote: post #34

Earlier quoted context omitted.

I think a good answer is going to depend heavily on your goals (applied or theoretical). Maybe you could elaborate on that?

Um ... bit of both. My goal is personal enjoyment - I've done graduate level maths [way in the past] but graph theory never really featured for some reason. Thanks for your continued consideration.

There are a lot of books out there for really applied and really theoretical versions. I personally prefer the CS perspective, which spends a lot of time on problems about graphs (finding matchings, covers, cliques, flows, traversals satisfying certain properties). A good overview text is Bondy & Murty[1]. This text sort of straddles theory and practice in that you get lots of topological intuition (like Euler characteristic), and lots of algorithms and applications. One thing that's conspicuously missing is a treatment of random graphs, which is a huge topic both in theory and in applications. I do like that the book covers some basic Ramsey theory, as this is one of the most popular topics in combinatorics and it gives you a good flavor of what's going on in modern research there.

[1]: http://www.maths.lse.ac.uk/Personal/jozef/LTCC/Graph_Theory_...

Re: Math for seven-year-olds

#54

Post by anifow »

lifeofanalysis wrote: post #32

Interesting co-incidence. Just last week, I sent out an email to my friends, saying that I want to teach mathematics to their kids by a math-by-email service, kinda like the chess-by-email of the old days. The idea is quite simple: I will send out a daily email with a grade appropriate set of math questions and/or games. Your child provides the answers back by email. I check the answers, provide corrections/feedback.…

I may be of assistance. Send me a PM

Re: Math for seven-year-olds

#55

Post by arm »

oldbuzzard wrote: post #44
lifeofanalysis wrote: post #42

Earlier quoted context omitted.

Your URL is broken -- has extra dots at the end.

Fixed

EDIT 4: The solution: use a dash. 😤

―――――――――

EDIT 3: Okay, I give up.

―――――――――

EDIT 2: Wow, okay, so my ZERO WIDTH SPACE was automatically escaped instead of treated as a separator. Anyway, I’m pretty sure the comment system accepts Markdown, so you should be able to use Markdown’s URL syntax to clearly mark which part is the URL without using a space to do the same:

[1] See [http://gcpm.rutgers.edu/books.html](http://gcpm.rutgers.edu/... this was a pale imitation of what Soviet era math circles would offer but is still way beyond anything extant.

―――――――――

EDIT 1: Scratch that! Looks like as long as there’s no space, it’s still considered a part of the URL regardless! Perhaps using U+200B ZERO WIDTH SPACE would still be considered a valid separator and could be used in place of U+0020 SPACE:

[1] See http://gcpm.rutgers.edu/books.html​… this was a pale imitation of what Soviet era math circles would offer but is still way beyond anything extant.

―――――――――

Just a tip—instead of adding a space after your three periods, you could have used U+2026 HORIZONTAL ELLIPSIS instead, like so:

[1] See http://gcpm.rutgers.edu/books.html… this was a pale imitation of what Soviet era math circles would offer but is still way beyond anything extant.

The HORIZONTAL ELLIPSIS isn’t be interpreted as part of the URL since '…' isn’t a legal character to use in URLs (unless you write it in escaped format (UTF-8 encoding), which would be '%E2%80%A6').

Re: Math for seven-year-olds

#56

Post by shirro »

Thanks, this was great. I got through the coloring with my 6yo this morning. I printed out two copies and we shared a desk and did it together. He enjoyed it and got mostly optimal answers. He got bogged down in the maps because coloring big areas frustrates him. So he is drawing robots now. I would suggest not trying to do this in one session with easily distracted boys.

Re: Math for seven-year-olds

#58

Post by webnrrd2k »

kirsebaer wrote: post #27
j2kun wrote: post #23

I'm surprised he used the formal terminology here. When I teach graph theory to a younger audience I usually make up (or have them make up) names. I think it gives them a feel for inventing mathematics, but then again it's usually aimed at high school students who have already been convinced as to what math is and isn't, and saying words like "chromatic number" turn them off. I imagine these girls don't suffer from t…

Here is TEDx talk, "Why Math Education is Unnecessary", by a math teacher arguing that compulsory math classes should be replaced with voluntary math-based games: https://www.youtube.com/watch?v=xyowJZxrtbg Here is an essay by a mathematician, A Mathematician's Lament by Paul Lockhart (2002), arguing that math education is completely stupid, like teaching art only through paint-by-number exercises, and should be repl…

This is a little off-topic, I know, but I'd really appreciate some suggestions for good math-based games for my kids, ages 7 and 10.

So does anyone have good math games to suggest?

Re: Math for seven-year-olds

#59

Post by webnrrd2k »

oldbuzzard wrote: post #41
lifeofanalysis wrote: post #32

Interesting co-incidence. Just last week, I sent out an email to my friends, saying that I want to teach mathematics to their kids by a math-by-email service, kinda like the chess-by-email of the old days. The idea is quite simple: I will send out a daily email with a grade appropriate set of math questions and/or games. Your child provides the answers back by email. I check the answers, provide corrections/feedback.…

or like math in the old days [1]. Israel Gelfand's stuff is model for enrichment at an upper level. Alexander Zvonkin's "Math from 3 to 7" book published by MSRI could be a model for younger kids. I think the "new math"materials for the '60s and '70s and the Eastern European materials from a similar period provide a model for education. Unfortunately, they require mathy folks to present and interpret the material. PS…

This reminded me of a book that is, I think, an excellent way to teach math to kids: Mathematical Circles: Russian Experience, by Dmitri Fomin, Sergey Genkin, Ilia V. Itenberg (http://www.amazon.com/Mathematical-Circles-Russian-Experienc...)
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