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Math for seven-year-olds

jdh.hamkins.org

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Re: Math for seven-year-olds

#61

Post by kaj_sotala »

webnrrd2k wrote: post #58
kirsebaer wrote: post #27

Earlier quoted context omitted.

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?

DragonBox ( http://www.dragonboxapp.com/ ) is fantastic. I have literally seen elementary school kids argue over who gets to be the next one to solve equations playing it.

If you have an iOS or Android tablet, they also have a new game called DragonBox Elements up that teaches geometry. After playing it for a while, I'd see triangles everywhere.

If DragonBox gets them hooked on algebra, another fun algebra game is Algeburst (currently only available for iOS platforms AFAIK), which employs a basic get-three-of-the-same-color-in-a-row mechanic, but requiring you to interpret simple algebraic expressions in order to figure out which tiles are of which color. E.g. if there's a tile called 3X + 2X, you can recognize it as being a 5X tile and give it whatever color 5X tiles happen to have on that particular level. (I was only going to try this game to see whether it was any good, but then ended up losing several hours to it.) They also have a "topics in arithmetic" version which doesn't have algebra but rather focuses on basic arithmetic.

10 might be getting a little old for it, and it teaches the basics of programming not math, but in general I would also recommend the Robot Turtles board game. On the topic of games teaching programming, I've also heard good things about the CodeSpells computer game, in which you're exploring a world and can cast spells by writing Java code, but I haven't tried it myself.

Re: Math for seven-year-olds

#62

Post by ColinWright »

arm wrote: post #55
oldbuzzard wrote: post #44

Earlier quoted context omitted.

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](h…

  > Anyway, I’m pretty sure the comment system
  > accepts Markdown, ...
I suspect that's where you're wrong - I suspect the comment system is hand-rolled.

Re: Math for seven-year-olds

#63

Post by judk »

Someone wrote: post #37
vanderZwan wrote: post #4

> Next, we considered Eulerian paths and circuits, where one traces through all the edges of a graph without lifting one’s pencil and without retracing any edge more than once. We started off with some easy examples, but then considered more difficult cases. Wait, there's math devoted to that? I used to do that as a kid for fun!

Yes, but it is somewhat dull math because the problem is relatively simple. See http://en.wikipedia.org/wiki/Eulerian_graph , and compare it with http://en.wikipedia.org/wiki/Hamiltonian_path and http://en.wikipedia.org/wiki/Hamiltonian_path_problem

Not dull. Fascinating, but small and quickly used up. For a novice it is a wonderfully accessible and inspiring intro on the field. It shows the magic of math, who tiny patterns underlying whole classes of seemingly disparate individual cases.

Re: Math for seven-year-olds

#64

Post by rquantz »

quadrangle wrote: post #38
sgustard wrote: post #30

Earlier quoted context omitted.

Music is taught by the equivalent of paint by number, which is reading sheet music. Or play, which is improvisation. There's room for both.

Music as paint-by-number is one of the worst failings of music education. The most robust and life-long music in the world is in cultures that actually use notation only as appropriate if at all and don't think of it as the music. Most of the world's music is not so notation-focused.

I don't think this is the fault of music notation. Prior to widespread availabity of recorded music, playing music from sheet music was a common activity in the West. If anything, I would say the death of lifelong musical performance is more the result of recording -- "this disc here is the music" rather than "this sheet music is the music" -- the sheet music still needs a performer.

Re: Math for seven-year-olds

#65

Post by adidum »

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 wish I was your friend, and on that email list. Your idea of "math by mail" sounds great, I am interested to be included on your list, please contact me if it is acceptable. Email in profile, thank you in advance!

Re: Math for seven-year-olds

#66

Post by pbhjpbhj »

j2kun wrote: post #53
pbhjpbhj wrote: post #49

Earlier quoted context omitted.

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 charac…

Excellent, thank you for your insight and your patient answers.

Re: Math for seven-year-olds

#67

Post by dubya »

pbhjpbhj wrote: post #26
j2kun wrote: post #22

Earlier quoted context omitted.

I have given lectures to students of this age range (13-18 years), but I don't have a booklet. See this blog post: http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t...

That's great, an enjoyable and inspiring read. Can you - or another reader - recommend a resource that's perhaps just a little more advanced though, please? What's the next step after formalising the language used, understanding connectivity and path traversal ... perhaps, what would the subheadings of a follow up lesson to this be? I'm not asking to be spoonfed, really!, there are just so many resources on the web a…

I remember reading "Graphs and their uses" by Oystein Ore in high school and liking it.

Re: Math for seven-year-olds

#68

Post by betaclass »

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…

Well, I find Dad Meyer's talk to be helpful in thinking about math school education: https://www.ted.com/talks/dan_meyer_math_curriculum_makeover .
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