9 ms·

Math for seven-year-olds

262 points by liotier 12y ago

nemasu 12y ago
Wow, pretty sure I learnt this stuff after high school...kinda awesome/scary.
- purringmeow 12y ago
  Yeah, math education is ordinary schools is terrible. I still haven't learned this, although I am 20...
leorocky 12y ago
The coloring of vertices is a great idea. I'm going to try that with my daughter.
vanderZwan 12y ago
> 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!
- aidos 12y ago
  Ha! There's a whole branch of math dedicated to variations on it (http://en.wikipedia.org/wiki/Graph_theory http://en.wikipedia.org/wiki/Graph_theory).
  - crasshopper 12y ago
    For graph colouring I think the right WP link is Ramsey theory. Also not sure graphs are a "branch" of mathematics, that would be like saying polygons are a "branch" of mathematics. (Branches would be like CA, AT, DG, ... as in http://arxiv.org/list/math/recent. http://arxiv.org/list/math/recent.) I see graphs as just a common object that relates to a variety of mathematical areas.
    - ColinWright 12y ago
      > For graph colouring I think the right WP link > is Ramsey theory. That turns out not to be the case: Ramsey theory is an area of Graph Theory that overlaps with, but neither subsumes, nor is subsumed by, questions related to coloring graphs. > Also not sure graphs are a "branch" of mathematics, ... It may be the case that you are unsure, but my PhD is in Graph Theory, specifically, and I can assume you that it is a recognized area of mathematics. > I see graphs as just a common object that relates > to a variety of mathematical areas. Similarly groups, topological spaces, sets, etc. Math is built on abstraction - the idea is to find commonality, extract it, then study it in its own right. Then anything you prove there applies to everything it came from. Graph Theory is like that, and it is its own subject within math.
      - oldbuzzard 12y ago
        Hmmm... Sets, Groups, Topology, Algebraic Structures... Sounds alot like the Bourbaki "Mother Structure's". Sets and Algebra, I can teach as a homeschool dad. Group theory, topology, and abstract algebra are to difficult for me. I don't think this is intrinsic. Lots of Rosen is hard for me.I suspect Smaullyan's math logic book coming out this Summer will be transparent(Euler diagrams alone make it clearer). Likewise, lots of Stewarts Calc is obscure. Yet, strangely Spivak's Calc is clear and simple. I suspect there are similar resources for abstract algebra and topology.. I assume that I will have worked through baby Rudin before DS finishes highschool... however, there must be a more direct, less abstract path.
  - cpher 12y ago
    It also underpins the foundations of my field (GIS). It's used to describe network routing (e.g. streets, streams, utility systems) and topology (for vector datasets--points, lines, polygons).
- Someone 12y ago
  Yes, but it is somewhat dull math because the problem is relatively simple. See http://en.wikipedia.org/wiki/Eulerian_graph http://en.wikipedia.org/wiki/Eulerian_graph, and compare it with http://en.wikipedia.org/wiki/Hamiltonian_path http://en.wikipedia.org/wiki/Hamiltonian_path and http://en.wikipedia.org/wiki/Hamiltonian_path_problem http://en.wikipedia.org/wiki/Hamiltonian_path_problem
  - judk 12y ago
    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.
aidos 12y ago
Great project. Strangely enough I was thinking about going through something similar just yesterday (to teach my work mate about graphs). My daughter isn't even 3 yet so this would still be a little beyond her. Not by much though, given how approachable it has been made. I've downloaded the kit for later in life.
mollerhoj 12y ago
This! Graph theory should be taught very early to all children. It is as fundamental and important as simple algebra, and yields great insights without requiring tough computations.
- mkesper 12y ago
  When I was a child, we had set theory in elementary school. They dropped it shortly afterwards, though I still think it's very elementary.
kneth 12y ago
I introduced graph theory to my son when he was about 8 or 9 years old. By Nature, he's a networker (like to connect to people) so "friends of a friend" was very intuitive to him. I have also tried to introduce the concepts to teenagers. In Denmark, we have an annual, national science weeks in primary and secondary schools. I have given http://www.slideshare.net/geisshirt/naturvidenskabsfestival-2012 http://www.slideshare.net/geisshirt/naturvidenskabsfestival-... as a talk/lecture at 4-5 schools and most 13-15 years old children get the ideas quickly - Facebook and other social medias are a big help :-)
zhte415 12y ago
I appreciate the polish of making this into a small book. When educating kids, the 'take away' of having things in a format to take home and play with / show parents makes a big difference (as it does for adult learners).
peteretep 12y ago
All of this looks awesome: http://jdh.hamkins.org/category/math-for-kids/ http://jdh.hamkins.org/category/math-for-kids/
blisterpeanuts 12y ago
Fantastic! I'm going to print this out for my 9-year-old daughter to play with, and to teach to her friends when they come over (she loves to play school teacher). This is the kind of intuitive math games that I've been looking for to challenge her a bit without scaring her off with dry, boring stuff. There's also the game of Sprout (or Sprouts) that is easy for kids to learn and has interesting mathematical implications. http://en.wikipedia.org/wiki/Sprouts_(game) http://en.wikipedia.org/wiki/Sprouts_(game)
pbhjpbhj 12y ago
What I'd like is a companion booklet that looks with a bit more rigor and formalism at the topics - but not too much! - that would suit a Y13 (17-18yo) or an introductory lecture at undergrad level. I've never really had a proper introduction to graph theory. Incidentally this has come at the perfect time. I was just discussing with my 8 yo different fields of mathematics and which symbologies he's used and starting him on Boolean set operations. Graph theory was mentioned (by me!) so this will be a good flexi-day if he wants to follow up on it. A nice accompaniment might be a lightbot like game for exploring Eulerian paths.
- j2kun 12y ago
  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-theory/ http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t...
  - pbhjpbhj 12y ago
    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 and shooting off I tend to get lost in Wikipedia and drift around too much without getting a reasonably rigorous overview.
    - j2kun 12y ago
      I think a good answer is going to depend heavily on your goals (applied or theoretical). Maybe you could elaborate on that?
      - pbhjpbhj 12y ago
        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.
hellbreakslose 12y ago
wth is this article... alex bellos advert or something? formula? that seems like insanity, what ill take everyone and interview him? YOU DONT INTERVIEW THE WOMAN YOU'LL MARRY, if you do you are an idiot that doesn't enjoy life and takes everything as a freaking robot.
remon 12y ago
Amazing project! Does anyone know why a (2D?) map will need at most four colors while avoiding neighboring areas with the same color?
- jonsen 12y ago
  "The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer.": http://en.wikipedia.org/wiki/Four_color_theorem http://en.wikipedia.org/wiki/Four_color_theorem
- j2kun 12y ago
  This is a monumental theorem called the four-color theorem, which specifically states that ever planar graph is 4-colorable. It actually took mathematicians many years and many pages (and computer programs!) to prove. There is a simpler proof that every planar graph needs at most 5 colors. [1] Also, 2D is not quite specific enough. It turns out that there are non-planar graphs that can be drawn on a different kind of 2D-surface (the surface of a torus) that need more than four colors. [2] It turns out that for tori, the max number of colors is seven. And you can keep going up, culminating in this cool thing called the Euler characteristic. [3] [1]: http://jeremykun.com/2011/07/14/graph-coloring-or-proof-by-crayon/ http://jeremykun.com/2011/07/14/graph-coloring-or-proof-by-c... [2]: http://en.wikipedia.org/wiki/Toroidal_graph http://en.wikipedia.org/wiki/Toroidal_graph [3]: http://en.wikipedia.org/wiki/Euler_characteristic#Examples http://en.wikipedia.org/wiki/Euler_characteristic#Examples
danielweber 12y ago
The Google Drive download link isn't working for me. Are there any mirrors?
j2kun 12y ago
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 the same afflictions. Still, this blog post was excellent. I don't understand why all elementary math education isn't in the form of games and activities like this.
- kirsebaer 12y ago
  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 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 replaced by play: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament.... And here is a short video of a democratic free school, Sudbury Valley School, where kids play freely all day long and learn math through video games, card games, and voluntary study: https://www.youtube.com/watch?v=awOAmTaZ4XI https://www.youtube.com/watch?v=awOAmTaZ4XI
  - sgustard 12y ago
    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.
    - j2kun 12y ago
      I agree, but I think the amount of "paint by number" in mathematics should be minimized, and most of it (learning multiplication tables, isolating variables in simple equations) is already in the form of games. I'd be interested to hear of a topic in math that you would argue can't be turned into a non-superficial game.
Pxtl 12y ago
I remember when my wife took a course on set theory I was fascinated with the graph theory stuff. I wonder if there are other academic fields of math that you could customize for elementary schoolers - I know my dad taught me Boolean algebra and logic gates in Grade 4, so there's one.
slackpad 12y ago
This is the kind of experience would never be allowed with the Common Core type approach. I can't imagine people spending a classroom day on something like this (even though it's awesome and super valuable), but alas it's not content that will appear on the standardized tests.
- kaitai 12y ago
  Why wouldn't this be allowed with the Common Core? The Common Core is a set of standards for what students should have learned by the end of a year, and for fourth grade, for instance, the Core consists of things like "Use the four operations with whole numbers to solve problems," "Understand decimal notation for fractions, and compare decimal fractions, " and "Generate and analyze patterns." One can fault the Common Core for not including enough discrete math -- it really focuses on numbers, algebra, and eventually modeling with polynomial and trigonometric functions -- and one can fault America for putting people into the classroom who don't know math [1] and then telling them they'll be awarded tenure or not based on student performance on some test [2]. People are confusing the same old problems we've always had (poor teacher training, stupid cobbled-together curricula like Integrated Math mandates by school boards, teaching to tests with high stakes for teachers and little value for students, etc) with Common Core. Read the standards [3], folks, and decide based on what they actually say what you might actually think. [1] http://www.nsf.gov/statistics/seind12/c1/c1s3.htm http://www.nsf.gov/statistics/seind12/c1/c1s3.htm , http://www.math.vcu.edu/g1/journal/Journal7/Part%20I/Sterling.html http://www.math.vcu.edu/g1/journal/Journal7/Part%20I/Sterlin... [2] http://education.ohio.gov/Topics/Teaching/Educator-Evaluation-System/Ohio-s-Teacher-Evaluation-System/Student-Growth-Measures/Value-Added-Student-Growth-Measure http://education.ohio.gov/Topics/Teaching/Educator-Evaluatio... [3] http://www.corestandards.org/Math/Practice/ http://www.corestandards.org/Math/Practice/
  - slackpad 12y ago
    That's a fair point - his content is certainly compatible with the Common Core's standard. I was really venting about your point [2] and shouldn't have implicated the standard for that. Thanks for the references.
lifeofanalysis 12y ago
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. And the next day's worksheet is customized to the child's history. If there is an interest, I could follow the child all the way from pre-K to graduate level Math subjects. Think about that -- wouldn't it be awesome if when you are getting your PhD, you could look back over 20 years of daily problems you solved and how you progressed in your conceptual understanding? Naturally, you want to balance the gaming aspect with the rigorous aspects. You can start learning Graph Theory with diagram filling, but as you get more serious, there is no substitute to solving several hard problems to get a deeper/intuitive understanding of the concepts. There is no question that people learn different ways, some visually, others through games, and others through mental modeling. I am convinced that if we could tailor math teaching to each kid, we could get rid of the stigma that "Math is hard", or, worse, "Girls can't do Math". Math, as I say, is a contact sport, not a spectator sport. You have to grab a pencil and a piece of paper to work on 20-30-40 harder and harder problems to master each concept. But to learn new concepts, you also have to cross the significant hurdle of climbing the first few rungs of each concept, so to speak. So let's learn by balancing games and theory.
- oldbuzzard 12y ago
  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. I'm not criticizing public school teachers. I also feel inadequate. In order to teach DS7, I feel like I should probably work through Herstein's Abstract Algebra. I'll put it on the list... Currently I'm working through Euclid... Next Fall our homeschool will have a geometric focus... after that... who knows. [1] See http://gcpm.rutgers.edu/books.html 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.
mathattack 12y ago
This is great - thanks for sharing!
oldbuzzard 12y ago
If this sort of thing interests you, then either the modern Moebius Noodles[1] material or the vintage Young Math[2] materials like "Maps, Tracks, and the Bridges of Konigsberg: A Book about Networks by Michael Holt" would also. [1] http://http://www.moebiusnoodles.com/ http://http://www.moebiusnoodles.com/ [2] http://www.valerieslivinglibrary.com/math.htm http://www.valerieslivinglibrary.com/math.htm
keppy 12y ago
Great material! Can we get a follow up article for seventy year olds? Not a lot out there for the elderly. Math for seventy-year-olds Thanks!
shirro 12y ago
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.
jestinjoy1 12y ago
Graph Theory for Maths :D
arctangent1759 12y ago
Using CHILDREN to solve NP-Complete problems? What have we become? Monsters, I tell you.

262 points by liotier 12y ago

nemasu 12y ago

Wow, pretty sure I learnt this stuff after high school...kinda awesome/scary.

purringmeow 12y ago
Yeah, math education is ordinary schools is terrible. I still haven't learned this, although I am 20...

leorocky 12y ago

The coloring of vertices is a great idea. I'm going to try that with my daughter.

vanderZwan 12y ago

> 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!

aidos 12y ago
Ha! There's a whole branch of math dedicated to variations on it (http://en.wikipedia.org/wiki/Graph_theory http://en.wikipedia.org/wiki/Graph_theory).
- crasshopper 12y ago
  For graph colouring I think the right WP link is Ramsey theory. Also not sure graphs are a "branch" of mathematics, that would be like saying polygons are a "branch" of mathematics. (Branches would be like CA, AT, DG, ... as in http://arxiv.org/list/math/recent. http://arxiv.org/list/math/recent.) I see graphs as just a common object that relates to a variety of mathematical areas.
  - ColinWright 12y ago
    > For graph colouring I think the right WP link > is Ramsey theory. That turns out not to be the case: Ramsey theory is an area of Graph Theory that overlaps with, but neither subsumes, nor is subsumed by, questions related to coloring graphs. > Also not sure graphs are a "branch" of mathematics, ... It may be the case that you are unsure, but my PhD is in Graph Theory, specifically, and I can assume you that it is a recognized area of mathematics. > I see graphs as just a common object that relates > to a variety of mathematical areas. Similarly groups, topological spaces, sets, etc. Math is built on abstraction - the idea is to find commonality, extract it, then study it in its own right. Then anything you prove there applies to everything it came from. Graph Theory is like that, and it is its own subject within math.
    - oldbuzzard 12y ago
      Hmmm... Sets, Groups, Topology, Algebraic Structures... Sounds alot like the Bourbaki "Mother Structure's". Sets and Algebra, I can teach as a homeschool dad. Group theory, topology, and abstract algebra are to difficult for me. I don't think this is intrinsic. Lots of Rosen is hard for me.I suspect Smaullyan's math logic book coming out this Summer will be transparent(Euler diagrams alone make it clearer). Likewise, lots of Stewarts Calc is obscure. Yet, strangely Spivak's Calc is clear and simple. I suspect there are similar resources for abstract algebra and topology.. I assume that I will have worked through baby Rudin before DS finishes highschool... however, there must be a more direct, less abstract path.
- cpher 12y ago
  It also underpins the foundations of my field (GIS). It's used to describe network routing (e.g. streets, streams, utility systems) and topology (for vector datasets--points, lines, polygons).
Someone 12y ago
Yes, but it is somewhat dull math because the problem is relatively simple. See http://en.wikipedia.org/wiki/Eulerian_graph http://en.wikipedia.org/wiki/Eulerian_graph, and compare it with http://en.wikipedia.org/wiki/Hamiltonian_path http://en.wikipedia.org/wiki/Hamiltonian_path and http://en.wikipedia.org/wiki/Hamiltonian_path_problem http://en.wikipedia.org/wiki/Hamiltonian_path_problem
- judk 12y ago
  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.

aidos 12y ago

Great project. Strangely enough I was thinking about going through something similar just yesterday (to teach my work mate about graphs). My daughter isn't even 3 yet so this would still be a little beyond her. Not by much though, given how approachable it has been made. I've downloaded the kit for later in life.

mollerhoj 12y ago

This! Graph theory should be taught very early to all children. It is as fundamental and important as simple algebra, and yields great insights without requiring tough computations.

mkesper 12y ago
When I was a child, we had set theory in elementary school. They dropped it shortly afterwards, though I still think it's very elementary.

kneth 12y ago

I introduced graph theory to my son when he was about 8 or 9 years old. By Nature, he's a networker (like to connect to people) so "friends of a friend" was very intuitive to him. I have also tried to introduce the concepts to teenagers. In Denmark, we have an annual, national science weeks in primary and secondary schools. I have given http://www.slideshare.net/geisshirt/naturvidenskabsfestival-2012 http://www.slideshare.net/geisshirt/naturvidenskabsfestival-... as a talk/lecture at 4-5 schools and most 13-15 years old children get the ideas quickly - Facebook and other social medias are a big help :-)

zhte415 12y ago

I appreciate the polish of making this into a small book. When educating kids, the 'take away' of having things in a format to take home and play with / show parents makes a big difference (as it does for adult learners).

peteretep 12y ago

All of this looks awesome: http://jdh.hamkins.org/category/math-for-kids/ http://jdh.hamkins.org/category/math-for-kids/

blisterpeanuts 12y ago

Fantastic! I'm going to print this out for my 9-year-old daughter to play with, and to teach to her friends when they come over (she loves to play school teacher). This is the kind of intuitive math games that I've been looking for to challenge her a bit without scaring her off with dry, boring stuff. There's also the game of Sprout (or Sprouts) that is easy for kids to learn and has interesting mathematical implications. http://en.wikipedia.org/wiki/Sprouts_(game) http://en.wikipedia.org/wiki/Sprouts_(game)

pbhjpbhj 12y ago

What I'd like is a companion booklet that looks with a bit more rigor and formalism at the topics - but not too much! - that would suit a Y13 (17-18yo) or an introductory lecture at undergrad level. I've never really had a proper introduction to graph theory. Incidentally this has come at the perfect time. I was just discussing with my 8 yo different fields of mathematics and which symbologies he's used and starting him on Boolean set operations. Graph theory was mentioned (by me!) so this will be a good flexi-day if he wants to follow up on it. A nice accompaniment might be a lightbot like game for exploring Eulerian paths.

j2kun 12y ago
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-theory/ http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t...
- pbhjpbhj 12y ago
  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 and shooting off I tend to get lost in Wikipedia and drift around too much without getting a reasonably rigorous overview.
  - j2kun 12y ago
    I think a good answer is going to depend heavily on your goals (applied or theoretical). Maybe you could elaborate on that?
    - pbhjpbhj 12y ago
      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.

hellbreakslose 12y ago

wth is this article... alex bellos advert or something? formula? that seems like insanity, what ill take everyone and interview him? YOU DONT INTERVIEW THE WOMAN YOU'LL MARRY, if you do you are an idiot that doesn't enjoy life and takes everything as a freaking robot.

remon 12y ago

Amazing project! Does anyone know why a (2D?) map will need at most four colors while avoiding neighboring areas with the same color?

jonsen 12y ago
"The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer.": http://en.wikipedia.org/wiki/Four_color_theorem http://en.wikipedia.org/wiki/Four_color_theorem
j2kun 12y ago
This is a monumental theorem called the four-color theorem, which specifically states that ever planar graph is 4-colorable. It actually took mathematicians many years and many pages (and computer programs!) to prove. There is a simpler proof that every planar graph needs at most 5 colors. [1] Also, 2D is not quite specific enough. It turns out that there are non-planar graphs that can be drawn on a different kind of 2D-surface (the surface of a torus) that need more than four colors. [2] It turns out that for tori, the max number of colors is seven. And you can keep going up, culminating in this cool thing called the Euler characteristic. [3] [1]: http://jeremykun.com/2011/07/14/graph-coloring-or-proof-by-crayon/ http://jeremykun.com/2011/07/14/graph-coloring-or-proof-by-c... [2]: http://en.wikipedia.org/wiki/Toroidal_graph http://en.wikipedia.org/wiki/Toroidal_graph [3]: http://en.wikipedia.org/wiki/Euler_characteristic#Examples http://en.wikipedia.org/wiki/Euler_characteristic#Examples

danielweber 12y ago

The Google Drive download link isn't working for me. Are there any mirrors?

j2kun 12y ago

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 the same afflictions. Still, this blog post was excellent. I don't understand why all elementary math education isn't in the form of games and activities like this.

kirsebaer 12y ago
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 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 replaced by play: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament.... And here is a short video of a democratic free school, Sudbury Valley School, where kids play freely all day long and learn math through video games, card games, and voluntary study: https://www.youtube.com/watch?v=awOAmTaZ4XI https://www.youtube.com/watch?v=awOAmTaZ4XI
- sgustard 12y ago
  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.
  - j2kun 12y ago
    I agree, but I think the amount of "paint by number" in mathematics should be minimized, and most of it (learning multiplication tables, isolating variables in simple equations) is already in the form of games. I'd be interested to hear of a topic in math that you would argue can't be turned into a non-superficial game.

Pxtl 12y ago

I remember when my wife took a course on set theory I was fascinated with the graph theory stuff. I wonder if there are other academic fields of math that you could customize for elementary schoolers - I know my dad taught me Boolean algebra and logic gates in Grade 4, so there's one.

slackpad 12y ago

This is the kind of experience would never be allowed with the Common Core type approach. I can't imagine people spending a classroom day on something like this (even though it's awesome and super valuable), but alas it's not content that will appear on the standardized tests.

kaitai 12y ago
Why wouldn't this be allowed with the Common Core? The Common Core is a set of standards for what students should have learned by the end of a year, and for fourth grade, for instance, the Core consists of things like "Use the four operations with whole numbers to solve problems," "Understand decimal notation for fractions, and compare decimal fractions, " and "Generate and analyze patterns." One can fault the Common Core for not including enough discrete math -- it really focuses on numbers, algebra, and eventually modeling with polynomial and trigonometric functions -- and one can fault America for putting people into the classroom who don't know math [1] and then telling them they'll be awarded tenure or not based on student performance on some test [2]. People are confusing the same old problems we've always had (poor teacher training, stupid cobbled-together curricula like Integrated Math mandates by school boards, teaching to tests with high stakes for teachers and little value for students, etc) with Common Core. Read the standards [3], folks, and decide based on what they actually say what you might actually think. [1] http://www.nsf.gov/statistics/seind12/c1/c1s3.htm http://www.nsf.gov/statistics/seind12/c1/c1s3.htm , http://www.math.vcu.edu/g1/journal/Journal7/Part%20I/Sterling.html http://www.math.vcu.edu/g1/journal/Journal7/Part%20I/Sterlin... [2] http://education.ohio.gov/Topics/Teaching/Educator-Evaluation-System/Ohio-s-Teacher-Evaluation-System/Student-Growth-Measures/Value-Added-Student-Growth-Measure http://education.ohio.gov/Topics/Teaching/Educator-Evaluatio... [3] http://www.corestandards.org/Math/Practice/ http://www.corestandards.org/Math/Practice/
- slackpad 12y ago
  That's a fair point - his content is certainly compatible with the Common Core's standard. I was really venting about your point [2] and shouldn't have implicated the standard for that. Thanks for the references.

lifeofanalysis 12y ago

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. And the next day's worksheet is customized to the child's history. If there is an interest, I could follow the child all the way from pre-K to graduate level Math subjects. Think about that -- wouldn't it be awesome if when you are getting your PhD, you could look back over 20 years of daily problems you solved and how you progressed in your conceptual understanding? Naturally, you want to balance the gaming aspect with the rigorous aspects. You can start learning Graph Theory with diagram filling, but as you get more serious, there is no substitute to solving several hard problems to get a deeper/intuitive understanding of the concepts. There is no question that people learn different ways, some visually, others through games, and others through mental modeling. I am convinced that if we could tailor math teaching to each kid, we could get rid of the stigma that "Math is hard", or, worse, "Girls can't do Math". Math, as I say, is a contact sport, not a spectator sport. You have to grab a pencil and a piece of paper to work on 20-30-40 harder and harder problems to master each concept. But to learn new concepts, you also have to cross the significant hurdle of climbing the first few rungs of each concept, so to speak. So let's learn by balancing games and theory.

oldbuzzard 12y ago
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. I'm not criticizing public school teachers. I also feel inadequate. In order to teach DS7, I feel like I should probably work through Herstein's Abstract Algebra. I'll put it on the list... Currently I'm working through Euclid... Next Fall our homeschool will have a geometric focus... after that... who knows. [1] See http://gcpm.rutgers.edu/books.html 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.

mathattack 12y ago

This is great - thanks for sharing!

oldbuzzard 12y ago

If this sort of thing interests you, then either the modern Moebius Noodles[1] material or the vintage Young Math[2] materials like "Maps, Tracks, and the Bridges of Konigsberg: A Book about Networks by Michael Holt" would also. [1] http://http://www.moebiusnoodles.com/ http://http://www.moebiusnoodles.com/ [2] http://www.valerieslivinglibrary.com/math.htm http://www.valerieslivinglibrary.com/math.htm

keppy 12y ago

Great material! Can we get a follow up article for seventy year olds? Not a lot out there for the elderly. Math for seventy-year-olds Thanks!

shirro 12y ago

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.

jestinjoy1 12y ago

Graph Theory for Maths :D

arctangent1759 12y ago

Using CHILDREN to solve NP-Complete problems? What have we become? Monsters, I tell you.