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Math for seven-year-olds
21–30 of 68 posts
Re: Math for seven-year-olds
#22What 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…
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...
Re: Math for seven-year-olds
#23I'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.
Re: Math for seven-year-olds
#24> 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!
Ha! There's a whole branch of math dedicated to variations on it ( http://en.wikipedia.org/wiki/Graph_theory ).
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).
Re: Math for seven-year-olds
#25I 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.
Re: Math for seven-year-olds
#26What 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…
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 and shooting off I tend to get lost in Wikipedia and drift around too much without getting a reasonably rigorous overview.
Re: Math for seven-year-olds
#27I'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 replaced by play: 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
Re: Math for seven-year-olds
#28This 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.
Re: Math for seven-year-olds
#29This 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.
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.math.vcu.edu/g1/journal/Journal7/Part%20I/Sterlin...
[2] http://education.ohio.gov/Topics/Teaching/Educator-Evaluatio...
Re: Math for seven-year-olds
#30I'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…
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.