Math Enrichment

I have to say I'm not orderly about enriching math, so this is all very scattershot and random, but someday I aspire to orderliness..... Right now this is working for us. Also just as a general thing, I should admit that I have very little interest in enriching arithmetic. As far as I'm concerned, arithmetic is arithmetic and (provided you are really understanding it) if you can get it done fast then definitely do so. There are some things that will contribute to the understanding (I'll save my essay about the abacus for another post), but it's only once you have that basis that I'm really interested in all the options, because SO MANY suddenly open up when you have the tools to figure through them.

1. Lots of books... I really like Martin Gardner's books of puzzles, at least in part out of nostalgia, since I read them as a child. And there's something about learning card tricks and calling it schoolwork that lets a kid think he's getting away with something. George Gamow wrote about math and physics in fun and interesting ways (very dated, both in the style and the content, but I like them anyway!), Lewis Carroll, The Number Devil, Flatland... someday I want to read Godel Escher Bach, but I haven't gotten to it yet.... That sort of thing. We don't actually read any of these on any schedule or with any kind of linear progress... they just get picked up and put down and found and discussed and whatever. I've only flipped through Mathematics: A Human Endeavor at the library, but it did look good, and I really do like Jacobs' books in general. TOPS science has some math kits too, but I've not used them myself (I do like their science though!)

2. Proof... Anything worth doing (mathematically) is worth proving. So even with arithmetic, if you are learning about dividing by a fraction, can you PROVE that it works in every case (multiplying by the reciprocal). I print out "proof paper" in the two-column format just because I'm such a geek, and we write it up with steps and justifications. Once you have a couple rules under your belt you can put them to really good use. Of course geometry is the classic application (and we have our copy of Euclid and a study guide, and a really good pointy compass to go with it) but Algebra can be just as "proofy" -- we have a copy of Algebra by I.M. Gelfand that I adore.... Very thin but VERY dense, and it does two things for me. First, it asks for proof -- will this work for all values of x? And second it dumps you right in the middle of seemingly impossible problems and asks that you just start digging your way out. We do that one more-or-less collaboratively. .. insofar as he does the work but we discuss it at great length, before, during, and after.

3. Statistics -- This isn't really enrichment as much as it is just my little pet peeve... statistics education is severely lacking in the standard curricula and no one is getting out of my house without understanding enough to read original scientific research and enough so you'll know, when the news report cites a scary-sounding number whether you really need to be terrified, or amused, or just sensible. Annenberg has a telecourse called Against All Odds, which I like. The textbook is cheap because it's a few years out of date, and we got some extra books to go with it that set up the lessons and give extra exercises in using Excel and SAS. Someday we'll buy a SAS student edition and DS will find out how much he could make as a programmer and I'll have a heck of a time convincing him that he needs anything else to make it in the world... so maybe I'll put that off for a while.... But we're surrounded by statisticians among our friends, so it's not just practical education; it's necessary to keep up with the dinner conversation.

4. Random other stuff... Every so often something just comes up. We listen to a CD in the car and go off on a long tangent about rhythm and fractions and meter in poetry and somehow I end up at the sheet music store... Origami makes for interesting topological problems... There's a whole long list of math stuff related to handiwork -- knitting and crochet can be fantastic if you're discussing non-Euclidean geometry (google crochet hyperbolic plane, or check out this article), and there is a Japanese decorative craft called Temari that's perfect for geometry on spherical surfaces. Spanish blackwork embroidery has a lot to do with fractals. Whatever comes up can frequently be expanded on: when you learn about pi there are dozens of ways to try to find it yourself (and learn about irrational numbers and approaching a limit at the same time!) We just had a simple statistics problem that took on a life of its own when I asked DS in the car what the chances were that I'd blindly grab two identical jelly beans from a bag of 50% red and 50% yellow... and how it changed if you started out with 4 (2 of each) or 4 million.... Opportunities present themselves all the time.