On Tue, Mar 29, 2016 at 04:15:25PM -0600, Nick Thompson wrote: > Hi, everybody, > > > > I have a granddaughter on vacation who is showing some interest in maths. > We have been fooling around with graph paper, you know, "the squaw upon the > hippopotamus is equal to the suns of the squaw's on the other two hides", > etc., and playing race track on graph paper (which didn't grab her (used > squares that were too small) but that's about all I have in my repertoire. > > > > Any suggestions for really nifty stuff on the web (or that I could learn > from the web quick enough) for 9 year olds. I;ve been told that early > childhood is the best time to teach calculus, but not by anybody who > actually knew how to do it. She is quick on a computer. >
Not sure about the web, but you would need to get in algebra first. A bright 9yo should easily be able to handle the concept that letters can stand abstractly for a number. Lack of algebra prevent the ancient Greeks from getting calculus. I'd avoid trig, though, it's not necessary for getting the concepts of differentiation and integration (unless Norm Wildberger's approach helps?). Then once you have algebra to hand, you need to teach the concept of limits. eg If x->0 and y->0 twice as fast, what is the limit of y/x? The answer is 1/2, not 0/0. With limits and algebra on hand, you can tackle differentiation and integration of polynomial functions. If she's any good at computer programming (eg perhaps using Scratch or Alice*), then get her to write a program printing out the value of something like (x+1)/x as x->infinity. Its a really good way (IMHO) of grokking limits. Then you can write a program to estimate the area of some random shape by tiling it with rectangles and then letting the tile size go to zero. That will give an excellent introduction to integration. * It might be possible to use a spreadsheet for this as well, with the added advantage of being easily able to graph the results. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
