Dear Nick I firmly agree with John Kennison.
Develop their basic arithmetic, geometry and algebra at this age while boosting their basic mental computational abilities (mental maths) . Develop their foundations / concepts firmly. All this should be done in a way so that it is not imposed on the child. Calculus especially is a subject which the child has to be slowly eased into and correlated to physical and biological phenomena. Some non-US boards do this very well,eg. the IGCSE and the IB. Checkout www.desertacademy.org in Santa Fe. Sarbajit Roy http://www.mathspro.in/ On 3/30/16, John Kennison <jkenni...@clarku.edu> wrote: > Nick, > > Do NOT try to teach your 9 year old granddaughter calculus. Instead give her > challenging problems that can be solved by elementary methods. If you try to > teach her something she is not ready for, math will become a chore > --possibly a chore for which she is greatly praised, but still a chore. > Something bad happens when people see math as a chore. They try to memorize > a lot of methods and go further than their understanding will normally take > them. Doing math by memorizing without understanding is a dead end street. > > Many high schools, maybe most, now teach calculus and think they have taken > a big step forward in their math education. But if they rush through algebra > and geometry to do this, they have ruined their teaching of math. Instead of > turning out people who understand algebra and geometry, they produce people > who get by on memory. A Clark U., we have, for quite some time, required > that students pass placement exams in algebra, geometry and trig before > being admitted to Calculus. The first year we did this (in the 1980s) a > student came to my office saying there was a serious mistake in his math > placement because he was placed in remedial algebra when, in fact, he had > already taken calculus and gotten an A in it, so was ready for second year > calculus. I thought Clark had made a mistake, but, to be sure, I asked him > some elementary algebra questions, such as to expand (x+1)^2 (IN THIS email > I use ^2 for "2 in the exponent" > when I talked to the student I simply wrote the 2 as a superscript.) The > student produced x^2 + 4. When I suggested that this was incomplete, he > seemd to feel that I was asking him an unfair question because that sort of > math problem was what he had studied 4 years ago and it was unreasonable for > me to expect him to remember things from a long ago. --I have heard similar > stories from colleagues in other schools. > > > Give her some simple word problems and allow her to solve them by trying out > values. (Algebra teachers disallow this approach --for the seemingly good > reason that it shortcircuits the learning of algebra) but trying out values > allows the student to develop intuitions about how a problem works. Tell > your granddaughter to make a note of any patterns she sees in the different > numbers she tries. When she can detect patterns and express what they are > coherently, that is the time to teach her algebraic notation. > > --John > ________________________________________ ============================================================ 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
