In article <firstname.lastname@example.org>, email@example.com (Herman Rubin) wrote: >I was deliberately stating that this is what at least many children >at age 5 are easily capable of learning; learning abstract concepts >directly.
>The child's brain is quite capable before the schools knock it out >of them.
>So it's a good idea to expose the child to >>new language elements and to make them part of the world the child >>sees and absorbs. And so this is a good time, as you suggest, to >>intoduce elements of mathematical language.
>You do not understand. The language of mathematics is extremely >simple, and is not "explainable" in terms of the real world. >This is a good example of confusion, by attempting to manipulate and >use a large number of different concepts, all poorly understood. The >mathematical world is FAR simpler than the real world. The use of >unknowns is completely linguistic, anyhow, and should not be limited >to mathematics. > You need to be very careful to distinguish between A) understanding mathematics, and B) learning how to manipulate symbols. Yes, small children can be taught to manipulate symbols-- without any understanding of what they mean. Yes, small children can be taught to understand mathematics -- without using symbols. To get to "real" mathematics where abstraction is crucial, a child needs both. There is nothing wrong with introducing symbols-- empty boxes, etc., to a 5 year old. It is unnecessarily confusing, however, to use letters as symbols until the child has gotten past using letters as symbols for sounds. Example: Johnny has twice as many apples as Billy. Together, Billy and Johnny have nine apples. How many apples does Billy have? Until a kid can solve this in his/her head "intuitively", the equations will hinder understanding.
================================================================== | Steve McGrew, President | firstname.lastname@example.org | | New Light Industries, Ltd. | Phone: (509) 456-8321 | | 9713 W. Sunset Hwy | Fax: (509) 456-8351 | | Spokane, WA 99204 USA | http://www.iea.com/~nli | ==================================================================