
Re: Math Standards: Anyone Like *Any* of Them?
Posted:
Dec 18, 1996 10:04 AM


In article <592ddm$n18@b.stat.purdue.edu>, hrubin@b.stat.purdue.edu (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
==================================================================  Steve McGrew, President  stevem@comtch.iea.com   New Light Industries, Ltd.  Phone: (509) 4568321   9713 W. Sunset Hwy  Fax: (509) 4568351   Spokane, WA 99204 USA  http://www.iea.com/~nli  ==================================================================

