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Topic: Math Standards: Anyone Like *Any* of Them?
Replies: 46   Last Post: Dec 27, 1996 8:50 PM

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Steve McGrew

Posts: 9
Registered: 12/6/04
Re: Math Standards: Anyone Like *Any* of Them?
Posted: Dec 18, 1996 10:04 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

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Date Subject Author
12/9/96
Read Math Standards: Anyone Like *Any* of Them?
Michael Ames Connor
12/9/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Michael Ames Connor
12/10/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Donna Mettler
12/10/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Brian M. Scott
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Powell Jay
12/11/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Kim or Melodie Mackey
12/11/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/11/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/11/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Brian M. Scott
12/11/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Brian M. Scott
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Powell Jay
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Brian M. Scott
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Alberto C Moreira
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Shyang Hwang
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Charles J. Masenas
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/11/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
penn@warwick.net
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Philip Cain
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Donna Mettler
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Carol
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Alberto C Moreira
12/15/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Philip Cain
12/15/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Donna Mettler
12/16/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/15/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/18/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Steve McGrew
12/19/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/24/96
Read Re: Math Standards: Anyone Like *Any* of Them?
John Burnette
12/24/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin
12/25/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Dan Underwood
12/27/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Philip Cain
12/21/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Alberto C Moreira
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Alberto C Moreira
12/14/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Steve McGrew
12/19/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Philip Cain
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Philip Cain
12/15/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Gary A. Wirsing
12/12/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Keith.Minkel, Lake.Mills, IA
12/13/96
Read Re: Math Standards: Anyone Like *Any* of Them?
Herman Rubin

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