Date: Oct 30, 2012 11:34 AM
Author: Paul A. Tanner III
Subject: Re: Why?
On Tue, Oct 30, 2012 at 5:17 AM, Robert Hansen <email@example.com> wrote:
> Also, children don't understand "replacement of numbers with symbols for
> arbitrary numbers".
> If my several clues of the form "Children don't understand X" don't make
> sense then add a couple words as in...
> Children don't understand THE SIGNIFICANCE of X.
> Bob Hansen
Why do you think Chinese kids are less capable than their elders in China think they are capable of? Stated another way, why do they think their children are more capable than you think they are?
In general, I ask these questions for East Asia in general - the treat their kids are more capable than you think they are. Why? They are wrong and you are right as to what their kids can handle?
I draw the readers' attention to my post in this thread
and in my post
"Re: The Teaching of Fractions"
where I document fromIn my 1999 edition of "Knowing and Teaching Elementary Mathematics" by Liping Ma that they seem to think that their kids are capable of understanding what you seem to think that they are not capable of understanding, namely using letters of the alphabet to represent arbitrary numbers.
Here is part of what I said, and this includes quotes from the book:
"...in the footnotes at the bottom of page 109 of my edition (paperback 1999) we see that third graders are taught the algebraic properties of the commutative and associative laws of addition the abstract way (that's right, using abstract symbols) using letters of the alphabet - we see the following, taught to third graders (that's right, third graders) in the textbooks themselves: "If a and b represent arbitrary addends, we can write the commutative law of addition as:
a + b = b + a."
Notice that not only are they using letters of the alphabet to make a statement that is true for all numbers, they are using the abstract term "addend" here, making the statement even more abstract. In fourth grade they get these algebraic properties stated abstractly for multiplication along with the the distributive law. (See page 132 and surrounding text for a discussion about Chinese textbooks for elementary school.)"
In terms of the question of what elementary school kids are capable of, why should we believe that you are right and that perhaps all of East Asia is wrong?
I would add that if the Chinese kids are capable of understanding what their elders in China think they are capable of, then so are American kids.
Message was edited by: Paul A. Tanner III