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Topic: Re: Rat-sense
Replies: 2   Last Post: Aug 17, 2013 1:58 PM

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 Guest
Re: Rat-sense
Posted: Aug 17, 2013 1:21 PM
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On Sat, 17 Aug 2013 01:53:54 -0600, Robert Hansen <bob@rsccore.com> wrote:

> This type of reasoning shows up often in education science. Arguments
> that young children understand advanced concepts. I think it took me a
> year to unravel the >basic principle behind this scam and why it is
> effective. But first, why did I question these arguments to begin with?
> Simple. My basic problem with all of these >arguments is - If young
> children understand these things so well then why don't they understand
> them when they get to algebra? Some educationalists simply ignore >that
> question, like a comedian ignores a heckler, while some educationalists
> offer a conspiracy theory. They propose that there is some dark force
> that stifles that >innate understanding. Then of course I ask "Why would
> anyone do that?" and then they resort to the heckler approach.

You are scamming yourself here. "An intuitive understanding" (the words
Dehaene used) isn't the same thing as a "formal understanding". It is the
step from intuitive to formal that kids have trouble making.

Most kids can tell you that it doesn't matter which order you add a pair
of numbers in. There's the intuitive understanding. And you haven't dealt
at all with Dehaene's observation that kids, by the age of five, already
intuitively select the larger of two numbers to begin counting from when
they add by counting. If that doesn't demonstrate a grasp of
commutativity, I don't know what would.

But it's a big step from that simple understanding of the commutativity of
addition to an understanding of the statement "For every a and for every
b, a + b = b + a" \it{and its connection with the simple, intuitive
statement.} One of the conceptual difficulties here is the formal notion
of a fixed, but *unspecified,* number. That notion appears twice in the
"For every" statement---possibly even three times, if we think about the
sum itself. That notion---a fixed but unspecified number---is one of the
biggest hurdles kids have to pass in going from arithmetic to algebra.

--Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver

<http://rowdy.msudenver.edu/~talmanl>

Date Subject Author
8/17/13 Guest
8/17/13 Robert Hansen
8/17/13 Robert Hansen