Re: Abolish Fractions?

On Thu, 31 Jan 2008 04:17:01 -0500, David Bernier
<david250@xxxxxxxxxxxx> wrote:

The video & transcript of the mini-lecture are under DeTurk here:
< http://www.sas.upenn.edu/home/news/sixtysec_lectures_archive.html#D >

I waited to see his actual words before trying to make a judgement.

From the transcript:

It?s not that writing ratios like 385 over 23 should be banned.
But such expressions should simply no longer be considered to
be numbers.

If he had only been proposing not to teach all children all of the
rules for calculating with fractions, he might have a decimal point,
and I'd even have 48.7134% of a mind to agree with him (and put all
the fuss down to poor reporting by the Press, or canny promotion of
his forthcoming book), although I'd be worrying about the education
of children who do have mathematical curiosity. I hope they would
have at least the option of learning how to work with fractions, so
that operations with decimals would make sense. I also don't see
how operations with decimals (i.e. decimal fractions - to give them
their full title) could possibly make sense to /anybody/ who hasn't
been taught at least what they /are/, as fractions. Which leads me
to ... "simply no longer be considered to be numbers"? That just
seems to be 99.999% unequivocally 'irrational'! I don't see how it
could even be explained away as being provocative, or making a joke.

After all, what kind of answer is "385 over 23," when "about
16.7" conveys the same information so much more directly?

The information being, sixteen and seven tenths? Or if not that,
then /what/ information? Just a string of decimal digits, to be
manipulated blindly, and with ignorant trust in the accuracy and
reliability of computing machinery?

Are we to have a mathematical Newspeak in which we can no longer
even think the thought that sqrt{2} is irrational? I say, teach
them Eudoxus's theory of proportions! Then the little blighters
will be glad only to have to worry about fractions! :-)

(The smiley is sadly necessary, because my modest proposal seems
scarcely any dafter than the one actually under consideration.)

I thought quasi was just being silly (after all, he has given me
the "kook" treatment once or twice), but after reading DeTurck's
actual words, I really do find myself wondering what on Earth he
thinks he's on about.

I keep thinking that, as an obviously respected researcher (also
a former associate editor of the American Mathematical Monthly),
he /must/ have a serious point, but he seems to be going to great
lengths to make it hard for anybody to see what his point is.

Am I just missing the joke?

--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
.

Relevant Pages

  • Re: Abolish Fractions?
    ... rules for calculating with fractions, he might have a decimal point, ... that operations with decimals would make sense. ... Am I just missing the joke? ... really is a kook. ...
    (sci.math)
  • Re: devreden
    ... Apparently, high school texts don't ... in my high school algebra 1 text about converting repeating ... We knew from grade school long division that some fractions ... give rise to repeating decimals (and if this is all that you're ...
    (sci.math)
  • Re: Abolish Fractions?
    ... later math, and so needs to be taught _early_, as early as possible, ... decimals are boring -- there is no ... except the underlying depth of fractions. ... The quality of math literacy of elementary school teachers is so low, ...
    (sci.math)
  • Re: devreden
    ... Apparently, high school texts don't ... We knew from grade school long division that some fractions ... give rise to repeating decimals (and if this is all that you're ... using geometric series, but since this was a small rural school, ...
    (sci.math)
  • Re: Abolish Fractions?
    ... He's a kook. ... Without a solid understanding of ordinary fractions, a student ... Rather I think he is proposing that one ...
    (sci.math)