Re: Abolish Fractions?

MrKofner <matthew.smedberg@xxxxxxxxx> wrote:
Gerry Myerson <ge...@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
quasi <qu...@xxxxxxxx> wrote:
amzoti <amz...@xxxxxxxxx> wrote:

Thoughts?
http://www.usatoday.com/tech/science/mathscience/2008-01-23-fractions_N.htm

He's a kook.

When you've accomplished one-tenth of what he has,> maybe you can
call him a kook. In the meantime, I suggest you
1. don't believe everything you read in usatoday,
2. keep a civil finger on your keyboard, and
3. wait until you see a detailed exposition by the man himself.

The man may or may not be a kook, but he's dead wrong.
Ignorance of fractions literally dooms a student in middle-school and
high-school math. And not because "they have to learn fractions there
too". It's because competent high schoolers can think in terms of ratio
and proportion, and those who cannot deal with fractions cannot.

But such ratios and proportions can just as easily be expressed
in terms of decimal fractions for the purposes of the layperson.
I suspect DeTurck's proposal is that one should first teach
decimal fractions, delaying integral fractions till a later point.
It is very rare that one needs integral fractions in applied
mathematics, i.e. the "diophantine" aspects of fractions occur
rarely in the real world (or non-number-theoretical mathematics).
In fact I suspect most readers will have a hard time thinking
of any real-word problem that requires integral fractions as
opposed to decimal fractions. How about it naysayers?

Otoh teaching fractions has numerous *pedagogical* virtues.
Most importantly it is usually the first example of a
equivalence relations (congruences) and quotient structures
that the student will encounter, and the first time the student
learns to compute operations on elements in quotient structures.
Such abstract reasoning is best learned in a mathematical context.
Indeed, one might argue that the primary purpose of teaching
math to the layperson is to encourage abstract logical thought.
Perhaps DeTurck is proposing that one should delay the teaching
of integral fractions until the student has sufficient background
to appreciate some of these finer points, esp. if there is no
other need to introduce them earlier. And I have yet to see
any critic demonstrate even one such need.

--Bill Dubuque
.

Relevant Pages

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    ... quasi wrote: ... He's a kook. ... if you cant work with fractions. ... he should have better said abolish aleph_3 instead of fractions. ...
    (sci.math)
  • Re: Abolish Fractions???? the nutty professor 3 -> out now !!
    ... quasi wrote: ... He's a kook. ... if you cant work with fractions. ... he should have better said abolish aleph_3 instead of fractions. ...
    (sci.math)
  • Re: Abolish Fractions???? the nutty professor 3 -> out now !!
    ... quasi wrote: ... He's a kook. ... if you cant work with fractions. ... he should have better said abolish aleph_3 instead of fractions. ...
    (sci.math)
  • Re: Abolish Fractions?
    ... He's a kook. ... "The problem, he says, is that in grade schools "fractions are where the wheels come off for many kids." ... In one class, a student posed the question of why it was necessary to find common denominators to add fractions, ... just wrote more equations on the chalkboard. ...
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  • 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)