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Re: focus
Posted:
Jul 29, 1996 2:23 PM
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Andre TOOM wrote:
> By Guidelines you probably mean the documents published by NCTM and
> often called `Standards'. I would rather call them misguidelines.
> Let us look at p.139 of ``Curriculum and Evaluation Standards'':
>
> ``Real-world problem situation. In a two-player game, one point is
> awarded at each toss of a fair coin. The player who first attains
> n points wins a pizza.Players A and B commence play: however, the
> game is interrupted at a point at which A and B have unequal scores.
> How should the pizza be divided fairly? (The intuitive division, that
> A should receive an amount in proportion to A's score divided by the
> sum of A's score and B's score, has been determined to be inequitable.)''
>
> Let us leave aside the mysterious phrase ``has been determined''.
> (This phrase alone tells any competent math educator that this is a hoax.)
> >From the text in the brackets we learn that the pizza should be
> divided equitably. But the most equitable division is half-and-half!
> What do the authors really want?
>
> Then they set a mathematical problem, which has nothing to do
> with equity, solve it and write:
>
> ``Validation in original real-world problem situation. Empirical evidence
> gained from actually playing out the game many times or, more easily,
> from computer simulation (using random numbers to represent coin tosses)
> confirms this solution.''
>
> Here the verb `confirms' is in the Present Indefinite tense,
> which is normally used in the English language to denote action
> which actually takes place in present. Does it mean that somebody
> actually played this game or simulated it using a computer when
> the book was written? I am sure that not. NOBODY PLAYED THIS
> GAME AND NOBODY SIMULATED IT. How do I know it? Because if
> somebody tried to do it, he or she would immediately notice
> that playing or simulation does not confirm anything, because
> there is nothing to confirm.
> So much about Guidelines, their authors, their concern about
> probability and solving problems and their competence
> in mathematics, education and English.
>
Contrived? Perhaps. But surely Professor Toom recognizes this classic
problem--The Problem of the Points--which by many accounts spawned the
modern era in probability. Here the Standards suggest using a geometric
approach to solving the problem, but certainly one could eventually make
the connection to Pascal's Triangle and extensions. I'm not sure I
would disguise the problem as was done here, but that's a matter of
taste.
I have played the game and simulated it many times on a computer. I do
not however recognize the term "Present Indefinite" tense. Perhaps
others will clarify.
H^2
--
Howard L. Hansen
Assistant Professor of Mathematics
Western Illinois University
Macomb, IL 61455
http://www.ECNet.Net/users/mfhlh/wiu/index.htm
"Good mathematics is not how many answers you know,
but how you behave when you don't know the answer."
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