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Replies: 28   Last Post: Aug 9, 2000 4:20 PM

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 Wayne Bishop Posts: 5,465 Registered: 12/6/04
Posted: Aug 6, 2000 6:33 PM

At 12:12 PM 8/6/00 -0600, me@talmanl1.mscd.edu wrote:
>
>I don't know a mathematically literate person who disagrees with the last
>with the last two of Wayne's statements above.

Well, my computer seems to have eaten my response based on one main-line
publisher, so I'll use another. This one is Book 3 of a middle school
curriculum that includes lots of names but the first five, and in larger font
size, are Randall I. Charles, John A. Dossey, Steven J. Leinwand, Cathy L.
Seeley, and Charles B. Vonder Embse. From P. 370 [with a picture of a New
England farmstead] we have, "A number that cannot be expressed as a repeating
or terminating decimal is an *irrational number*. Not mentioned is why there
needs to be a new definition at all, since rational numbers already exist, and
why the new definition is not the negation of the other. This definition is
then followed by:

Example 2 Use your calculator to determine whether each square root is
rational or irrational.
a. -sqrt(723) b. sqrt(256)
Enter 723 [sqrt-key][+/-]. -26.88865932 -sqrt(723) is irrational.

The following exercises are just as inspired along with more irrelevant
pictures; e.g., a cabbage seed splitting open.

The other book had similar problems, such as discovering that sqrt(1.21) is
rational, from the calculator of course, whereas it did not have the
calculation that mine gives of sqrt(1.21 + pi/10^80) which has exactly the same
display; i.e., no superfluous zeros, simply 1.1.

This book doesn't have the list of such well-known names but inside the front
cover it touts its teaching package as "Uniquely developed to help you
implement the NCTM Professional Standards for Teaching Mathematics" and that it
is "Complete with in-text correlations to the NCTM Curriculum and Evaluation
Standards."

I did not invent this absurd calculator misuse nor did Milgram and Klein.

Wayne.
-------------------------------------------------------------

At 12:12 PM 8/6/00 -0600, me@talmanl1.mscd.edu wrote:
>Wayne Bishop wrote:
>

>> Let kids check their decimal arithmetic on a calculator? Sure, I even
>> tell her to but she usually doesn't. Noting that pi, sqrt(2), and
>> 111/113 are irrational because the screen doesn't indicate a repeating
>> pattern? Get people who push for such idiocies out of the decision
>> making process.

>
>I don't know a mathematically literate person who disagrees with the last
>two of Wayne's statements above.
>

>> Don't even mention the words if the kids aren't
>> familiar enough with the (and it is *the*) division algorithm to be
>> helped to understand the joke.

>
>I've currently been mulling over a paper, written by Klein & Milgram,
>and titled "The Role of Long Division in the K-12 Curriculum". It's a
>very interesting combination of good mathematics and bad polemics--the
>latter including rationalizations and even baldly false statements.
>It's available at
>
> http://math.Stanford.EDU/ftp/milgram/long-division/longdivsiondone.htm
>
>I'd be interested in other folks' take on this note.
>
>--Lou Talman
>