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Topic: single digit addition
Replies: 10   Last Post: Aug 11, 2000 11:21 AM

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RayM

Posts: 308
Registered: 12/3/04
single digit addition
Posted: Aug 10, 2000 10:08 AM
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OK. So we can't agree about long division. Let's try something simpler:
single digit addition.
1. Is there any rational basis (along Lou's line of thought) for requiring
memorization?
2. Can anyone PROVE that addition even needs to be taught?

Now take the above and successively substitute
single digit subtraction
single digit multiplication
single digit division
mlutiple digit, multiple addend
single digit division
long division with remainders
perfect squares
square roots
trig functions
Bessel functions
the Turing busy beaver function, W(n)

Now add on to that the question of when each topic should be introduced and
when formal instruction should be finished. It would probably be an
enormous waste of human potential if everyone was required to include
essays on each of the last three in their portfolios as a condition for
graduation of high school. Should there be some evidence of ability to do
the first 3? Should proficiency and speed on the first 6 be an ABSOLUTE
requirement for ALL students? I don't think so.



My personal spin on long division is that it is no big deal. Introduce it
it the second grade, formal instruction is over in the 3rd. If a
particular student can't do it by the 9th grade and in the absence of any
other knowledge, my recommendation would be to give up. If a large
identifiable group of students can't do it, there then arise the questions
of why?, what can be done?, and should we? Is it worth the additional
expenditure of scare resources? By that point, the arguments are so
complex, it seems unlikely to me that even (especially?) a proof could be
"clear".

----------
> From: me@talmanl1.mscd.edu
snip
> >
> > iii. Is no improvement necessary, much is ill in public education but
> > there is nothing we can do about it or

>
> There is much we can do about it, but we must be clear about our
> purposes, and about our reasoning, and about what we know and what we
> don't know. I, for one, will be the first to admit that I don't know
> very much. And one of the things I still don't know is this: "What is
> the place of long division in what Mark Van Doren once called 'the
> natural history of a mind'?" An attempt at a rational, instead of a
> rationalized, answer to that question might be a good place to start.
> K/M is full of sound bites and fury bites, but they are all also
> signify-nothing bites, as Andy Isaacs has amply shown.
>
> And it might prove, in the end, to be an intractible problem. Or it
> might prove to be intractible in a culture that, say, does not perceive
> teachers to be working if they are not directly engaged with students or
> with students' work. Simply changing this single cultural perception
> could have a salutory effect. K--12 teachers work in dreadful isolation
> from each other, and one of the things that Ma has identified as an
> important part of something successful is the collegiality of the
> Chinese system; *that* is something that is not predicated upon a single
> personality. How does that fit into your suggestion that we emulate
> what has been shown successful? (Hint: "Exactly what has been
> 'shown'?" is the first question a rational skeptic must ask.)
>
> --Lou Talman






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