Re: Sixth grade science teaching

In article <dh72o3$cb1$1@xxxxxxxxxxxxxxxxx>,
Paul J Gans <gans@xxxxxxxxx> wrote:

> Grace Haliburton <kaosgrace@xxxxxxxxx> wrote:
> >I beg to differ. If a 7th-grader knows 7x6 by rote...so what? He should
> >be at least in pre-algebra, where he'll have to solve for x*6=42, and
> >if he doesn't know what 7x6 means, where 42 came from, and why...he'll
> >have no understanding of the new stuff he's learning, and by the time
> >he gets to Calculus he's royally screwed. Same with grammar- you can
> >recite off the definitions of adverbs and adjectives all day and still
> >have no grasp on how to use them properly in a sentence. Rote learning
> >vocabulary is even worse because it results in so-called educated
> >people using words completely wrong because they don't know what they
> >mean; they just memorized the definition. The absolute only place rote
> >learning has in elementary education is //after// understanding the
> >basic concepts: once you know what "times" means and you can work out a
> >multiplication problem in your head, then and only then, memorizing the
> >times tabes can make you more efficient (but so can a calculator).
>
> Whoa. I was with you up to this last bit. You *can'*
> work a multiplication problem if you don't know the
> multiplication table.
>
> The one exception is if you equip yourself with a huge
> number of pebbles and do 7x9 by counting out seven piles
> containing nine pebbles each, and then counting the entire
> bit.

[Arrange the problem with the smaller number on the bottom.
repeat for each digit starting with the digit on the right of the bottom
number

Write the number on top the current bottom number of times, appending
the current number position from the right zeros to the right of it,
that is zero extra zeros for the right most digit, 1 for the second
right most digit etc.

end repeat

Add up the numbers giving the product.
]

This works better in binary of course.

Used by the old Friden mechanical calculators.

> All this does, of course, is reduce multiplication to
> addition. It does nothing to make a student fluent in
> multiplication.
>
> There is simply no way to get around memorizing tables.
>
> Now, nobody ever said that you teach multiplication as
> a mystical exercise devoid of reality. You can demonstrate
> the nature of multiplication to a student with pebbles and
> the notion of counting, not by ones, but by twos and threes
> and fours. This will introduce multiplication because what
> it really is is a recital of the multiplication table.
>
> The analog in reading is memorizing the letters. There's
> no way around *that* either.
>
> I have no idea why folks have such a resentment against
> learning things by rote. That's the only way *to* learn
> many things.
>
> Sure, many of us were tortured by incompetent teachers when
> we were young, but then, they tortured us even when *not*
> having us memorize things.
>
> ----- Paul J. Gans

--
Guns don't kill people; automobiles kill people.

.

Relevant Pages

  • Re: Sixth grade science teaching
    ... have no understanding of the new stuff he's learning, ... he gets to Calculus he's royally screwed. ... multiplication problem in your head, then and only then, memorizing the ... I agree that a lot of the newer concepts in education are idiotic. ...
    (talk.origins)
  • Re: Sixth grade science teaching
    ... >have no understanding of the new stuff he's learning, ... >he gets to Calculus he's royally screwed. ... and then counting the entire ... There is simply no way to get around memorizing tables. ...
    (talk.origins)
  • Re: Sixth grade science teaching
    ... >> have no understanding of the new stuff he's learning, ... >> he gets to Calculus he's royally screwed. ... The absolute only place rote ... >> multiplication problem in your head, then and only then, memorizing the ...
    (talk.origins)
  • Re: Sixth grade science teaching
    ... > have no understanding of the new stuff he's learning, ... > he gets to Calculus he's royally screwed. ... > multiplication problem in your head, then and only then, memorizing the ... > I agree that a lot of the newer concepts in education are idiotic. ...
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