I recently made the brash statement that spending very much time
teaching long division to children is sort of a silly thing to do
because
1) Most people have only a vague idea what they are doing when they
carry it out and it therefore does not increase intuition.
2) As a calculational procedure it is becoming less and less useful
with the ubiquity of calculators.
3) A pencil and paper method that is both faster for humans to carry
out, and converges faster on the answer could probably be designed.
1 and 2 are matters of opinion to be informed by educational
psychology and I don't think it's worth it to discuss them here, nor
do I think my opinion is very well informed.
3 however, is an interesting exercise to keep one occupied on a long
transcontinental flight or otherwise. Does anyone have suggestions for
references to division algorithms other than wikipedia?
I came up with a method that uses powers of 2 and their combinations
to approximate the quotient using only multiplication by 2, 10 and
addition but although each step is relatively easy, it converges
linearly giving only a fixed number of binary digits per iteration
(note, it's carried out in decimal on paper, but the answer is
computed in an essentially binary manner)
Is there a method amenable to pencil and paper computation that will
converge super-linearly which uses operations that 10 year olds could understand?
enjoy the challenge, and happy new year to all of you.
Dan
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Daniel Lakeland