On Jun 19, 2013, at 1:18 PM, Dave L. Renfro <email@example.com> wrote:
> Robert Hansen wrote (in part): > > http://mathforum.org/kb/message.jspa?messageID=9139927 > >> I have always chalked it up to the simple fact that numbers (mostly multi >> digit numbers) are every where and they tell stories and without some >> fluency in their construction and use, you would be unable to read >> those stories. > > This is very nicely put, poetic in fact! > > Dave L. Renfro
Devlin doesn't seem to get it. He writes...
"Those standard algorithms sacrificed ease of understanding in favor of computational efficiency, and that made sense at the time. But in today?s world, we have cheap and readily accessible machines to do arithmetical calculations, so we can turn the educational focus on understanding the place-value system that lies beneath those algorithms, and develop the deep understanding of number and computation required in the modern world, and prepare the ground for learning algebra."
He needs to open his mind a bit and recognize that the need for multi digit arithmetic is probably greater now than it was 50 years ago or even 100 years ago. That is not to say that there is a need to add columns of large numbers and produce financial ledgers by hand. We have computers for that now. But we still have to pour over those ledgers and discuss them quantitively. A task that cannot be performed without arithmetic fluency.
Devlin's argument isn't against teaching any particular arithmetic algorithm. He is against all of them. Sure, introduce an algorithm, whatever it is, but dare not teach it long enough that the student develops a personal fluency with arithmetic. Heavens no. That would be a total waste of time because we have machines that can add and subtract.
I have been in thousands of meetings and I have never seen any machines making financial or quantitive decisions. But I agree, they add and subtract damn good.