On Jun 18, 2013, at 10:20 PM, Joe Niederberger <email@example.com> wrote:
> "It's time to recognize that, for many students, real mathematical power, on the one > hand, and facility with multidigit, pencil-and-paper computational algorithms, on the > other, are mutually exclusive. In fact, it's time to acknowledge that continuing to > teach these skills to our students is not only unnecessary, but counterproductive and > downright dangerous." This is just a personal opinion, but this person was selected by > the government to make an important decision about mathematical education." > > That's rather strong, and wrong.
I have never met a person with "real mathematical power" and without facility with multi-digit arithmetic. Granted, I am in an environment where math is applied, not just thought about, and that requires numbers of all kinds. I also note that calculators, except for a brief stint in the 70's, never really caught on. It's kind of hard to make a statement that these things are exclusive when empirically at least, they are not. I think the main problem with these theories, other than their stark contrast with reality, is that the authors of them have a poor remembrance of how they got from there to here and what here is.
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. These algorithms are still the most effective means with which to develop that fluency and I have seen no evidence that a worthy alternative exists.
The other thing wrong with these characterizations of pencil and paper arithmetic is that they are taught like they were 70 years ago. Maybe some of these authors are that old and they are referring to a time when humans competed with adding machines. That competition ended in the 50's. The adding machines won. Even when I was in school (60's and 70's), pencil and paper algorithms were taught in their entirety but not to the point of competing with an adding machine. The only difference between my time and today is that they don't follow up the lessons with as many exercises and word problems like they used to. Except for those cases where they abandoned arithmetic altogether (which is rarer than you think).