Actually I did respond to you -- and more. I argue against its usefulness in business and the STEM fields. I'm shrinking the sphere in which your argument is useful.
I argue that calculations are working-memory bound, and that common uses of time go beyond 12 x 12.
For time, we often go by units of 5, 10, 15, 30, 45, 60, of these only 60 can find 12 as a divisor. You don't get to claim usefulness for all time. For the rest of these units, it's working memory doing arbitrary integer computation for us.
If we're talking about months in a year -- what's the use case for fast mental calculation? Is this the little sphere where we say 12 * n is useful?
We're talking about a policy for education for all children here. Your use cases sound really limited, if it at all impacts later cognitive performance outcomes.
It's working memory that's going to be the differentiating line between "fast mental math" and "busting out calculator" or "punching in numbers into SAS or SPSS". It's difficult to believe that Taiwanese children are going to have trouble versus American children in time based operations, if that at all continues to be a practice under the common core.
I can't imagine asking some Taiwanese business man, "Quick, what's 6 * 12 in a business context", and he goes, "Let me quickly grab a calculator."
Can you do 15 * 14? I think you can. Why can we do it? Is it because we learned 12 * 12? No. It's working-memory bound. We're doing capricious calculations with distributive property via 10^n multiplicands.
How about 24 * 17? I think you can do that too. Why can we do it? Working memory. Not because we learned 12 * 12 when we were little.
I argue that calculations are working-memory bound, and that common uses of time go beyond 12 x 12.
For time, we often go by units of 5, 10, 15, 30, 45, 60, of these only 60 can find 12 as a divisor. You don't get to claim usefulness for all time. For the rest of these units, it's working memory doing arbitrary integer computation for us.
If we're talking about months in a year -- what's the use case for fast mental calculation? Is this the little sphere where we say 12 * n is useful?
We're talking about a policy for education for all children here. Your use cases sound really limited, if it at all impacts later cognitive performance outcomes.
It's working memory that's going to be the differentiating line between "fast mental math" and "busting out calculator" or "punching in numbers into SAS or SPSS". It's difficult to believe that Taiwanese children are going to have trouble versus American children in time based operations, if that at all continues to be a practice under the common core.
I can't imagine asking some Taiwanese business man, "Quick, what's 6 * 12 in a business context", and he goes, "Let me quickly grab a calculator."
Can you do 15 * 14? I think you can. Why can we do it? Is it because we learned 12 * 12? No. It's working-memory bound. We're doing capricious calculations with distributive property via 10^n multiplicands.
How about 24 * 17? I think you can do that too. Why can we do it? Working memory. Not because we learned 12 * 12 when we were little.