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I was a proponent of "New Math" types of philosophies before I had a kid. It was only when I tried to teach concepts did I realize how important it was to be a

I was a proponent of "New Math" types of philosophies before I had a kid. It was only when I tried to teach concepts did I realize how important it was to be able to be able to arithmetic quickly off the top of your head. Its hard to explain, or even to grasp, how fundamental basic arithmetic is to almost everything in math. For us arithmetic is as simple as thinking a thought -- but only when I tried to actually explain concepts to a young kid did I realize how difficult it is for them to understand these concepts when arithmetic isn't ingrained in their brain. I hate to admit it, but I am now a believer that strong arithmetic skills are important, and drills get you there. I don't like to call it memorization, since I'm not sure it necessarily is simply memorization. But you do need the answers at a moments thought. It should be as natural as saying a word. And its not to say that you don't teach concepts concurrently... but that the arithmetic is fundamental. That said, I still believe that the long division algorithm taught isn't so useful. :-)

brlewis 9y ago
I generally agree with your comment but have specific disagreements with two parts: Its hard to explain, or even to grasp, how fundamental basic arithmetic is to almost everything in math. I disagree. Not hard to explain at all. Point the person at a page of geometry problems and say, "Imagine struggling with 90 + 90 at the same time as you struggle with the concepts here." Point the person at a page of polynomials to factor and say, "Imagine trying to do these if you hadn't memorized basic multiplication facts." And so on. I still believe that the long division algorithm taught isn't so useful. At the risk of not knowing precisely which algorithm you're talking about, I can't imagine one that doesn't work by taking a large/hard division problem and breaking it down into small/easy division problems. And that's useful because it's a great example of what math does for your thinking. To be specific, I think the important principle math teaches is that, when faced with a big, hard problem, break it down into smaller, easier problems. I would rather describe math as a "learn how to break down problems" discipline rather than use the vague and pretentious "learn how to think" description. All areas of education help your thinking.
zbobet2012 9y ago
I never memorized my times tables and do just fine with graduate level mathematics. If you ask me 9 * 7 I still do 10 * 7 = 70 - 7 = 63 in my head; but, I seem to handle spectral graph theory just fine.

brlewis 9y ago

I generally agree with your comment but have specific disagreements with two parts: Its hard to explain, or even to grasp, how fundamental basic arithmetic is to almost everything in math. I disagree. Not hard to explain at all. Point the person at a page of geometry problems and say, "Imagine struggling with 90 + 90 at the same time as you struggle with the concepts here." Point the person at a page of polynomials to factor and say, "Imagine trying to do these if you hadn't memorized basic multiplication facts." And so on. I still believe that the long division algorithm taught isn't so useful. At the risk of not knowing precisely which algorithm you're talking about, I can't imagine one that doesn't work by taking a large/hard division problem and breaking it down into small/easy division problems. And that's useful because it's a great example of what math does for your thinking. To be specific, I think the important principle math teaches is that, when faced with a big, hard problem, break it down into smaller, easier problems. I would rather describe math as a "learn how to break down problems" discipline rather than use the vague and pretentious "learn how to think" description. All areas of education help your thinking.

zbobet2012 9y ago

I never memorized my times tables and do just fine with graduate level mathematics. If you ask me 9 * 7 I still do 10 * 7 = 70 - 7 = 63 in my head; but, I seem to handle spectral graph theory just fine.