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[quote=Anonymous][quote=Anonymous]For all the upset about the current system of teaching children (and I am worried about quite a bit of it) I will say that the focus on UNDERSTANDING numeracy, and really GETTING math at it's fundamental level, is very different from when I was in being educated.

I was never taught to be "flexible" with numbers, that I could get the answer to 29+14 by doing 30+14 (which is easy) then taking away 1.  I picture 29+14, start carrying the one in my head...  it's a riot to see me!  And takes me forever.    My husband does that stuff in his head.

We were just talking about fractions the other day (we're in late 40s) and I realized that I have never stopped to really THINK ABOUT what multiplying fractions is - I learned the "rule" of how to figure it out and boy, do I follow rules well.  But if I don't remember the rule (and I didn't 2 days ago) then I'm flumoxed.  Since he knows the intention of multiplying fractions, he understands what he is doing.

I'm just a trained monkey.  A well-trained one who got all A's in math classes, but a trained monkey.

I would rather my kids not be just trained monkeys.

And, yes, I also think children need to have their "addition tables" and "times tables" memorized at some point, but it seems to make more intuitive sense to wait until they understood what adding and multiplying mean before they just memorize stuff.  Memorizing is important - you can't stop in geometry to use your fingers to figure out what 8+5 or 8x5 is - you gotta have that memorized.  Just not before they understand what the concept is.

Of course, all children can "say their ABCs" and can count to 10 by walking up stairs and saying the numbers in the correct order way before they understand what each letter sounds like, how to combine it to make a word, etc.  But that feels different than memorizing multiplication tables.

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I'm embarassed to say this is the same with me and my DH.

We both got excellent grades, and we both aced our SATs etc.  That's not the issue.

But when we went off to college, he had with a far deeper and more conceptual understanding of math than I ever did.

For him, math is intuitive and easy.  For me, it's mostly rule-based and tedious.  Also, I found higher math far more difficult in college.  I just lacked that conceptual foundation for math, and it held me back.

The sad part is that I very much enjoy conceptual and abstract learning.  I would have loved to learn elementary and middle school math the way it's taught now, and it would have given me a much better math foundation for the long run.  But that's not the way it was taught at my schools, and my parents did not know or have an interest in helping me understand it conceptually.

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