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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]What in the world is a "brittle understanding of multiplication"

It's really not a hard concept at the basic level.  Sure, eventually there is more to learn, but understanding the basic concept (ie, repetitive addition) isn't a hard one, and the vast majority of 2nd or 3rd graders, and most 5 or 6 year olds, can understand that.  
I can't begin to imagine a problem with a kid memorizing their times tables after a 10 minute explanation of what the x means.  it doesn't mean that they won't learn more and develop a deeper understanding.  But it's crazy to pretend that somehow by having quick recall of multiplication tables that you are hurting their math ability.[/quote]

If your child memorizes the times tables up to 12x12, that's great.  It will help a lot.

AND

At the same time she will also need to understand the concepts enough that she can do 12x17 in her head.  Quickly.

A child who can do the first but not the second is to me an example to me of one who has a "brittle understanding of multiplication."  It's not just about the basic concept of repetitive addition.  It's about understanding the concepts enough to think on your feet and apply strategies to solve problems you haven't seen before or memorized.

A well-educated child needs to do both.  Memorize the tables and have an ability to apply the concepts well beyond the tables.

Along those lines, I also agree with the PP who said that the timing of memorization depends on the child.  Some can memorize them early and still tune in later in class and even have fun playing with the basic concepts and manipulations, even though they can immediately call up the "right answer" from memory.  Others who already have done the memorization feel crazy bored by all the repetitive "process" work and tune out because they already "know the answer" from memory.  Those are the kids who miss out on the deeper learning and struggle to catch up later, even though they seem ahead in third grade.
[/quote]

What is your "quick way" to you of multiplying 12 x 17? I can think of several, but maybe there's a quicker way I haven't thought of that should have learned.[/quote]

I'd use the base 10.

10x17=170 and 2x17=34.

170+30=200  and 200+4=204

[/quote]

In Russia back in a day we'd would do:
10x17=170 and 2x17=34 and then add 170 and 34 by heart. That's it, keep it simple.
There is so much going on in your education system and I don't understand half the words used in math, but it hasn't helped your children learn to calculate.
I had a coworker(she has Bachelor's degree) who asked me if 20% tip on a $100 tab paid by 1 card is more than the same  check paid by 4 credit cards plus 20% tip on each card based on their amounts.WTH!
The other girl had to divide cash into 5 piles equally. At the end she was left holding $5 bill. She had enough dollar bills in piles to make the change- put $5 into first pile and take 4 1-dollar bills out, then put one into each pile. Couldn't figure it out, went and got more change for the $5. 
Even though I have worked with many more foreigners than Americans, it has always been an American who can't figure out how do calculate something. What gives?[/quote]

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