I have to agree with Lily on this one. The original question was "How do you know when they have learned the facts using these timed drills?"(or something like that.
Actually, I learned quite a bit about how young children learn math, in the past couple of years, mostly from Ruth Beechick's booklets on the 3R's (An Easy Start in Arithmetic). The first mode of thinking you go through is the manipulative mode, with real objects that can be moved around, added and grouped.
The transition mode is where you can think in pictures of objects, then symbolic pictures(like dots).
Then comes the mental image mode where they can think about touchable objects (example would be word problems, like, you have one cookie and I have 2 cookies, so we have 1 + 2 = 3 cookies.
Lastly, the symbolic mode comes, where they do the math facts found in the drills they were talking about.
I had never heard of these modes, however, they are important, and worth reading about before you get too far into doing math together. It cuts the frustration way down.
So, look for Ruth Beechick's booklet set called "The Three R's".
Another place I found this information was a booklet from Mary Hood, Phd., called "Taking the Frustration Out of Math". She has some suggestions for games and books to use in the different modes. Her website where you can find out more information and order her booklet is:
http://www.archersforthelord.org
Mary avoided math, she says all the way up until she was an adult, thinking she could never master it. She learned about the modes you need to go through and after that she did all her math up to Algebra. So, it is never too late to learn math, and if you learn along with your child, you will help them, and yourself.
I know that learning with your child is good because when my son wanted a challenge, I had him learn some arithmetic tricks, and we did some mental math. Now, we like to do math in our head, and only do calculators for the times it's a complex problem.
How do I know he is learning it? I give him a mental math problem. He gives me the answer. Then, I ask him how he got the answer, and he tells me. Many times he comes up with the answer in a different way than how I got it.
Well, I hope this will help somebody. Thanks for letting me share it with you.