One of our biggest public school frustrations had been in the area of math. We were absolutely certain that Tom could and should be moving forward much more quickly - but the teachers either wouldn't or couldn't do so. TouchMath had been a helpful tool for teaching some calculation (especially basic addition and subtraction), becaue it had him count "touchpoints" on each number and thus add and subtract without having to use his fingers.
But he had been doing double digit adding and subracting with and without carrying/borrowing for two solid years!
Finally, at the very end of fourth grade, his teacher started using our Touchmath materials with the whole class to work on "skip counting" (counting by 2s, 3s, etc.) as a prelude to multiplication. TouchMath also using skip counting by 5s and 10s to teach money and time concepts, so he had those sets of numbers pretty well memorized. But why wasn't he doing multiplication? Fractions? Measurement? Decimals? I was determined to push him forward.
I started out using some math sheets I generated and/or printed from sites like softschools.com and enchanted learning - and they worked well for certain types of problems. I quickly saw that he could do simple word problems (Joe has 6 apples. He gets two more. How many does he have in all?) without any prompting or visual tools (though he never had come home with word problems from school). And basic fractions were no problem at all: he could identify and even create representations of 1/3, 1/2, 2/3, etc.
But he was still having terrible problems with basic addition subtraction - because he'd forget all about carrying/borrowing. He didn't seem to grasp bigger/smaller beyond the number 10. And when I asked him to count by two's, he could do so only up to number 26. Then he pooped out.
Within a few weeks, I figured out the problem.
It seems that, in teaching Tom skip counting, his teachers used a chart and had him memorize 2, 4, 6, 8, etc. But they neglected to TELL him about the pattern he was forming. As a result, he could count by twos to 26 - but had no idea what came next. I used a number chart and a pencil, and we went through saying skip, 2 (put an X on the 2), skip, 4 (put an X on the four). We did the same thing for threes and fours and fives. He has NO trouble using the charts to multiply up to 100!
I ran into the same problem with bigger/smaller. He seemed to be guessing about bigger/smaller when the numbers got bigger than 10 - and I finally realized that no one had given him rules for deciding relative size of symbolic numbers (as opposed to piles of objects). I explained more digits means a higher number. If there are the same number of digits, compare the digits on the left. If they are the same, go on to the next pair. When you find a pair that don't match, compare them. The number with the highest digit is the biggest number.
He got it.
In short: being autistic, he didn't "see" patterns just because they were repeated. He needed to have the patterns explained. But once they were explained, he whizzed forward!
The down side of all this is that I am having to create my own worksheets at odd hours to let him practice all of this. But I'm hoping that, within the next couple of months, I'll be able to return to computer-generated worksheets - and even get online with Tom (so far he's not really very excited about computer games, but I think I can get him going...).