My kids are not big on flashcards either. They especially didn't work for DD8. She just got fast enough in her calculations that it didn't matter that she didn't memorize them. I tried flashcards with her for several frustrating weeks, until I decided that it wasn't getting her anywhere (except frustrated!)
DS4 does arithmetic in his head by visualizing items to count. He visualizes the counting, too and counts silently. You wouldn't know that he didn't just memorize it. He once did a calculation like this and told me the answer. When I praised him for figuring it out, he said, "But Mom, I cheated because I just counted the dots in my head!" He also thinks sounding out new words is "cheating" because he didn't just read them instantly.
