My daughter is so cute when she tries to cut food. She's 4 and has just started asking to learn to use a knife, which is a relief. I'll grab any opportunity to pass off another duty.
But my right-handed girl can't understand the concept of using her less dominant hand yet, so when she tries to cut her fish sticks or chicken, she'll hold the dinner knife in her right hand and start sawing away. But then she doesn't know what to do with the fork, so it sort of dangles floppily in her left hand, and doesn't do a very good job of restraining the meat, which is still intact and sliding all over the plate.
If she lived in Ireland with her grandparents, this Continental style would be correct (her technique aside). The Irish, as well as the Brits and most Europeans, hold their forks with the tines facing down in their left hands and sort of push or pile food on top of it with their knives, in their right hands. Then you eat from the fork in your left hand.