DD5 worked out a trick for multiplication recently and while i expect she'll be able to remember the entire table soon, she's REALLY enjoying her trick. working out your own way seems like a one-way ticket to confidence, so that works for me.
Yea, there's a trap there. I probably get too eager to share tricks with my DS to the detriment of his own discovery/ownership/pride. Though he won't take things at face value. Last week I told him one shortcut, and he tried it, then tried the regular way and did that for a few more problems before deciding my input was valid.