Teach the rote memorization but explain why it is true in terms of some understanding.
Yes, but this only really works if, when the student is presented with an example they didn't memorize, they can still solve it using their understanding. And to make sure they do understand, after they've practiced on the simple cases they can memorize, you routinely set problems that require understanding.
You can't start with understanding because when solving a few simple cases (like 5x5), memorization really is effective, and students may choose to memorize even if you don't explicitly tell them to.
As a teacher, I wonder if it is possible to instill this skill into students the skills of rationality and critical thinking. I teach the third grade, and it is not immediately apparent how to apply this with my own class.
The problems I foresee are as follows:
In the sequences, it is suggested teachers should drill into students words don't count, only anticipation-controllers. How practical is this for an elementary school level? Also appreciated would be any ideas or experiences on how to do this, or how to combat the above problems. Hearing from other teachers would be excellent especially.