For some introductory material, memorization really is required. 5 x 5 = 25 is a true fact that I expect a young student to simply memorize.
Looking back, we can understand why it is important to learn those types of things - but the explanation of why is often far more complex than the object level fact.
I recently spent a bunch of time realizing that memorizing multiplication tables, formulas, and random numerical facts about the world is a really good idea. (fermi estimation). I notice you need some theory to actually connect the memorized facts to reality, though.
What use is 5*5 = 25 is you don't know how to use numbers and recognize when multiplication is appropriate?
Maybe the trick is to get students to solve mostly complete world-connected problems so that they develop the skills of connecting the memorized procedures to something useful.
Still, as yo...
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.