I don't know about this "What without the how and why." Every time it happened to me - finding the inflection point of a quadratic equation, for example - I was pissed off about how much time I had wasted on stupid crap. Re-deriving Calculus would have been entertaining and educational, and loads more useful than memorizing a formula so I could draw ugly graphs over and over and over again.
What about 'this is what an inflection point is'; here are some ways to find them on specific equations. Now, here is how to find the inflection points of arbitrary equations.
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.