The great majority of students aren't capable of re-deriving calculus, even with guidance, let alone in the third grade. There's a difference between letting the capable ones do it, and asking a whole class to do it.
I wasn't graphing quadratic equations in third grade. Actually, I never did third grade. In fourth grade I was doing fractions, and that only because they let me take math classes with the fifth and sixth graders.
It's not important that they succeed. It -is- important that they try.
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.