I think the worry is that they are only concerned about getting the answer that gets them the good grade, rather than understanding why the answer they get is the right answer.
So you end up learning the symbols "5x5=25," but you don't know what that means. You may not even have an idea that corresponds to multiplication. You just know that when you see "5x5=" you write "25." If I ask you what multiplication is, you can't tell me: you don't actually know. You are disconnected from what the process you are learning is supposed to be tracking, because all you have learned is to put in symbols where you see other symbols.
But surely in math, of all subjects, it's easily possible to construct problems that cannot be solved without thinking and understanding, that do not reduce to mere memory and recognition of a known question "5x5". Then students who want the "right" answer will be forced to understand.
This isn't absolute, of course. When learning elementary multiplication, pretty much all you can ask about is multiplying, and there are only a few dozen pairs in the 10x10 multiplication table, and students generally just remember them, they don't calcula...
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.