Better than their thinking they don't need to accept correction at all, but then, if you don't teach them measures for determining whether "corrections" are actually correct, they're liable to get their heads filled up with garbage.
And teaching the stupid students to learn to accept correction gracefully from smart students is a lot less good and useful than teaching all the students to accept correction gracefully from their peers whenever they're mistaken and receive it.
Well of course, if after hearing an explanation they realize they were wrong and why, then they should accept that correction no matter where it came from. And they should be open to listening to such proposed corrections from all sources.
But often even after the error is pointed out and explained, they still don't understand why they were wrong. The one correcting them needs to know more than the minimum to be able to teach others, and needs to invest the time to explain it. There's a long way from "remember correctly the right answer" 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.