You are probably seeing a trend here, between unlearning and embracing failure... that students shouldn't see knowledge and learning in black and white terms.
Let me nuance that with a 3rd skill we should emphasize in schools: how to engage in a dialectic. In other words, how does one have a conversation with another to reach a truth together?
Tapping into my former teacher mode, I will now use a bit of dramatic dialogue to emphasize my point.
Teacher: Suzie, what is the answer to number four?
Suzie: Two? (or Blue? or Yttrium? or Dwight Eisenhower?)
Teacher: Yes (you have met my pre-defined parameters for truth-i-ness on this particular question)
- or, No, can someone else help Suzie (find my pre-defined parameters)?
If you agree that students don't have this skill, you can see why. They are never given the opportunity to learn and practice it. Knowledge, be it in the form of classroom discussion or tests, is always in the form of right or wrong.
Now, what if students were taught how to answer questions with "Let me show you what I'm thinking", or "Consider this perspective"? Dialogue that prompted a discussion. And furthermore, what if students honestly believed that they could persuade teachers to think about the content in a different way? You suddenly are working with an autonomous learner who takes pride in their individual thought.
Let me put it this way, I knew this rather drab first-year teacher... (okay, it was me), who wasn't meeting his expectations with student engagement. Except when he threatened to change his policy around allowing mp3 players in study hall. And suddenly, there were many people highly engaged in the outcome of the mp3 debate. Their thoughts were suddenly sharp, their examples more vivid,.. and they had to be. Their mp3 players were at stake. And, because the teacher actually continued discussion and probed their thinking, the class became an enjoyable learning experience for all.
That brings up the flip side of this skill. A dialectic means you have to understand you might not be correct, either. Which, is why debating a teenager is very difficult (I'm tapping Dr. Phil now).
We don't do either of these well. We give the illusion that all learning is either right or wrong (and the teacher is always right), but then we also don't help students understand that they can't find the answer without being willing to change their understanding. In other words, we cut off learning before it has a chance to happen. And we have to stop kidding ourselves... this won't happen naturally. We have to teach students how to engage this way.
The end result to the mp3 discussion was a new, common understanding about the purpose of study hall. Both the teacher and the students came away on the same page, seeing the issue differently than before. We handled ourselves well, not arrogant, not a pushover, but as people seeking out what the right answer is. Socrates would be proud.