It's a bit ironic that when scientists need to study how people learn in the fMRI scanner, it's almost the complete opposite to how students are taught in the classroom. For researchers to see brain changes associated with learning, they have to provide regular feedback about errors; whereas in the classroom, the 'learning' process is mostly watching and listening passively.
In the figure below, you can see that test subjects need to activate less brain when they learn a spatial categorization task. They learn by receiving feedback with each trial when they make an incorrect response.
Without knowing what you don't know, you may have woefully unrealistic ideas about your own knowledge. Cornell researcher Dunning and colleagues have several papers (and now a new book) examine the dilemma of inaccurate self-knowledge. There are various factors involved (for instance the "above-average" effect in which most people think they are above average), but an inaccurate knowledge of omissions was significant.
In the figure below, look at the "double curse of incompetence" - in a classroom study, the bottom quartile was the poorest at estimating what they understood. That's why, the authors say, don't trust how confident people feel about what they know or don't know - it's unreliable!
Re: the classroom... Mathematics is one subject where 'right' or 'wrong' are pretty clear, but endpoints of knowledge are more fuzzy for writing, reasoning, or creative work. If you're a parent, try this trick at home - after explaining something or reading something outloud to your child, ask them to explain it back to you. If you don't have a habit of doing this, you may be shock about what seems to go in one ear and out the other, or what they misunderstand.
In the classroom, it's easy to be attacked either for teaching too much "to the test" or not testing enough. Often a delicate balance needs be struck, and the composition of the classroom may put limits on what differentiation and feedback one can provide. The science of learning does suggest, though, we only really learn with regular feedback (positive and negative) about our performance.
As far as writing or factual learnign is concerned, one suggestion is to allow students to revisit unsatisfactory work until it is satisfactory. For some tasks such as writing, students may also need to see alot of examples of well-written and supported essays before they can predict what's expected of them, and write their own.
Overrating Our Abilities
Why People Fail to Recognize Their Own Incompetence
Common Errors in Reports
Common Errors with Reasoning
Finding Errors in Problem Solving
Spatial Learning From Mistakes and fMRI