When a student is allowed to find their own mistakes and correct them on their own they are able to grow and learn from their mistakes. There is nothing wrong with getting a problem incorrect because it will help show learning growth when they work through things on their own.
I feel I learn better when I make mistakes. Throughout elementary and middle school we would take spelling tests on mondays without knowing the words and then have the week to practice and learn the words and their definitions and we would retest on fridays. The words I got wrong from the begining I would remember better and work harder at to learn to make sure I had them by the end of the week and they stuck with me because I didn't like getting things wrong and it drove me to work extra hard and correct my mistakes.
Its always a learning oppertunity to make mistakes and fumble through life. It's no fun to always be right about everything. Sometimes it's a bummer to be wrong, but seeing where you went wrong and being able to fix the mistake on your own is an extremely rewarding experience.