A key element in being a college-educated person, especially in mathematics, is what athletes call mental toughness. This term can be a pop-psychological artifact with no real meaning, but if you look here and here and other places on the web, the general idea is that mental toughness is a combination of resilience in the face of minor and major failures; the ability to cope with difficult and numerous demands; confidence; focus; and determination. Or better yet, it looks like this:
I believe mental toughness is key because, in college, you are preparing yourself for the rest of your life out of school, where the edges are harder and the difficulties far greater than just doing well on the next exam or getting a decent grade in your calculus class. Real people in the real world have to handle adversity, especially the particular adversity that comes from having ideas, thoughts, and proposed solutions shot down in flames.
College is an excellent training ground to develop mental toughness, and in mathematics that development is particularly acute because of the clarity with which right things are right and wrong things are wrong. Math students, especially math majors, ought to have the toughest minds around, because they have been tested and pushed to their utmost, they have summoned the intellectual honesty to admit it when their work has flaws — sometimes major ones — and they have developed the habit of working on through the injuries to finally win the match, so to speak. They should not be the ones who, when confronted with flaws in their performances, simply take it as a personal offense and fold up, unable to summon the will to keep on working.
So, a question:
How can an academic course or program, accomplish this task, when the very thing that catalyzes mental toughness – adversity couple with reality — is seen as offensive and humiliating? I can understand it if the professor is visibly and intentionally acting to humiliate or intimidate students; but if the prof is impassively and objectively pointing out problems in a student’s work, and the student feels that the prof is intimidating and humiliating them, then what is to be done? Does the prof overcompensate and become a sort of Barney-like figure, exuding love and goodwill while at the same time pointing out that does not, in fact, equal ? At what point should the student just take his/her lumps and deal with it?