This is triggered by @AmyB's and @DanielHast's remarks.
I think it would be useful in the OP's environment to understand and foster Carole Dweck's growth mindset theory. This theory is memorably described in Malcolm Gladwell's article, "The Talent Myth." There Dweck says,
"Students who hold a fixed view of their intelligence care so much about looking smart that they act dumb."
Recognizing when students have the fixed mindset, and nudging them toward the growth mindset, can dramatically change their ultimate achievements, at the same time as reducing their stress. The website Growth Mindset Maths offers a number of practical strategies. That website quotesattributes this quote to Thomas Edison (but see Benjamin's comment):
"You must learn to fail intelligently. Failing is one of the greatest arts in the world. One fails forward towards success." —Thomas Edison