Math With Bad Drawings had a terrific series on how students try to avoid thinking in math class. A quote:
As for students, it can be frightening to start a math problem. You don’t know quite where it will lead. Will my approach be fruitful? Will it falter? Where do I even begin?
But unlike my desk-perching student, most kids don’t recognize that one rope holding them back is fear of the unknown. They just hesitate: too afraid to leap without a net, but never bothering to go in search of a net for themselves…
In all these cases, students are refusing to engage with their uncertainty. But if you’re uncomfortable with doubt, you’ll never break through to the other side. You’ll never have a “Eureka!” moment or an intellectual “Aha!” You’ll never… well… learn. After all, if you can’t bear to face the unknown, how will you ever come to know it?
I find that my desk-percher has it right. At times like these, the mere presence of an expert can supply the confidence you’re lacking.
Here is Part 5, introducing what happens when students get stuck getting started on a problem: http://mathwithbaddrawings.com/2015/02/04/fearing-the-unknown/