Researchers from Carnegie Mellon found that students solving 'regular' problems based on an example showed overlapping, but distinct patterns of brain activation when 'exception' problems were presented. 'Cognitive' pathways were activated whether a problem was hard or easy; 'metacognitive' pathways were activated especially when challenging problems were presented, and they were activated for a much longer time after problems were already solved. Regular problems involved small positive number values and a single unknown, whereas exception problems used fractions, negative numbers, or repeated variables.
If our students are up to the challenge, it's important we give them a chance to work on very hard problems. If they aren't getting anything wrong, then they're probably not getting any workouts to their metacognitive network. It's not just students, of course. If you're not making and analyzing you're mistakes, then maybe you're coasting too much on cognitive auto-pilot.
The metacognitive regions included sites like the superior prefrontal gyrus, angular gyrus, and frontopolar regions.