Being able to control the game and progress on demand is still mastery, even if the spectacular failure is interesting to explore first. I blow up plenty of th

Being able to control the game and progress on demand is still mastery, even if the spectacular failure is interesting to explore first. I blow up plenty of things in Kerbal Space Program in interesting ways before deciding to buckle down and get more science. Playing around with the "wrong" geometrical proof instead of taking the straightforward and known-to-myself approach isn't harming me, either. Young kids like exploring the whole state space-- not just the ones we're likely to label as success or useful. Then at some point later they get afraid to fail-- especially to be seen failing. It's a mixed bag: motivation to push "forward" is useful, but fear of failure prevents deeper understanding or full effort sometimes.