Something I think about a lot is how to help my girls appreciate taking risks and potential failure and how the ability to let yourself fail actually builds self-confidence. For kids there’s lots of pressure to succeed, so much that they may not even try in the first place. So how do we teach them to see failure as a good thing? Some platitudes you've heard before: if you learned from it you did not fail; success is about gaining experience to get you closer to your ultimate goal; the only way to fail at anything is to not try; you don’t have to be the best, just try your best.
These are all well and good but, at the risk of sounding redundant, I actually think helping kids to embrace failure is all about modeling. If you want to teach your kids to value it for real, start by sharing with them where you have failed. Tell them how you overcame whatever it was and what you learned from that experience. Or maybe you didn't overcome it and gave up. Tell them about that too. You were once a child and should know that kids (below a certain age!) pretty much think their parents are perfect. So, knowing you did not succeed the first time at everything is going to mean more to them than any platitude.
I'm also not just talking about past failures. Share the current ones too and what you're doing about them. Maybe make it a habit to celebrate every day's failures at dinnertime. Take turns telling everyone about a problem you solved that day, what you did to figure it out, and how you overcame unexpected blips. Or maybe you're still knee deep in it, haven't found the answer, but are persisting in your quest! Soon enough they'll start to get that failing is part of the process, moves you forward not backward and makes you better and stronger in the long run.
At our dinner table, we've begun sharing the puzzles, problems and mysteries solved each day but I haven't specifically incorporated the failure piece. I will though and will be sure to let you know how it goes!