I recently started teaching music through AmeriCorps to K-8th grade kids in rural Oregon. I've been working with praising the process over the result. It's certainly required a mentality shift, but I can see it working with students (especially those who might not grasp a concept as quickly as others).
I've adopted this mentality for myself as well. Growing up, I had never been good at math. I would make mistakes and fall behind in class and wasn't really ever able to catch up. I've recently started learning math again (starting at Algebra I) and have been loving it. Yes I move slow and still make mistakes. But I've been noticing that overcoming those mistakes is one of the most rewarding feelins ever. More than that, it motivates me to continue. I plan to tackle Geometry, Calc, and Physics next.
I was also bad at math as a youth, had a bit of undiagnosed dislexia and a bad attitude. Went back to school and placed into math 60. By the time I left colledge I had worked my way up to linear algebra and enjoyed most the journey I took to get there (not the hard work but the satisfaction of revealing the world with the tools I had earned).
Music is an incredible thing to teach kids. They learn to make something greater than themselves. It teaches how to be a good follower and for many good leaders and team members. It helps to train kids to anticipate and prepare for the near future both the next class or performance and the next note it bar. It builds phisical and mental dexterity and it shows the elegance of a complex system and how it can be ordered to create usefulness and beauty.