Now, I'm 29, and never excelled at school, dropped out of University after one year, travel across Europe working as a programmer in many interesting projects and can say I live a normal balanced life. I don't dwell much on problems, and accept that things change and I can change.
My wife on the other hand, she has very low self esteem mostly because she believes that what she does is what she is. She can't change it. If she forgets about something she says she is dumb. If she breaks a glass, she says she is clumsy, and has a very hard time believing these things can change. She is stuck at a miserable job because she is too afraid to move and fail at the new one (even though she had better offers). She can't really separate what she 'is' from what she can become. For her, mostly due to the way her parents praised as a child, she came to believe we are born a certain way and can't really change.
Long story to mostly tell you (though, I'm not a parent yet so I can't say I know what the hell I'm talking about) that as long as you can teach your kid that what we become is product of what we do, and not who we are born, she will probably be ok. Try to find thing you can point to hard work. She does her homework? Nice, then tell her next time she gets a good grade "Good thing you did all you homework, see how it payed up". She may still think it was easy, but she her subconscious will link hard work and results.
I too, was raised on a Fixed Mindset; "You're not good at math/physics/chemistry? That's ok, I'm sure you have other skills.". This caused me some level of discomfort in trying new things (which are necessary for any sort of growth) because at some point I could just reach 'the end of the road' and the limit of 'talent'. This has often caused me to avoid new and challenging things altogether.
Since a year or so I've been trying to adapt the Growth Mindset by interrupting my thought process when I feel this discomfort and (often literally) say to myself that it is not the outcome that matters, but the chance to improve your skills and extend your abilities. Failure is not about you and it should just be a trigger to try harder; the road does not end. I still fall in the same traps I used to, but I've said Yes to more (challenging) things this year than any other year and I haven't 'failed' nearly as much as I thought I would, nor did the failures have the impact I feared them to have. Growth really is a marvelous (and endless) thing.
As it should, since that was the point of the posted article...