I think pigpokey makes a great point. Coaching is the kind of area where encouraging towards mastery works well. Also, kids probably see other kids up close who are working or have mastered the skills they're working on. And they usually get opportunities to 'show off' the fruits of their labours, like recitals or competitions. Schoolwork doesn't really work the same way, unless you set it up specifically that way.
I think a big key here is for the kids to see you pushing yourself the way you want them to push themselves. "Be type A with yourself, type B with your kids' is a phrase I like. They will be more likely to work towards mastery if they see others in their life doing the same. So if you used to play the piano or wish you did but bemoan your lack of talent or time to practice, that's what they'll learn. If you have your own interests and talents that you are working on, or skills you are pushing yourself to master, or if you are training towards, say, being able to run or swim a certain distance, or whatever, they will be more likely to learn to push themselves that way.
And I don't think this kind of coaching/pushing/encouraging usually works for kids younger than, say, teenagers. When it does, I think it is because the child is motivated and talented. It might seem like it's the parents being able to motivate them the right way, but I really don't think it works with every kid. Only kids who are ready for that at a young age. It might be nice for the child to be 'ahead of the game' with, say, proficiency on the piano, so they don't have as much slogging through the basics to do when they are older, but in the majority of cases, I think it's wasted time. And likely to result in the child deciding that they hate the piano because they're being pushed or simply cannot reach that level of proficiency at that age.
I do like some of her points about having faith that your children can do things and not treating them like delicate sugar cookies that will crumble under the slightest pressure, but I don't agree with the obsession with excellence for such young kids. Teens? Yes, I think they can handle more pressure and higher expectations, when they show interest and after a more relaxed, playful childhood.
I don't know if this article has been posted here, but he makes some similar points about teaching math: it doesn't get you further ahead overall to be further ahead as a young child.