Some people believe we're born with natural talent; others believe we create what we're good at by working at it. Dr. Carol Dweck classified these viewpoints as different types of mindsets, namely fixed mindset and growth mindset.
Fixed mindset entails believing we have limitations on our ability. The focus is typically on being smart rather than growing, which leads someone to want to look good rather than work to improve. Piano students show this in statements like "I can't," "I always make that mistake," or "It's out of my reach." They hesitate to try new things as well as work on problem areas in pieces, preferring instead to just be praised for what they did well. And there's nothing wrong with wanting to know what we did well--the issue comes when we're so focused on looking good in the moment that we shut out chances to grow.
Growth mindset entails believing anyone can do anything given the right instruction and time. The focus is on progress, not only an outcome. Here, growth is unlimited, enabling the student to go further and stretch themselves to improve. Piano students show this in statements like "I can do it," "I'm learning," or "Let me try that again." They take delight in challenges and have an attitude of never giving up, seeking instruction on how to improve as well as feedback on what they did correctly. In practice, sometimes we hit a difficult spot and want to skip past it or give up because we weren't able to immediately fix the error. The problem with this is the mistake remains there, whether or not we think people will notice. We can strive for excellence by persevering and fixing the mistake in any way we can: addressing the root of the problem, slow practice, hands separate practice, mentally practicing the section a couple times first, etc.
Practice may take longer, but has better outcomes when we work through tricky spots--and remember they're just that: tricky, not impossible. Our teachers don't give us anything they don't think we can handle! And if it seems impossible today, we can ask our teacher about it and remember we can do it--it's just not happening YET. The students who persevere in the face of obstacles will always eventually succeed. They have trained themselves to be able to so. Because of this, anyone can be an honors student. They may need to practice longer each day, but chances are, honors students already practice longer and with more focus. If you're willing to practice longer, focus more, and fix the parts that need more attention, you can do it too--remember, some things are just tricky, not impossible.