It makes sense to me that you learn by making mistakes. If you do not try anything new, then you will only know what you have done before. Almost always, when you try something new, you make some kind of mistake because you have never tried it before. You may have gotten it partly or mostly right so you just need to figure out the wrong part and add on to your knowledge.
The quote about the expert making all of the mistakes in a narrow field of knowledge also makes sense. If you try something similar to what you know, then you can add on your knowledge and relate what you are doing new to what you already know.
You can keep taking little steps out to learn new things about a subject that you are really interested in. If you make a mistake this way, you do not have to throw away everything you did or tried just the new little step. Then you can try something new without feeling hopeless like you wasted your time.
The research about what adults say to students is interesting. I did not know that telling someone that they were smart, would discourage them so much from trying something new or difficult. I think it is good to sometimes encourage another person by telling them that they are smart enough to try something, but also not so much as to make them fear looking dumb if they do not always look smart. I think the combination of recognizing great ideas that show someone is smart with recognizing hard work will encourage a student to try the most new things and learn.