There is no "working to learn" anything with him right now. He either knows it or doesn't. And if he doesn't know it he generally thinks it isn't really necessary anyway.
As a parent of an 8 year old boy who is really smart, I might have some input relevant to this. My DS knows his abilities and has a good idea of what he is naturally capable of and what takes much effort and learning. In his case, small motor tasks are like pulling teeth - he cannot cut, color, paint, write etc with ease and needs a person at his elbow to constantly push him to complete these tasks.
Kids like these follow the path of least resistance and need to be taught explicitly how to work hard to learn something that is not easy for them. My son is used to most things coming easily to him that he does not know how to handle a situation where the learning does not come naturally or is very challenging.
My son pursues 2 activities that teach him how to "work to learn" - a musical instrument study at a fairly advanced level with a teacher who sets the bar high and a martial arts at a high level with a Master Instructor who expects perfection. His experiences with them on a weekly basis include taking constant criticism (they are helpful, well intentioned and constructive, but still criticism), to be unable to do something well despite explicit instruction and close scrutiny, to actively monitor himself and change details of his technique and recheck with his teacher if he has incorporated the feedback, to do all of those under the pressure of an expert's watchful eye and worst of all (for him) to not forget what he has learned and to make the changes to his techniques permanent (being "present" and focused for long periods of time).
So, you could try explicitly teaching your DS to work to learn. Starting with a skill that he is not good at and working on it until he can master it and then heaping on the praise for his efforts. This might model what it is like to "work to learn" for him.
I am not sure what the "growth mindset" means - I have not read the book. Praising the effort and not the intellectual abilities, does not work for my child. He knows his strengths and many times when I praise him for a 100% score in his math or grammar tests (his areas of strengths where he is working ahead of his grade level) he tells me that he did not study for those tests and that it would be unfair to accept the praise and give the impression that he worked hard for the result. And when I praise him for learning his new Form in martial arts and for putting in considerable effort and considerable time on it - he still refuses the praise because to him, the skill did not come naturally and he slogged on it and it is still not perfect, so, not worthy of praise in his opinion.
When kids have a high degree of self awareness, I find that praise for effort does not matter a lot (in our case). Instead, helping them look at long term goals, helping them plan towards those goals, supporting them and cheering them on helps.
