Ultimately, you 'know' your child and their cues.
You know, their personality and disposition.
You go by that.
You also sure, expose them to things, life, concepts, experiences, that are enjoyable or different. "Enjoyable" being the key word.
Nurturing their own talents and interests too.
Teaching them to not be 'perfect' or only according to their 'smartness' ...but according the KNOWING themselves. BEING themselves.
For my kids, teaching them to be 'themselves'... has now at their ages, promoted children that is very self-assured and they do really know themselves, quite well. They have good self-image and feelings about themselves.
I always taught them to be themselves.... and with that, they are really self-assured and 'happy.'
I did not concentrate, only, on how "smart" they were... but that they 'try their best...." and work toward something. THAT being the 'enjoyment' once the complete something. It is very fulfilling...
This is a good article as well
http://nymag.com/news/features/27840/
Another thing is, interaction with others her age.
Doing creative things... exploration, hiking, problem-solving fun things, experiments. So that they 'learn' self-reliance and problem-solving in fun ways and by hands-on, learning.
Make "challenges" fun. Not that it 'has to be' done in only 1 way. Because the 'lesson' of it... is not necessarily getting the answer 'right'... but formulating other ways of thinking, other ways of figuring things out.. and that there are MANY MANY ways, of doing the same thing.
Some people, don't try... because they don't want to be wrong or think they have to be 'perfect.' But that is not the 'lesson' about it or life... it is about creative thinking and exploring MANY ways, of doing something.
Also, cultural differences... is great for children.
My daughter is 8. For example, my Husband who is going to school... he SHOWS her what he is studying and the concepts of it online... show her his books etc. AND she is interested. She thinks it is very... interesting. SHE even learned some advanced math, this way. And she learned about the environment and about her body that way. We know her... and what will take or not. What she can handle or not. And how to promote "curiosity."
Curiosity.. .is really a seed... that helps a person learn many things.
Just make things FUN for her.
And about the 'process' of it. Not that she is correct or not. Often.... when making 'mistakes', this is a GREAT 'opportunity' for a child to learn....
all the best,
Susan