> How do I get her to love math (or other good things) in the first place? The hard part isn’t getting by kids to do things they love, it’s getting them to do things they DON’T love.
My suggestion; Kids learn by mimicking and playing. Our Education System beats this out of us in favour of formalism/competition/goals/etc. So if you sit and "play" with her using objects/manipulations of objects (set theory/abstract algebra/formal systems), measurements (quantities/units/coordinate systems), walking across the room with even speed vs. sudden acceleration/de-acceleration (calculus) you can teach Abstractions/Mathematics/etc. This will build up their intuition and hook their interest. Then you can teach them the necessary "formal notation" using paper/pencil and textbooks. You always go from concrete to abstract with enthusiasm and a playful attitude i.e. no right/wrong answers but exploring ideas/concepts.
Just to add, building intuition is the same thing as struggling to solve a problem. The process creates solution shaped holes in your brain, in which the formalism and abstract algebra fit naturally.
But it is important to actually give the formalism and abstract algebra at this point. Unless your child is an age defining genius, they will benefit from some handholding, and theres not much of that that can be done without having access to it yourself.
> building intuition is the same thing as struggling to solve a problem.
Not necessarily.
Intuition (borne out of Imagination) is for understanding the domain concepts even before there is a problem to solve.
This is the reason i am against the oft repeated advice "solve a lot of problems to learn Mathematics" which merely leads to mechanical "plug and chug problem-solving" with no real understanding. Instead one should spend a lot of time trying to grasp the concepts well, map them to the appropriate notations used and then study a few fully-worked out problems to grasp the "applications".
My suggestion; Kids learn by mimicking and playing. Our Education System beats this out of us in favour of formalism/competition/goals/etc. So if you sit and "play" with her using objects/manipulations of objects (set theory/abstract algebra/formal systems), measurements (quantities/units/coordinate systems), walking across the room with even speed vs. sudden acceleration/de-acceleration (calculus) you can teach Abstractions/Mathematics/etc. This will build up their intuition and hook their interest. Then you can teach them the necessary "formal notation" using paper/pencil and textbooks. You always go from concrete to abstract with enthusiasm and a playful attitude i.e. no right/wrong answers but exploring ideas/concepts.
PS: You might find the videos of the famed educationalist Sir Ken Robinson (https://en.wikipedia.org/wiki/Ken_Robinson_(educationalist)) useful in this regard - https://www.youtube.com/results?search_query=ken+robinson