You might be interested in Thomas Jefferson Education. They advise a phased learning system, love of learning, reading great books, and a variety of other concepts that you might be interested in.
First, they recommend letting kids learn through playing and having fun. Then, when they are ready, you start them on a Core, rather like the old reading, writing and arithmetic, although they recommend a character/religion component depending on your values. They don't proscribe what you use for materials, so if you want to use a mental math program, they would say go for it.
The second phase is love of learning, so children are recommended to explore what they are interested in. So if she is interested in science, find some books on experiments and others that relate to what they are interested in exploring, then explore them together. If that leads to an interest in a related subject or a new interest comes about, follow where the child leads, and they will lead themselves to a great education.
The final phase, begins in junior high or early high school and runs through college and can last rest of their life, and is called scholar phase. In this phase, the scholar structures their education with more rigor, and there are specific subjects that should be covered, like making sure any holes from their love of learning phase are covered.
My primary role in my children's education is to read to them on a regular basis. I've made a list of a couple of thousand books that are considered classics (I do have a website for this called Fanatics 4 Classics), and I pick and choose things that I think they are ready for based on their interests. So, in the past few years, we've read a lot of Roald Dahl because the kids laugh and giggle at the silly things that happen in his stories. Finding ways to make reading enjoyable is one of the most important things to get a child interested in books and learning. My second daughter has especially liked reading the Ramona Quimby stories, and my son has found he loves the Prydain novels even though he didn't care for the Disney Black Cauldron movie. (This is also great because I get to read the stuff I never had access to when I was younger.)