These are the ideas that inspire me.
How to observe your child and work with his strengths. This is the style that most describes how we school. I lean towards unschooling in the early years, with small bits of structured learning. As my children grow, I observe and attempt to provide what they need. Structure, freedom, guidance, supplies … each child is different, and each child changes from year to year (even month to month!).
The natural ebb and flow of life and homeschooling.
Ambleside Online (Charlotte Mason, with a Protestant twist)
An educational philosophy that focuses on reading and discussing great books. No worksheets, and very little written work in the younger years. Emphasis is on oral narration as a preparation for later writing. 15 minute lessons. Lots of exposure to nature and big ideas.
(Charlotte Mason if you are not religious: Secular Charlotte Mason)
(Charlotte Mason if you are Catholic: Mater Amabilis)
(Charlotte Mason if you are Muslim: Eternal Muslim Learner)
My personal philosophy: We are Christian, and do study religious topics as part of our education. However, I have a distaste for most History and Science books that attempt to frame those topics from a Christian (usually Protestant) perspective. I feel they ignore the experiences and perspective of so many other groups. One of my central purposes for homeschooling is to expose my kids to things they would not be exposed to in public or private schools. The books I have recommended might have the occasional reference to religious themes (they are old books after all), and usually have a western bias, but none of them is written with an overt religious bias, unless I have noted it.