How I mentor my children to learn, and what I suggest for others, reflects influences over many years of reading educational resources. I have become rather eclectic and do not conform to any one homeschool or educational style or label. The authors/writings that have influenced me the most:

Frank Smith's writings, particularly The Book of Learning and Forgetting

Charlotte Mason and Ruth Beechick, particularly for younger children A Charlotte Mason Companion: Personal Reflections on the Gentle Art of Learning is the most readable to me)

A Thomas Jefferson Education: Teaching a Generation of Leaders for the Twenty-first Century This book did not influence me nearly as much as attending a seminar put on by a number of speakers on seven principles of learning. While I don't share all of the author's religious or political views, these principles have been very helpful for me to achieve an educational balance.

Cythia Tobias, The Way They Learn

Classical education writings, although I tend to apply them in a relaxed, child-led manner. A more recent and influential read has been Climbing Parnassus: A New Apologia for Greek and Latin by Tracy Lee Simmons, as the principles are applicable to environments of parental mentoring of the value of education. One of my favorite elists other than the LivingMathForum is LatinClassicalEd.

Math Learning

Kenschaft, Patricia, Math Power  Recently revised and reprinted

Vision in Elementary Mathematics
(unimaginative title, but a classic on math education!)

Marilyn Burns, many many resources, Math: Facing an American Phobia

How to Solve It (Classic work relevant today, I recommend highly, but the math can be intimidating)

Do I use math curriculum?  Yes, as a teaching tool, just not the primary teaching tool.   See FAQ for discussion from LivingMathForum on this topic, and Articles