The Jewish attitude towards homeschooling philosophies can be summarized by a Talmudic statement of "Chachma b'goim taamin, Torah b'goim al taamin", which means that there is wisdom among the nations but there is no Torah. Judaism is G-d centered i.e.only G-d is worthy of worship, and both nature and man, no matter how brilliant are both only His creations. Torah is G-d's mind, His word to us. So what this means for using homeschooling philosophies that are out there, is that Judaism views everything within the Torah framework, it takes what is consistent with our values and discards or replaces the rest. It doesn't cut G-d down to size and try to make things fit when they don't. The world and all the wisdom out there is for us to learn from but it is not there to provide us with a direction in life, we already have that. I read a lot of educational books, blogs, etc and sometimes one finds that people almost make a religion out of their homeschooling philosophies, sometimes it takes a form of nature worship and sometimes that of man/science/art worship. Naturally both of these extremes are inconsistent with Judaism. Having said that, there is plenty within the existing homeschooling philosophies that can be beneficial to Jewish homeschooling and learning. So I'd like to go through a few popular homeschooling philosophies one by one and share my thoughts on how they could work within a Jewish context.
Classical Education - This approach works well for children that are very cerebral and academically inclined. It is very much reading and writing based. There is a lot of structure. Learning is very much sequential. In many ways the approach itself is very consistent with traditional Jewish learning, book based, things are taught in a certain sequence based on the developmental stage of the student,etc. The content though has to acessed and adjusted. However this approach won't work well for the student who has trouble with either reading or writing and who doesn't care for so much structure.
Charlotte Mason - This approach is a sort of toned down Classical Education and is sometimes used in conjunction with the above. Ms. Mason had lots of wonderful ideas on how to introduce and teach many subjects to children and get them to love learning. I like the idea of using what she called Living books, books that make the subject come alive, instead of sanitized textbooks. I like the idea of short lessons for young children, teaching appreciation of nature and beauty. This approach, gentler and less rigorous than Classical Education can work very well in a Jewish setting. Again the content has to be adjusted.
Unit Studies - This approach could go hand in hand with the above two. What it is, is basically thematic learning, where different subjects are taught organized about a certain theme . The idea being that the more ways are used to introduce something, the more absorbed and understood the information will be by the student. So for example if one is learning about the Jews, one can learn Jewish philosophy, the geography and history of Israel, Jewish history in the Diaspora, Jewish culture, art and music, cook Jewish foods, make Jewish crafts and fit math and science around the Jewish theme as well. This approach could obviously work well within a Jewish context. If one was to use unit studies prepared by someone else then one should check content for suitability.
Thomas Jefferson Education - More classics and living books instead of dull textooks. Mentoring and inspiration by personal example. Somewhat structured based on developmental readiness of the student. All of the above could work very well in a Jewish context with allowances for content adjustment.
Unschooling - Basically this is a child's interest lead approach, with maximum freedom allowed for children to explore and learn things on their own. The world as a classroom is its ideal with minimal interference from anyone. While I am very much in favor of following the child's interests and natural talents and allowing the child to discover things in a pressure free environment, I do believe that children need limits to function optimally. That sometimes we all have to do things that we might not love like paying taxes or cleaning up messes. But this too is part of life. Also, children could use guidance and be encouraged by their parents to explore certain things or study certain subjects. There is nothing wrong with that as long as it's not heavy handed and one is not trying to fit a square peg into a round hole. So one has to use one's discretion not to go overboard in either extreme. Unschooling could work quite well for some in a right kind of an environment.
Montessori - Great hands-on ways to teach many different skills and subjects to a young child. I haven't delved too much into how it works beyond the elementary age. Prepared environment ensures learning can take place. Teacher/parent serves as facilitator. Room for child to explore and follow his interests within the framework. All of the above could work in a Jewish context. I would leave Maria Montessori's political and cultural views out, but that doesn't impact on the usability of the system in any way and one could always improvise one's own materials, as many do.
Waldorf Education - While the Waldorf ideology is not consistent with Judaism from what I've read, I haven't looked into it too deeply, there are aspects of Waldorf education that could be useful in a Jewish context. The ideas on how young children learn and creating a suitable environment, the idea that children need routine, introducing children to the rythmic nature of life, use of natural materials, crafting, etc. all work fine without theWaldorfian ideology. So for example when they talk about creating rituals and festivals, etc. there shouldn't be a problem because all these thing are already built in into traditional Jewish life with Shabbos and the Jewish festivals and various other rituals that Jews observe. No need to reinvent the wheel here. So minus the ideology and with adjustments for content, certain aspects of Waldorf education can be suitable.
I think this should cover most popular homeschooling ideologies. Parents have to chose what suits their individual child's needs and what would work with their particular family culture. So keeping all of this in mind, there is no reason why these learning approaches should not be implemented in Jewish home learning.