Here is a short run-down of some that I know about..
Classical: based on a classical approach that uses original texts, unabridged books, linear mathematics, and a history program that spirals every three years so that children learn about ancients three times, medieval history three times, early American history three times and modern history three times. The work becomes increasingly more involved and detailed as the child ages. This method is academically rigorous, involves classic reading, and offers hands-on projects. Classical is structured.
Montessori: based on the Montessori method that allows the child to be more in control of her/his learning. Items are placed around the room that will invite learning, such as stations containing math activities, a reading area, science projects and history projects. Montessori materials are specific and created to allow kids to use their hands to learn. For example, math materials are hands-on throughout K-8th in all areas. Montessori is child-led.
Waldorf: based on the anthrosophical philosophy of Rudolf Steiner that suggests that children will be free thinkers in society if they are allowed to remain in tune with the creativity of childhood for as long as possible. This method also has specific materials and a schedule of when and how lessons are presented. The Waldorf approach encourages the use of natural materials, such as beeswax crayons, wooden toys, wool clothing and natural pigment paints. Television and media is discouraged, and fantasy play and creative handwork is encouraged. Waldorf is highly teacher-led.
Charlotte Mason: based on the idea that children learn best when they are read to from well-written, colorful, interesting fiction and non-fiction books. Charlotte Mason encourages hands-on activities and lots and lots of reading, both from you and from your children.
Eclectic: this is one of the most common forms of homeschooling and involves using a variety of different curriculum to suit your particular needs. For example, you can use classical history, Waldorf math, Montessori science and Charlotte Mason literature.
Unschooling: based on the idea that children will learn on their own if provided with a stimulating environment. This method allows children to read what they want, learn math when they feel ready to, and studying whatever science and history they feel drawn to. Although controversial, there are many unschoolers out there.
