Informal
Thomas Jefferson Education focuses on the interests of the student and allows the child to develop and study areas of interest.
Semi-Formal
Charlotte Mason Education has a defined curriculum which will give the child the essentials but also allows them to discover on their own.
Structured
Classical Education is a structured curriculum which is logic based. It focuses on skills children need in an organized and structured manner.
Classical Education
Classical Education is steeped in history and can be traced back to the early Greeks and Romans. In the 5th century AD, Martianus Capella defined the seven Liberal Arts as: grammar, dialectic, rhetoric, geometry, arithmetic, astronomy, and music. In the medieval Western university, the seven liberal arts were divided in two parts:

the Trivium
1. Grammar
2. Logic
3. Rhetoric

the Quadrivium
4. Arithmetic
5. Astronomy
6. Music
7. Geometry

The term "classical education" has been used in English for several centuries, with each era modifying the definition and adding its own selection of topics. By the end of the 18th century the definition of a classical education embraced study of literature, poetry, drama, philosophy, history, art, and languages. Modern Classical Christian education is characterized by a reliance on classical works by authors such as Homer, Sophocles, Plato, Josephus, Dante, and Shakespeare, and an integration of a Christian worldview into all subjects. In addition, classical Christian education exposes students to Western Civilization's history, art and culture.*
Classical Education for your Children
Methods of classical education have been integrated in homeschooling, as seen in the wonderful book, "The Well-Trained Mind: A Guide to Classical Education at Home," by Jessie Wise and Susan Wise Bauer. It is a modern reference on classical education, particularly in a homeschool setting. It provides a history of classical education, an overview of the methodology and philosophy of classical education, and annotated lists of books divided by grade and topic that list the best books for classical education in each category. This has been a great resource in outlining the academic training of our children.
*Information summarized from wikipedia.com and other resources.