I can certainly answer the main question, "On what philosophy is education based?" I am not sure if you are asking about higher education or general public education, but I will give you the best answer for higher education in the United States.
At about the beginning of the 20th century, education in America shifted from an English philosophy to a German one. The English philosophy of higher education was based on the ancient Greek idea that rhetoric was the center of education. The purpose of educating people was to make them more civic minded and, thus, more responsible and participatory members of society. So, teaching students how to speak, read, write, and think critically was at the center of all subject matter. More importantly, faculty, staff and students were mindful of the whole school as a single collaborative unit. In contrast, German education is more analytical in nature, so the philisophy moves away from communication and collaboration and more toward categorization and data. Subjects/content areas exist separately from each other and are studied that way. Professors are more loyal to their discipline than to their school, and the amount and quality of research by a professor defines him or her as successful.
Today, the German model is still the basis of most colleges and universities. However, the English model can be found in many smaller colleges and even in some larger universities that have embraced the idea of learning communities.
There is no one philosophy of education. There are competing philosphies that often form into practical political alliances in interesting ways. I would suggest that you consider the Classical Liberal, Behaviorist, Progressive, Humanistic, and Radical groups of philosophical leanings. Some classify various educational philosphies into Essentialism, Perrinnialism, Behaviorism, Progressivism, and Existintialism. Philosophy helps us consider the purposes of education and how those purposes are to be met. What is to be taught? What are the roles of student and teacher? What methods shall be used to obtain our purposes? These are foundational questions that anyone interested in teaching should constantly explore. Unfortunately, many schools of education are cutting back on philosophy classes or eliminating them all together. This itself exemplifies a philosophy of education that critical educators explore.
The names provided in the references are good places to start your examination by seeing what they have written.