Being fresh out of college, my way of teaching was very essentialist, with no room for arguing points about what is and isn't important when it comes to education (as if I knew all along). I always liked the way college courses were taught, and didn't realize that learning was different for everyone. It was not until my first year of teaching that I realized how different today's high school students can learn math.
I now take on elements of progressivism, essentialism, and constructivism, rather than stick to one philosophy only. Teaching math allows me to use the assessment and basis aspects of essentialism; that everything has a basis to build upon. From progressivism, which is said to contrast essentialism, I take the idea that students should be taught how to think, not what to think. Finally, from constructivism, I think it is necessary for learners to apply knowledge and construct meaning from experience....even in mathematics.
Even more important is my general teaching philosophy that every teacher should help each student reach their highest potential, whatever it may be. Not everyone learns or has the same potential, which is why teaching is tough and requires a lot of patience.
I'm sure my philosophy will change as the teaching years go by. I'm counting on it. The trick is being open-minded to what does and doesn't work at various times, and how to apply what does work.