The following is a one-paragraph teaching philosophy statement I wrote for a college where I currently teach mathematics. As an avid poker player, I embarrassingly derived much of my philosophy from poker strategy books, though I will likely not mention that fact to the school.

Mathematics is based entirely upon logic; everything has a reason. The student must learn not only the proper problem solving techniques, but also the reasoning behind those techniques. When I demonstrate problem solving for the students, I not only show the proper actions, I also explain my reason for each particular action. If the student errs when attempting to solve a problem but can explain the reasons for their actions, then we can correct both their logic and their action, and the student learns. If the student can not explain the reasons for their actions, then, even if their answer is correct, the problem solving techniques appear mystical to the student, and the student does not learn.