What is your teaching philosophy?

I have found, both as a student and a tutor, that people understand mathematics and statistics when they have two things: 1. A clear understanding of the instructions for a given task; 2. A real-life example or metaphor of the purpose of that task. Mathematics and statistics, at their core, represent language in precise terms. If someone is building two parts of a machine that are supposed to fit together, their mathematical measurements have to match. If someone is designing a garage to fit a certain size of car, that person has to know the minimal length/height/width that the garage can have. Instruction can only be as precise as the terms used. Another important concept in learning mathematics and statistics is the cumulative nature of these subjects. People learn new ideas based upon the ideas they are already aware of, and people learn mathematics and statistics in terms of the structures and applications they already understand. Therefore, when teaching mathematics or statistics, it is important to explain the purpose of new structures and techniques in terms of applications that they already know to be useful, and the methods in terms of the structures and techniques in which they have experience. Once someone understands the structure and the purpose of a methodology, that student learns not only the specific practices that are being taught, but is able to understand those practices as part of the greater whole. This is not only invaluable for future classes, but for future endeavors as well. It is this high standard of engagement that I strive to create and maintain within my students, such that even if they are working with a mathematical or statistical subject other than what I have taught them, they have the ability to analyze the problems with the core philosophy I seek to instill.