Learning involves a process of acquiring knowledge by focused attention, observation, and practice, and then eventually forming, integrating, and using concepts as part of the student's full body of knowledge. Early in a child's life, a rudimentary form of learning may be accomplished through rote memorization and repetition of facts. Truly understanding a subject, however, requires a student to focus on the content and the meaning of a given subject, to isolate its essentials, to establish its relationship to what the student already knows, and to integrate it with the appropriate categories of other subjects. An education that trains a student's mind to think, therefore, would be one that teaches him to make connections, to generalize, and to understand the wider issues and principles involved in a given topic. The ideal teacher would achieve this feat by presenting the material to him in a calculated, conceptually proper order, accompanied by the necessary context, as well as the evidence that validates each new piece of information. Math is uniquely suited for demonstrating the consequences of such a theoretical approach to learning. It is my responsibility as a mathematician and math teacher not only to teach my students the concrete, factual knowledge of a geometry or calculus textbook, but also to examine with my students what this information communicates about ourselves, our world, and our culture, carefully balancing concretes and abstractions, identifying and explaining the reasoning at each point in the lesson, and preparing the students' minds for drawing connections between mathematical concepts and the world outside the classroom. Indeed, these are the processes that must first be absorbed each academic year by the student in relation to many different subjects. Upon graduation, such training will encourage an attitude of self-confidence and self-efficacy in regards to learning. My primary function and goal as an educator, therefore, is to help to instill in my students the skills and mental habits necessary for them to learn anything they want by themselves, which means, to be interested and excited about their own intellectual development.