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<p>Excellent teacher is a relative term. At a place like MIT, an excellent teacher would necessarily have to be one of the best in the field. That is the nature of the beast. MIT has a more limited set of offerings in terms of majors as compared to many other schools, but it is among the top 3 in virtually all of its offerings. </p>
<p>To understand the differences one can make the analogy with athletics. An excellent Div I football coach is fundamentally different from an excellent Div III football coach. A Div I coach trains some of the very best football players in the country and will place very different demands on his players as compared to a Div III coach. In Div III athletics, academics take priority and success on the field is secondary. </p>
<p>By analogy, a math teacher may be considered excellent at Williams and mediocre at MIT and vice-versa. In the same way that a school like Alabama identifies itself through its football team, so does MIT through the success of its engineering and science departments through various competitions, as well as the number of students who move on to advanced degrees. Math and science proficiency IS the core of the school. An excellent math teacher has to be able to motivate and drive some of the most talented math students on the planet. At Williams, the school is more concerned about providing each student with a basic understanding in math and science, as part of a broad liberal arts education, not turning out Putnam Fellows. An excellent math teacher at Williams may be one who helps students with no a priori interest or strong background in math achieve a reasonably solid foundation. The objectives are simply not the same.</p>