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I enjoyed most of Professor Rota's comments, but couldn't disagree more with his Lesson 6 and think it is pretty destructive. In my view, the ultimate proof as to whether you deeply understand something is when you can engage in rigorous synthesis using that thing, or correctly explain it to others without using terminology as a crutch. Getting to that level of understanding is not merely a function of the recognized accomplishment level of your peers or your instructor. What imbues people with a deep understanding varies from person to person, and many really benefit from a deliberative, instruction and discussion/conversation-focused instructor. My casual observation of MIT is that the level of instruction can be far from the best I've seen, because the students are so bright or so fast that they don't need much from the instructor in order to immediately see the conceptual space. Imagine however that you are no intellectual slouch, but maybe are a more contemplative and deliberate thinker. You may be penalized in an environment like this, which bears no representation on whether or not you can get to the same quality and depth of understanding as your peers. I once had an MIT-educated professor say, "I know how to grade these exams. My 'A' students will finish the exam in the time allotted, my 'B' students will finish most of the exam, the 'C' students less so." This infuriated me then, and infuriates me now. The counterpoint was a (well-known) UMich-educated professor, one of the best I had, that gave challenging exams with no practical timelimit. He inspired me to be very ambitious as the lead on a free-form semester group project, so much so that it was clear we wouldn't finish during the semester. He saw how ambitious it was, and gave us an incomplete until we could turn it in the next semester. We did, and it was a really nice body of work. I've seen similar patterns in the rest of my education. I've always gotten the most not from the best-credentialed professors, but from those who themselves understand deeply and make the material and themselves open to the interested learner. This is ultimately what teaching and learning should be about, and can easily take place at any good institution, not just the MITs of the world. In my field of engineering, there is no significant correlation between those who were educated at MIT or Stanford, and the impact of their contributions to what is in the field and has truly advanced the state-of-the-art. |