What can lectures teach that a book can’t?

Some people learn much better from books than from lectures. That probably depends in part on the quality of the lecturer (and the book), but also on personal learning style and preferences. And that is not a problem: there are plenty of good books to learn from. What can a lecture give on top of this (apart from determining the “examinable material”, which should be a secondary or third (ternary?) consideration at most)? The lecturer has (hopefully) spent a lot of time in selecting material, thinking about the order in which to teach it, what proofs and which examples to give, etc. In the shortness of Cambridge terms (but also in other contexts outside of Cambridge), it is extremely useful to get an “expert’s” point of view on what is important in a subject when one is first learning it. Having to pull all this together oneself from one or more textbooks is of course possible, but much more time-consuming. I dare say that if you do have the time to do it that way, you learn even more! But practically it is not feasible to do this for every course in a short Cambridge term. Of course, the lecture gives only a starting point, and much more material can be learnt by supplementing with learning from books and thinking about the topic oneself.

Of course, authors of textbooks have also (hopefully) spent a long time deciding on the order of their chapters, what material to include, what exercises to include, and they do generally contain more “prose” explanation than lecture notes do. But all this is usually on a different (time-)scale. So again, it depends a lot on the book. But it is much easier to include something “interesting but not essential” in a book (since people can skip it on first reading), than in a lecture.

Talking as a “Cambridge bred” mathematician (with also one year experience of German lectures), I am used to lectures delivering the “red thread” (this might be a Germanism) for me, to determine in what order I should be learning the material in a course, what is important, etc. I hear that it is very different for example in the USA, and I’m not saying this is the only good way. But I certainly think it is a good way. I’m happy to be convinced of any improvements 🙂

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One thought on “What can lectures teach that a book can’t?

  1. Some more thoughts after further conversations. Lectures should not only transmit knowledge (surely a textbook or printed lecture notes can do that). Lectures should explain, give alternative viewpoints, inspire, be a place for questions to be answered, point out what is important, make connections, … Can lectures really do all that? And the other question is: if we don’t give out lecture notes for students to study beforehand, can they do all that? I don’t know. All I know is that I do my best and I’m sure I don’t always succeed, but hopefully sometimes I do succeed a little bit.

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