Why do students who take courses with me (but colleagues tell me of similar experiences) routinely insist that I scan and post online my very own notes, the hard-to-read, disorganized and sketchy gibberish that I use for lecturing, whereas if I post a neatly put together summary of the basic concepts and formulae — typically after painstakingly making slides, drawings and animations — I am invariably told that “that stuff is useless” ?
The notes of a physics instructor cannot say anything fundamentally different from what students can find on their textbook — or any other legitimate physics book. There is no getting around this simple observation: physics is a subject which does not really leave much room for different “interpretations”. How the physical world works — not my opinion of that — at least to the best of current human knowledge, is what I try to illustrate to students. The laws of physics are what they are. Everything I describe can be (and has been repeatedly) independently subjected to the rigorous test of experimental reproducibility.
That is not to say that my job consists of rehashing the textbook , but ultimately I say the same things that the textbook says. So, what is the point of coming to class, one may ask.
My lecture, just like anyone else’s, consists a summary of my own way of thinking of a particular subject — one that I have developed in time, that I find intuitive, clear, and that I think should enable students to read the textbook on their own, comprehending concepts more easily and quickly than if they had to read it without any prior information.
Is this not the main goal of any lecture (irrespective of whether it is held in a classroom or in any other more technologically advanced format) ? I assume that we still agree that students should be active learners, i.e., do a fair amount of reading and thinking about the subject matter on their own…
Because the laws of physics are conveniently expressed in the precise language of mathematics, I am also charged with introducing students to the mathematical character of the discipline. This includes showing how to set up a proper formalism to help one formulate meaningful questions, define cogent physical quantities, carry out calculations, as well as how some important results can be derived, using simple algebra, from basic experimental starting points. Consequently, each one of my lectures involve a fair amount of algebra.
In my mind, a student would come to class, try to listen as concepts are presented, follow the derivations, including the more algebraic aspects, and then on her own, or in a small group of students, go through the material on the textbook, trying to reproduce all the math that is not worked out in detail, possibly using her own class notes as a guide.
Is the above exercise, namely going through the algebra and derivations, necessary ? I suppose that that is debatable, even though when I was a student, both in Italy and in the United States (and we are talking a little over 20 years ago, not back in the Stone Age), it was not regarded as such. We simply had to. I believe, based on my own experience as a student as and as a teacher, that going through derivations step by step, trying to work out all the algebra down to the last details, is exceedingly important.
I am not aware of any scholarly research on this subject. Surely much more authoritative sources have made this point in the past, for example Freeman Dyson in Disturbing the Universe , or Richard Feynman in Surely you are joking, Mr. Feynman !.
I am personally convinced that there is value to that practice, that the level of understanding that one will achieve of a subject is very different, much more in-depth if the time is taken and the effort made of going through pages of algebra, than if one just skips to the end and memorize the formulae. Perhaps doing the math develops an appreciation for orders of magnitudes, reinforces one’s comprehension of how a given physical effect unfolds from fundamental laws and mechanisms — I cannot claim to understand how it works, really.
Of course, sometimes one gets stuck, not being able to figure out how to go from one line of algebra to the next. I remember as a student spending entire afternoons trying to see how a particularly important result would be obtained, as I could not work the calculations out by myself. Sometimes I would have to ask fellow students, and if they could not explain that to me convincingly, I would go and see the instructor — very much the same as many students do these days, still.
There is also little doubt in my mind, however, that these days a substantial fraction of then students I teach, I may even venture to say the majority, have very little patience for that kind of practice. Whether it is because they regard it as unnecessary, time consuming, or whether maybe they lack the interest for the subject matter, I have become convinced that that is really why they want me to post notes, and act annoyed when I tell them that they can go through the textbook: they do not want to bother with the algebra. The textbook, or the kind of material that I have posted online so far, do not have the algebra spelled out — that’s why they are “useless”.
Now, my dilemma is: so far I have been pretty hard-nosed about it, not posted my own notes online, insisted that students do what was expected of me two decades ago, and “sweat it out”; should I instead give in to their requests (strongly supported by university administrations, for reasons that are unclear but that are unlikely to have anything to do with education), and post my notes online with all the algebra worked out, step by step ?
 Although there are times when I happen to think that the way in which the textbook expounds a particular idea is effective, and I happily adopt it, obviously rephrasing it in my own words.
 The book is not exclusively about the subject of this post. I doubt if that would warrant such a title, even though there are surely strong opinions out there.