Apologies if I sound like I want to have the last word in this thread. I do not, and it is not my intention.
I just feel like my points have been ignored by those who defend the lecture approach. I've been bitten by this myself (and it hurt my pride, being one of the few courses I've ever failed), and have overcome it quite successfully too, so I have rather strong personal opinions on this –– and I believe that applying something like this in practice will help others learn better, especially more thoroughly; leading to
understanding rather than
memorization (which I detest, but is sufficient to pass most University courses).
You will learn the nomenclatura, and this will make it an almost readable text with maximum efficiency of information.
Incorrect in this context.
Maximum
density of information ≠ maximum
efficiency in learning. This is the core of my point above.
There is a reason humans tell stories, why we have parables and archetypes. It is not cultural at all; only their content varies from culture to culture, but all human cultures have them. The reason is how we
learn.
Providing the minimal facts, or the proof of said facts, without proper context, is an extremely poor and inefficient way of lecturing/teaching/learning.
I realized this myself when I failed –– one of the very few courses I've ever failed –– a physics math course on special functions (Bessel functions et cetera) and second-degree and higher nonlinear calculus. The lecturer said absolutely nothing about applying these functions, and instead spent the lectures showing how to derive them and prove them, with
"applications left as an exercise". (About a third of the students in that class did pass.)
At that point, I'd already created a couple of courses for art and design students on basic computer skills and such, so I created my own lecture notes (about ten pages) from the opposite viewpoint: I noted the basis of the derivation and the proof, but looked up all the various applications, and their base idea, and how they linked to the proof or derivation or both, and the base solution methods (separation of variables and so on). Ended up getting 4/5 ("B" on A-F scale), on a course where pass rate was about 35%, and 65% or so failed.
There are many different ways to learn, and that is why you
do not want maximum density in your learning materials. The opposite, in fact: for best results, you want to provide multiple approaches to the same conclusion, from which the students can choose the one that suits them best. The most skilled lecturers do this automatically, testing the most likely one, and quickly changing to a different tack if the students do not respond positively to that particular one. The most skilled science popularizers can construct one that will work for almost all readers/listeners. For fun, just compare them to the structure of legends, parables, and archetypical hero stories!
It is also exactly that that makes teaching or lecturing a completely different skill to domain knowledge.
Information-dense exact notation does have its place: when that knowledge and understanding is applied, either in further science, or to solve problems or prove results in relation to that knowledge and understanding. It should be built either as part of the learning process (but always secondary), or afterwards. If you disagree, consider why learning Standard Chinese is easier if you learn Hanyu Pinyin first.