When I was a first year student at the Physics course of the University of São Paulo, I struggled with Calculus, as most of my colleagues. I remember the sense of incapacity when I wrote tests, getting negligible grades, because of some error in integrating weird combinations of functions, which would never see the light in a true application (after many years I learned that those tests were tainted, wrong, and not that my knowledge was faulty, but at that time I didn’t know that). The interesting was that I observed my older colleagues, who where on the fourth or fifth year, had no problem with calculus.
Then, an interesting idea came to my mind: learning has more to do with the time you spend in the university, rather than with the actual lecture you attend. Of course, one cannot bring this to the extreme to say that a student that spends all the time of his study in the university’s cafeteria will learn as much as the student who attends all the lectures.
I believe that attending the lectures is vital for learning, but not because of what the professor teaches, it is because of the how he teaches. Education has this “magical” property, you spend some time hearing a professor talking about some subject, and you learn, indeed. Sometimes the professor teaches by hypnotism. I remember the lectures on thermodynamics I had with Prof. Ferdinando Luiz Cavallante, during my Master in Engineering study. I swear to you, when I needed some key concepts on thermodynamics (reference states, Raoult and Henry laws, activity, thermodynamic potential) I saw in my mind Prof, Cavallante talking! But these are not the general cases, most professors (myself including) are simply boring. So, how do this work?
I believe, this “time dependency” of learning is tied to the subject I posted before “on the role of the professor“. It is a matter of exercising. Exercising the brain. As with any other activity which requires exercising (football playing, sewing clothes, playing a video game) learning requires practicing, but practicing of what? I believe the key issue are the mental processes going on in the brain of the student. The professor repeats many arguments which the student has to follow, even when he is asleep. In any of them, the student has to follow the logic behind of what the professor teaches. This logic expands the student’s mind. One single event, has limited influence, but repeating this process over and over again has a cumulative effect on the student’s brain, until education reaches the ultimate goal, to teach the student how to learn by himself. This requires time.