In class and out of class

Our tutoring consultant remarks on different ways of learning.

Our tutoring consultant commutes by bus to a tutoring center some miles away.  It’s a long commute, though by no means unusually long for this area, and he tries to put the time to some constructive use.  Most recently he’s been studying a certain branch of mathematics that, he thinks, might find applications in physics that haven’t been worked out yet.  When he gets to the center he is back in the world of students learning math in classrooms.

These struck him as very different ways of learning.  In a class the subject is fixed in detail.  What one is required to learn in Algebra II is a certain set of skills and knowledge, tested by more or less standard problems and methods.  The student must satisfy the teacher by meeting a set of requirements.  One may quibble about this or that, or whether there will ever be a reason to factor a polynomial in later life, but for the moment the standards are fixed.

On the bus, he has a certain application in mind.  He passes over details that apply to more esoteric bits of the theory and follows closely bits that seem more relevant.  His self-directed learning is both harder and easier than classroom work: harder, because he needs to know it well enough to apply it where no one has done so before; easier, because he doesn’t need to assimilate all of it.  Sometimes he makes a mistake, and has to go back and study something that didn’t seem important on the first time around.  But he’s used to passing over results that seemed terribly interesting to some mathematicians, because he has other objects in mind.

There are other differences between classroom learning and self-directed work.  In the latter, one many times runs into frustration because there’s no way to ask a question of a book; a single sentence of explanation (eventually found, much later, in a different text) could have saved much time and puzzlement.  In the former, one can ask questions, but cannot stop the class for a week or two to go over earlier things that he didn’t quite understand.

And, as we’ve noted, subjects in class can seem to have a different existence.  Spanish as a school subject can seem to have no connection with a way of communicating with other people.  Our astronomer ran into this for the first time in graduate school: friends of his, Medievalists, would take in stride the fact that to read a manuscript relevant to their work they might suddenly need to learn another language.  For them, there might be a one-semester course on reading Old Norse, or maybe they’d have to study it on their own for a month.  For him, a language had always been something that took years of classroom time to reach a passable level.  (He has revised that opinion since.)

Of course self-directed learning has the major drawback that it may get nowhere useful.  Without outside standards and pressure, no actual progress is guarateed.  And one’s motivation may fail at a critical point.  The real tragedy, however, would be to cease learning entirely.