We’ve all been told that the best way to learn is through active learning. Don’t be a spectator. Be a participant in the learning process by solving problems, writing code, writing papers, etc. But the following wonderful description points out that it is important to rise up and survey the landscape — be a spectator for a while.
In mathematics teaching, it’s a commonplace
that “Mathematics isn’t a spectator sport.”
You learn by doing, especially doing problems.
Like all truisms, this is half true. Mathematics
education as doing, doing, doing — no thinking,
no conversation — can seem dreary. An artist
isn’t prohibited from occasional art appreciation
— quite the contrary. You can’t learn a practical
skill as a spectator, but you can learn good taste,
among other things.
— The Mathematical Experience