"The first things i learned about mathematics was that there is a hell of a difference between, on the one hand, listening to math being talked about by someone else and thinking that you are understanding, and, on the other, thinking about math and understanding it yourself and talking about it to someone else." Sarah Flannery
Reuben Hirsch from his book What Is Mathematics Really? "Mathematics is learned by computing, by solving problems, and by conversing, more than by reading and listening."
It is fair to say that mathematicians enjoy doing mathematics. We enjoy solving puzzles, working on ideas, making connections, and all that. It is the so called "heart of the matter," and one of our goals as instructors is to make this happen for all our students, at whatever level they are at.
