“In mathematics you don’t understand things. You just get used to them.”
– Johann von Neumann
Math is one of those subjects that just scares most of us, and the above quote illustrates why. Without some form of meaning associated with what we’re learning, any subject becomes this formidable beast. When I teach, I try to give my students concrete examples that address the why and how of what we’re doing, and I don’t move the student on until I know they’re comfortable with the concept.
Students don’t just learn because we expect them to. They learn because they become interested in the content, and the best way to get them interested is to show them the inner workings of the content, show them what makes things tick. Students love that kind of knowledge because it helps them be able to handle these problems later on down the road, even if they’ve forgotten exactly what to do.