"The principle is called the power principle or "what comes first, using it or 'getting it'?" The natural mode of acquiring most knowledge is through use leading to progressively deepening understanding. Only in school, and especially in SME is this order systematically inverted. The power principle re-inverts the inversion."
-Seymour Papert, An Exploration in the Space of Mathematics EducationA phrase I often hear is "teaching for understanding", which is a personal goal of mine. I don't just want my students to be able to do, I would like them to understand. So I try to introduce new material with exploratory activities where they wrestle with the material, apply what they already know, and try to create something new. My success varies, and I'm sometimes at a loss for why.
It might be something as simple as this: I'm asking to students to understand something before they know what it is. I would imagine this is difficult indeed.