The idea that the students need time for accumulating knowledge (conscious preparation) followed by enough time to digest the information (unconscious incubation of creativity) is essential. And in the interplay between the two stages, we create the “new” – through combining things together and through colliding the ideas in our “mental pool of resources” – (illumination). Einstein referred to this as intuition.
In our everyday teaching practice, this means to create opportunities for students to explore a concept from different directions, to use the knowledge from different disciplines, to participate in valid extracurricular activities and to be good observers. This is where “illumination” occasionally occurs and translates later in a new product – the “verification” stage (assessment, essay, project, etc.). Every time when I allow this to happen in class, I am surprised by the outcome.