"Is a man what he seems to the astronomer, a tiny lump of impure carbon and water crawling impotently on a small and unimportant planet? Or is he what he appears to Hamlet? Is he perhaps both as once?” -- Bertrand Russell.The power of imagination is built quite strongly into the fabric of our very existence. One of the traits that separates us from other animals is that we read poetry and listen to Miles Davis. Other animals communicate and make sounds, but they don't write plays or compose music.
One of strongest and most consistent beliefs among the IBL teachers is that creativity can be taught. This is quite evident at the Legacy of R.L. Moore conferences -- IBL practitioners have this unending supply of belief in their students, and not assuming what a student can or cannot do.
I have internalized this for myself as the Teaching Axiom of Choice, which is stated as "Every student has the capacity to learn Mathematics." Our educational system (in the U.S.) has a tendency to label students at a young age. Mathematical ability it thought of by some as a fixed, unchanging attribute that cannot be altered significantly by effort.
What this does to teachers is set expectations, which then in turn affects teaching decisions. It goes like this. If you are a teacher who believe in fixed attributes of students and are given a track of students who are "low level," then you are likely to assign "easy" tasks and not challenge students. Effort is to be minimized and the goal is to just get some of these students through the material so they can pass and get on to the next level.
It is unlikely that problem solving, deep engagement in rich mathematics, and a developing other higher-level thinking would be part of the class. So then the labels lead ultimately to a dry, barren math experience (though unintentional -- no one means to do harm).
It's a choice. We can, though not always easily, believe in our students. Give them our best, and work hard on our teaching methods to provide the best possible chance for learning. I am the first to realize that the system plays a strong role in what we are allowed to do in the classroom. With that said, the Teaching Axiom of Choice then is a precondition to providing transformative experiences for students. If you do not believe in students (or at least willing to suspend belief), then you are unlikely to give your students the kinds of tasks and structured freedom to let them compose, to dream, and to be creative.