It is so hard to descibe how teacher develop related knowledge to teach a special topic.
I have come up with many analogies to assit my thinking and modeling of teacher knowledge development.
Here is another wonderful analogy Rock Climbing. The following is a picture:
More about Rock climbing
The teacher developed lots of intermediate representations (just like the cracks, faces, slabs in rock climbing) to help students learning the scientific concept.
Good teacher can “see” the postions of students and can “arise” the right representation to help. The subject matter knowledge is the moutain. The “safety rope” is the good teacher-student relationship which keep the safe environment for learning. The routes can be fun and the goal can be challenging. They all motivates student to climb and learn.
