These are raw notes for an eventual wiki page. Please return later.
Quote from Andy Johnson, Black Hills State University in a PHYSLRNR post on 090629 (ask for permission to use this)
(begin quote) I understand PCK as the specific knowledge that effective teachers use in teaching specific topics. It fills the space between content knowledge and pedagogical knowledge. In particular, I think that a big chunk of it can be boiled down to three things: 1) Knowledge of the common conceptions - alternative and otherwise - in a particular content area (in our case, force & motion) 2) Ability to identify how student is thinking based on how they talk or answer questions. (Basically, one would try to map students onto the list in category 1). 3) Having up one's sleeve a set of strategies that are likely to help students move forward from their current ways of thinking.
Maybe there is more to PCK than this, but I think these three categories comprise a large and crucial area of teaching expertise that teachers often lack, and if they just knew this stuff they would be way more effective. (end quote)
Notice the difference between this definition of PCK and the PER belief that it is impossible to know for sure what is going on inside a student's head. As a teacher, you must make the best guess that you can. Fortunately, at least in class (as opposed to grading written assignments and exams) and other face-to-face opportunities, you have the ability, as with any conversation, to check in with the student about whether or not your interpretation is in fact correct or at least close enough for them to acknowledge. “Are we communicating?” This act of checking in is very important.