This morning I got up and read my post from last night about the TA in my class, and realized what I was writing about: Skemp, again, and the difference between relational and instrumental understandings.
The TAs who have been in my class have, for the most part, only instrumental understandings of physics. They know some algorithms for solving problems. In addition, they probably also value those instrumental ways of understandings as they have been rewarded for acquiring such understandings. They have been successful with those algorithms: What more could there be? They also, I think, do not tend to have particularly strong relational understandings of the physics, nor do they immediately see much value in such ways of understandings. I think a common response to my ways of approaching problems is something like, “I have my way of solving the problem; and Brian has another way.” The difference isn’t that I have another way; the difference is that I have many inter-connected and related ways of making sense of the problem; for making sense of the relationships that exist among these various approaches; and for making sense of connections to other problems we might encounter. Both the kind of understanding I have is hidden from plain sight, but also why I value it is also hidden from plain sight.
I’m also not quite convinced that the future teachers I work with truly value relational understandings yet either, which is evidenced by their saying that I don’t like them to use equations. I do believe they are developing better relational understandings, but I think they still see much f this as a “school” thing–something they must do to do well in Brian’s class. I’m saying everyone is this way, or even that any single person is uniformly this way. I’m just saying that part of the ways in which they still make sense of it is in terms of what is expected from Brian. In that sense, I’d venture they are much more likely to think through problems when I’m around, then when I’m not.