I’ve been teaching using schema system diagrams, which I have just been calling interaction diagrams in my physics class. It’s the first time I’ve ever taught using them. I’m sold on them after one week.

Here is the biggest reason why I’m sold.

The diagrams provide a productive outlet for really good student ideas, which previously would have been considered misconceptions. An example:

Today, we started doing circular motion. We had a constant velocity buggy going around in a circle by means of a string. Just before we took some data for the time to get around and the radius of the circle, students were drawing interactions diagrams and free-body diagrams for the situation.

Three of eight groups included me in the interaction diagram, interacting with the string and the string interacting with the buggy. It’s a wonderful idea to think about that the motion we are observing hinges on the fact that I have pinned down the other end of the string. It’s insightful and correct—with out that interaction, there would be not constraint to move in a circle.  Now here’s the important thing: Previously, with out interaction diagrams to provide a place for that idea to go, that idea would have made its way to the free-body diagram. You could think that the reason I like the diagrams is because they prevented a mistake, but I really like the diagram because they provide a productive placeholder for valuable insights and ideas.

Three other groups included the motor in their interaction diagram. Each of those groups placed the bubble of the motor inside the bubble of the buggy. The really wonderful idea here is that none of the motion we are observing would not be happening without the motor. The buggy would screech to a halt.  Previously,when teaching without the interaction diagrams, that wonderful idea would not have had a productive outlet, so many students would have included a motor force on the free-body diagram.

So sure, one cool thing is that no group got the free-body diagram wrong. One reason to like the diagrams is that it leads to correct force diagrams. But the really cool thing is that students were thinking about the roles that both the motor and Brian were playing, which I hadn’t even thought about. It’s not merely preventing mistakes, it is generating insight and ideas about the different roles that interactions play inside, outside, or many degrees removed from a system.

Even if you showed me evidence that teaching system schemas doesn’t improve student learning, I’d still teach using them, because of how generative they are. It helps to create classroom environment in which student insights can be celebrated for what they are, rather than constrained to being misconceptions. By the way, the diagrams do seem to help student learning.

## 7 thoughts on “A misconception is just an insight without a productive place to go?”

1. I think these are great insights.

Pretty much every year, when we start learning about forces, my students want me to include a lot of objects in the system schema that don’t actually interact with the object we’re trying to model. Very quickly, a good number of the students will start to complain about adding these “extra” objects to the diagram, and I tell them that it is fine to include only the objects and connections that are relevant for drawing the FBD, but that it is also fine to include other objects and (correct) connections to see the whole picture.

The situation you are describing definitely happens (an object connected to another object which is connected to a third object that isn’t connected to the first) right away. Soon, though, we get to objects that used to be interacting, but currently aren’t. Later in the year, they can reason through those sorts of things pretty easily with just the FBD (especially the Honors kids), but at the start of the year, dealing with the objects, the types of interactions, the relative sizes, and the directions of the forces all at the same time is information overload. The system schema reduces that to just the objects and the types of interactions, making the cognitive load a lot smaller, I think, for the student who doesn’t have an immediate picture in his head before even picking up a pencil for what the FBD is going to look like.

For the reasons you described above, I think it is much easier for them to draw a correct system schema than for them to draw a correct FBD. So even late in the year, when they try to ask me about what should be on their FBD (this mainly comes back up with circular motion since they are mixing all sorts of ideas and not sticking to what they know must be true for forces based on their earlier models)—I just ask them what they should do if they’re having trouble drawing a free body diagram. They always say, “Oh, draw a system schema.” Then they draw it, and then they almost never need me again to confirm their diagrams. They know the system schema was correct, and that is enough of a foothold to move forward to the FBD.

1. Yeah, I’m not requiring interactions diagrams on exams…. but students seem to do them without demands. I agree that part of what it does is reduce cognitive load. What it also does it remind us that the world is very complex, and it’s OK to take in all that complexity before you narrow in and focus in on one piece.

2. Interesting. It sounds like you’re saying that students often perceive FBDs as interaction diagrams (i.e., would they define a FBD as “a picture of all the stuff that affects motion”?).

It reminds me of some of the things you’ve written in the past about electricity, trying to find out “what are they wondering.” If students are wondering “what stuff affects the motion of the buggy,” then it doesn’t make sense to answer the question “what forces affect the motion of the buggy.” It seems like FBDs are the answer to a question that the students haven’t wondered yet.

1. I think this is a great way of putting it… free-body diagrams are an answer to a question that students haven’t asked yet.