Bottorff Epistemic Forms & ADI

Epistemic forms as described by Collins and Ferguson actually lend themselves very well to ADI; epistemic forms guide inquiry and epistemic games allow analysis of phenomena, which are both major focuses of ADI activities. Two model types (epistemic forms) that would work well with an ADI unit on diffusion are aggregate-behavior models and constraint systems. Aggregate-behavior models work well for molecules, such as water diffusing in osmosis, that move randomly until interactions upon colliding with other molecules or barriers. Constraint systems involves holding most variables constant while manipulating a single variable to determine its role in a system. In a possible ADI activity centered on diffusion (i.e. driven by the question: why do molecules spread out in a container?), an aggregate-behavior model and a constraint system could work well together in an agent-based model, for example on StarLogo Nova.

I would provide students with resources on the paths of molecules (i.e. assumed to be straight lines until collisions) most likely from derivations for the kinetic theory of gases which could serve as an example of diffusion (since gas diffusion is no different than diffusion of molecules in a liquid besides the different phases). I could also provide a simple base model if I thought that students would struggle with creating an agent-based model. To factor in constraints, students could explore diffusion of water, osmosis, across a permeable barrier. The single changing variable could be the number of water molecules on a single side of the barrier. Alternatively, students could investigate the effects of adding a salt, the changing variable now being the salt concentration on a single side, that interacts differently with the semi-permeable membrane (unable to cross). In this way, students can study the effects of varying concentrations of salt and/or water molecules in a simple agent-based diffusion model.

With respect to activities and more resources that I could provide for students, I could ask students to treat think of this model using the analogy of playing pool, where balls ricochet off of each other but otherwise travel in straight lines. I could also ask students to consider the effects of the second law of thermodynamics which brings entropy into consideration. This law states that disorder in the universe increases or at least remains constant during cyclical processes. Perhaps confusing at first for high school students, this law can help them understand how entropy is the driving force behind diffusion, for the greatest entropy state is the one with the most disorder, i.e. the one with equal concentrations of certain molecules on either side of a membrane. It would be beneficial to incorporate this resource to help students avoid confusion about the cause of this phenomenon.

I don't think any of these model types don't work well for ADI activities; I simply wouldn't gravitate towards some models because of their more common use in social sciences, for instance, but they could definitely be well suited to ADI activities in softer sciences.