Jacob Kelter is a PhD student at Northwestern University in the joint program between computer science and learning sciences. His research focuses on using agent-based modeling for science education and computational social science research, both related broadly to complex systems science. Connected Learning and Computer-Based Modeling and co-founder of the Northwestern Institute on Complex Systems (NICO). His research interests are in computational science, complex systems, agent-based

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... and integration of computation into K-16 education. He is the author of the award winning NetLogo software, the most widely used agent-based modeling environment. He has published more than 300 scientific papers, and, through the NetLogo models library, has published more than 400 agent-based models across a wide range of content domains. He has also developed many computation-based curricular units for use in K-16 that are used internationally. He is the co-inventor of, and continues to develop restructuration theory that describes the changing content of knowledge in the context of ubiquitous computation, and its implications for making sense of complexity. Abstract Diffusion is a crucial phenomenon in many fields of science and engineering, and it is known to be difficult for students to learn and understand. Ideally, students should understand (1) the macro-level patterns of concentration change including Fick's laws which describe these patterns quantitatively, (2) the micro-level random-walk mechanism of diffusing particles, and (3) how these two levels of description are related, i.e. how the macro emerges from the micro. We describe agent-based models (ABMs) of diffusion designed to help students accomplish these learning goals and report the outcomes of implementing them in a university materials science course. The results indicate that the ABM activities helped students understand the micro-level processes of diffusion compared with students from the previous year, but that gaps remained in their understanding of the macro-level patterns of diffusion and the connection between the levels. We conclude with a brief description of our re-designed learning activities to improve outcomes in future years. Interviewer: There are these two different ways of describing diffusion in this question that you've used: the differential equation and an agent-based model. What's, the relationship between those? Like how do you think about: What's the relationship between them? What are the pros and cons of each? What are the strengths and weaknesses of each? Nothing in the learning activities in the course specifically asked students to compare the representations. The results for each of the five interviews are summarized. Peter's Response Peter answered that the two representations are different ways of describing the same phenomenon each with their own advantages: Peter: I think of them as this-as two different ways to describe the same phenomenon. To me, there isn't much of a difference. But I think this agent-based model is more like--I think it helps with like visualization, like at an atomic scale, what is happening. This (Fick's law) is more like at the macro scale, like you can draw the concentration profile, like, just by reading the curve. If you want to do that in agent-based model, you literally have to count each like, how many carbons there are in one column in NetLogo. So, this is more, this (Fick's law) is like a general overview. This (the ABM) is like more individual specific for me. Peter's response is concise, and he identifies one advantage for each representation: the ABM helps with visualization of the micro-level process while Fick's 2 nd law can be faster for generating concentration profiles. We would add that the ABM helps with conceptualizing the phenomenon as well, not just visualizing it. Parker's Response Parker answered the question in terms of probabilistic and ideal behavior: Parker: What is the relationship? Well, I think-Fick's second is like the mathematical relationship to show it (diffusion)...if you did an infinite number of agent-based modeling experiments, and then average them all up, you get, like the mathematical equation of Fick's second. So-because the agent-based modeling is just showing how, when you sort of have these things like random walk-like probabilistically it tends to go towards, like, approach this behavior, this mathematical model more and more....Fick's 2nd law is important because it's the mathematical model that describes what the ideal behavior is, but then the agent-based model is strong, because you can see how that behavior arises from these sort of, like things from random walk, and like, the probability of which one-of like how-the probability of each jump that it will take.