Quantitative Reasoning about Complex Systems, Jnl Learn Sci

Wilkerson-Jerde, M. H. & Wilensky, U. (In Press). Patterns, probabilities, and people: Making sense of quantitative change in complex systems. Online First in Journal of the Learning Sciences. doi:10.1080/10508406.2014.976647

[Link to Publisher][Accepted manuscript PDF]

Abstract: The learning sciences community has made significant progress in understanding how people think and learn about complex systems. But, less is known about how these understandings relate to the mathematical and quantitative formalisms often used to represent them. In this paper, we make a case for attending to and supporting those connections. We introduce a framework to examine how students connect the behavioral and quantitative aspects of complex systems, and use it to analyze interviews with 11 high school students as they interacted with an agent-based simulation that produces simple exponential-like population growth. While the students were comfortable describing many connections between the simulation’s behavior and the quantitative patterns it generated, they did not focus on connections between individual behaviors and patterns of change. Case studies suggest these missed connections led students who engaged in productive patterns of sense-making to nonetheless make errors interpreting quantitative patterns in the simulation. These difficulties could be resolved by drawing students’ attention specifically to the graph of quantitative change featured in the simulation environment, and the underlying rules that generated it. We discuss implications for the design of learning environments, for the study of quantitative reasoning about complex systems, and for the role of mathematical reasoning in complex systems fluency.

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