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ABSTRACT
Research has focused on students’ difficulties understanding phenomena in which agency is distributed across actors whose individual-level behaviors converge to result in collective outcomes. Building on Levy and Wilensky (Citation2008), this study identified features of distributed causality students understand and that may offer affordances for instruction. Students displayed more distributed reasoning than anticipated, used hybrid and flexible reasoning, and reasoned about additive effects of collections of agents and their interactions, even when intent was unaligned.
Ackowledgments
We appreciate the contributions of Heidi Fessenden, Evelyn Chen, Maya Bialik, Erika Spangler, Matt Shapiro, Nicole Brooke, Maleka Gramling, Reuben Posner, Shane Tutwiler, Suzannah Carr, Maureen Danehy, Sarah Blodgett, and Christine Fetter. We appreciate the very helpful editorial suggestions of Joseph Polman and three anonymous reviewers. We would like to give a special thank you to Amy Voss Farris for her careful and helpful copy editing. Her contributions have improved this paper.
Funding
This work is supported by National Science Foundation, Grant No. NSF#0845632 to Tina A. Grotzer. All opinions, findings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Notes
1. “Decentralized causality” and “distributed causality” are used interchangeably here, with distributed focused more on the spatial characteristics and decentralized as contrasted with centralized when referring to control structures.
2. The view adopted here is that systems can be complex in many ways, for instance, in terms of spatial and temporal scales; the inferred or obvious features of the variables; potential nonlinearities, and so forth (e.g., Fredericksen & White, Citation2000) and that distributed causality is one form of complexity that is critical to understanding many complex systems.
3. Chi does not consider the emergent (or pattern level as she calls it) to be causal and has focused (2005) on a distinction between causal processes and emergence which she deems “acausal” as a reason for students’ difficulties. In Chi et al. (Citation2012), the term cause is used but is placed in apostrophes.
4. Chi et al. consider behaviors “(inter)actions” (p. 16), for instance, ants all walking around. They also include interactions between agents (emitting and following pheromones) as interactions.
5. The framing here departs from Chi et al. (Citation2012) in that they consider interactions between interactions that are distinct, restricted, sequential, logically dependent, or contingent and that terminate with the pattern-level behavior to be causal, nonemergent processes.
6. It would indicate a direct causal sequence as articulated by Chi et al. (Citation2012).
7. Chi et al. (Citation2012) would not consider the aspects of sequential contagion to be emergent, but resulting simultaneous contagion might be; however, the feedback loop in escalation requires a sequentiality that probably puts this form of synergy outside their definition of emergent.
8. We are not arguing that self-organization is limited to converging forms.
9. This is not to imply that these are conceptions are ontologically static (Gupta et al., Citation2010).
10. Originally five students from each class were recruited (n = 10) for an interview group the size of the Levy and Wilensky study (Citation2008). A fourth-grade boy left the school during the semester and one sixth-grade boy participated in the pre-interview and then was absent for an extended period of time, missing most of the class sessions.
11. A full curriculum subsequently developed from these sessions will be available at http://www.pz.harvard.edu/resources/causal-learning-in-the-classroom-curriculum-modules.
14. Simulating the earlier work under the title of BOIDS as developed by Craig Reynolds (1987) in his investigation or swarming/flocking behavior. Reynolds, C. (1987). Flocks, herds and schools: A distributed behavioral model. SIGGRAPH '87: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques Association for Computing Machinery, 25–34. doi:10.1145/37401.37406. ISBN 0-89791-227-6
15. http://www.princeton.edu/main/news/archive/S26/40/20I71/index.xml?section=mm-featured (1 minute, 41 seconds).
17. Chi and colleagues refer to “distinct conditions and parameters” controlling behavior at each level but argue that these conditions are different at the agent and population levels (Chi et al., Citation2012, p. 6).