Complex systems as lenses on learning and teaching
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From metaphors to mathematized models, the complexity sciences are changing the ways disciplines view their worlds, and ideas borrowed from complexity are increasingly being used to structure conversations and guide research on teaching and learning. The purpose of this corpus of research is to further those conversations and to extend complex systems ideas, theories, and modeling to curricula and to research on learning and teaching. A review of the literatures of learning and of complexity science and a discussion of the intersections between those disciplines are provided. The work reported represents an evolving model of learning qua complex system and that evolution is the result of iterative cycles of design research. One of the signatures of complex systems is the presence of scale invariance and this line of research furnishes empirical evidence of scale invariant behaviors in the activity of learners engaged in participatory simulations. The offered discussion of possible causes for these behaviors and chaotic phase transitions in human learning favors real-time optimization of decision-making as the means for producing such behaviors. Beyond theoretical development and modeling, this work includes the development of teaching activities intended to introduce pre-service mathematics and science teachers to complex systems. While some of the learning goals for this activity focused on the introduction of complex systems as a content area, we also used complex systems to frame perspectives on learning. Results of scoring rubrics and interview responses from students illustrate attributes of the proposed model of complex systems learning and also how these preservice teachers made sense of the ideas. Correlations between established theories of learning and a complex adaptive systems model of learning are established and made explicit, and a means for using complex systems ideas for designing instruction is offered. It is a fundamental assumption of this research and researcher that complex systems ideas and understandings can be appropriated from more complexity-developed disciplines and put to use modeling and building increasingly productive understandings of learning and teaching.