Understanding scientific phenomena in terms of complex systems principles is both scientifically and pedagogically important. Situations from different disciplines of science are often governed by the same principle, and so promoting knowledge transfer across disciplines makes valuable cross-fertilization and scientific unification possible. Although evidence for this kind of transfer has been historically controversial, experiments and observations of students suggest pedagogical methods to promote transfer of complex systems principles. One powerful strategy is for students to actively interpret the elements and interactions of perceptually grounded scenarios. Such interpretation can be facilitated through the presentation of cases alongside general principles, and by students exploring and constructing computational models of cases. The resulting knowledge can be both concretely grounded yet highly perspective-dependent and generalizeable. We discuss methods for coordinating computational and mental models of complex systems, the roles of idealization and concreteness in fostering understanding and generalization, and other complementary theoretical approaches to transfer. Understanding Complex Systems 3 Promoting Transfer through Complex Systems Principles When and how do students transfer what they have learned to new situations? This is one of the most important questions confronting education and cognitive science. Addressing it has crucial practical consequence, while also touching on deep basic research issues related to learning, analogical reasoning, and conceptual representation. Considerable research suggests that students do not spontaneously transfer what they have learned, at least not to superficially dissimilar domains (Detterman, 1993; Gick & Holyoak, 1980; 1983). This is disturbing because teachers choose content with the hope that students will apply what they have learned to relevant new situations. We believe that students can transfer scientific principles across superficially dissimilar domains, and we are not alone in this belief (Bransford & Schwartz, 1999; Jacobson, 2001; Judd, 1908; Simon, 1980). To present our case, we will describe kinds of transfer that are worth “fighting for.” Identifying these turns out not to be only an educational question, but a scientific question as well. Accordingly, we will describe a novel approach toward science that seeks to unite phenomena from disparate domains according to general principles that govern complex systems. This complex systems approach to science offers unique educational opportunities for imparting scientific understanding that is both concretely grounded yet transportable. The notion of a grounded generalization may sound like an oxymoron, but it is key to our account of transfer. The time-honored method for conveying generalizations has been to use symbolic formalisms such as predicate logic or algebra. These formalisms can enable a student to transcend the specifics of a situation, but they also run the risk of disconnecting the resulting abstraction from an intuitive understanding of the situation. Instead, we propose learning and teaching methods that promote situation construals that are concrete insofar as they are perceptually, temporally, and spatially grounded. However, they are still idealizations in that many elements of a situation are ignored or highly simplified. In this paper, we will develop an approach to achieving grounded generalizations through the following steps: 1) Describe the 1 See also the notion of ‘situated abstraction’ in the section “comparison to other approaches to transfer.” Understanding Complex Systems 4 nature of complex systems accounts of science, 2) provide examples of general complex systems principles that appear in several case studies, 3) Describe pedagogical benefits of teaching science through complex systems, 4) Discuss the importance of transfer and generalization in relation to complex systems, 5) present a method for achieving generalization through perceptually grounded yet interpreted simulations, 6) compare generalization from grounded simulations to formalism-centered strategies, and 7) draw parallels between computational and mental models, with the aim of identifying design principles that allow the two kinds of models to mesh. Connecting Science with Complex Systems Principles One way to advance science is to progressively flesh out theories, adding experimental details and elaborating mechanistic accounts. By this account, the “devil is in the details” and the proper occupation of scientists is to pursue these details. This vision of science was most emphatically painted by John Horgan in his 1996 book “The End of Science.” He argued that the age of fundamental scientific theorizing and discoveries has passed, and that all that is left to be done is refining the details of theories already laid down by the likes of Einstein, Darwin, and Newton. The rapid rate of scientific specialization seems to support Horgan’s argument. We have gone from an era when the only major scientific journals were “Nature” and “Science” to an era with specialized journals such as “Journal of Contaminant Hydrology” and “Journal of Shoulder and Elbow Surgery,” each an umbrella outlet for several distinct sub-specializations. Well over half of the respondents to a Science Advisory Board believe that biologists are loosing track of the big picture by specializing in narrowly defined biological fields. Yet, many scientists feel compelled to specialize to still further degrees due to the sheer volume of scholarly output that competes for their eyes and minds. A small subset of scientists have chosen to reverse the trend toward increasing specialization. They have instead pursued principles that apply to many scientific domains, from physics to biology to social sciences. The principles are not applied to these domains in a metaphoric or vague fashion, as the terms “chaos” and “fractal” often were applied to art or interpersonal relations. Rather, the claim of complex system researchers Understanding Complex Systems 5 is that the same specific principle, sometimes expressible as equations or as sets of computational rules, can describe seemingly different phenomena. By complex systems, we refer to systems that contain numerous distinct elements that interact locally, resulting in a system globally changing over time. Over the past few decades, the field of complex systems theory has been rapidly developing (Bar-Yam, 1997; Holland, 1995; Kauffman, 1993; Wolfram, 2002). Complex systems theory and methods are now endemic to the sciences and can be found in just about every academic discipline and profession (Amaral & Ottino, 2004; Barabasi, 2002; Diermeir & Merlo, 2000; Epstein & Axtell 1996; Wolfram, 1986). It may at first seem that complex systems represent a small fraction of natural and social phenomena. But, this would be a misunderstanding of the field. What makes something a complex system or complex phenomenon is a matter of perspective. If you take a complex systems perspective, focusing on the interaction of system elements, then almost every system in nature and in society can be described as a complex system. Seen from this perspective, the system can then be analyzed using complex systems principles and methods. Complex systems theory has described a number of quite general principles that can describe natural and social systems across a wide variety of traditional disciplines. A few examples are in order. A commonly found system architecture in nature is: Pattern 1: An entity causes more entities like itself to be produced. At the same time, it causes another kind of entity to be produced that eliminates the