Modeling Students Modeling Abilities: The Teaching and Learning of Complex Systems in Education

The word Tao usually is translated as way or path, but it refers to the deep structure of patterns and regularities beneath surface-level experiences. Similarly, Taoists use the terms naming or telling to refer to nearly any formal statement, proposition, or rule. So, for our purposes here, a particularization of Lao Tsu’s famous saying might be: The structure of things that can be reduced to a formal statement, proposition, or rule is not the true structure of things. ... This is, or should be, the central challenge that confronts learning scientists who hope to create models of the models (and/or underlying conceptual systems) that students develop to make sense of complex systems that occur in their lives. The challenge occurs because of the following mismatch. On the one hand, many currently prevailing cognitive science theories continue to rely implicitly (if not explicitly) on mechanistic information processing metaphors in which everything that students know is reduced to lists of condition–action rules. On the other hand, the most fundamental (systemic) characteristics of complex systems cannot be explained (or modeled) using only a single function—or even a list of functions; they arise from interactions among lower order/rule-governed agents—which function simultaneously and continuously, and which are not simply inert objects waiting to be activated by some external source. It is here where I think learning scientists could really have an impact, especially in understanding how to teach and learn about complex systems. THE JOURNAL OF THE LEARNING SCIENCES, 15(1), 45–52 Copyright © 2006, Lawrence Erlbaum Associates, Inc.