What ideas from physics education research can be useful in teaching complex systems?
Andy Johnson, Black Hills State University
I have not been working on teaching complex systems - instead I have been studying physics teaching, which focuses on simple systems, yet still offers plenty of learning challenges for students. I want to learn about teaching complex systems, because very few members of our society seem prepared to think in terms of how complex biogeophysical, economic, and cultural systems function, or to act accordingly. This essay will highlight some of the learning challenges that are becoming well known in physics (and in science in general) and ask how these things play out in the teaching and learning of complex systems.
Students walk into our courses with feelings that they already understand things. They have constructed explanations that have worked for them up to that point, and while they may expect to learn something new, they will interpret everything they encounter in terms of their current understandings. The consequence is that learners often construct very different understandings of what was taught than what the teacher intended. And you have to listen carefully to hear the differences.
This happens because learning is not simply the acquisition of information. Learners instead have to form mental images, models and stories that use information, connect to existing knowledge, and provide meaning. It is not enough to just get facts - learning requires developing understanding which is something the learner must create. You can't do this step for your students no matter how hard you try. Instead, the students have to do it themselves. The challenge of teaching, then, is then to put learners in situations in which they need to make sense of something and then to provide appropriately crafted opportunities for this sense-making to get done. The task of the teacher and curriculum developer is one of arousing interest, focusing attention on particular issues, and providing appropriate structures that support sense-making and elaboration. This is what a well-organized inquiry classroom accomplishes.
In any classroom, including inquiry-driven ones, students interpret their experiences in light of what they already know. Part of the time they just "add new knowledge", a process Piaget called "accretion". However, sometimes students need to reconsider something they thought they already knew. They may need to substantially change their thinking in some way to accomodate something new. This is called "restructuring" (Carey, 1988, Posner et. al. 1982) or "conceptual change". Restructuring involves significant changes in one's existing knowledge and belief structures. For example, when studying motion and force, most students have to make major changes in their views of reality to understand Newton's laws because they typically use a "naive physics" that they developed in childhood with limited experience. They have to think in new ways about the causes and effects of motions. To use an analogy, restructuring is more wrenching than just rearranging the furniture in your living room - it may require deciding to use the TV as a countertop, turning the couch on its end, and bringing in a new set of bar stools. You might have to tear out a wall. As you can imagine, restructuring one's thinking is difficult and scary. Students don't generally make substantial conceptual changes like this without a lot of support, effort, and courage so in many cases they will learn to "talk the talk" without actually changing how they think. Thus, they probably don't understand but it's hard to tell because they sound so "correct" part of the time. You can't tell until you really dig into what they are saying and find the right questions to ask.
A restructuring event happened in my own classroom during an inquiry sequence on electric circuits. As students started constructing explanations about what was flowing in circuits, they talked about "electricity" flowing. Many of them used a general idea about one thing flowing that had some of the properties of current and some of the properties of energy. Only when the students made distinctly different measurements of electrical current vs. electrical energy and were explicitly asked to consider the differences did they start thinking that current and energy might in fact be two separate things that both flow in circuits. This was a type of conceptual change that Dykstra (1992) calls "differentiation". The students had to decide that the one thing they were talking about - electricity - was actually two different things - current and energy - with distinctly different behaviors and properties.
Another type of restructuring - class extension - requires students to see two things they previously thought of as different as manifestations of one thing. A third type, which Dykstra calls "reconceptualization", involves changing one's concepts of how things relate to each other and what are the relevant relationships. For example, students must abandon the common belief "force implies motion" in order to understand Newtonian dynamics, and they must construct a new idea - "force implies acceleration", and then use it reliably.
Physics education research has made some progress in identifying the conceptual changes that need to be made to understand various topics in physics, and some teaching schemes have been developed that support needed changes. What has been found in the teaching of complex systems? Are there known troubles that students encounter? What conceptual changes are required? Are there known ways to help students move into new ways of thinking?
There is some overlap between learning math, physics and complex systems. Researchers have found that students seem to have trouble distinguishing between rates and accumulated amounts. The notion of a "rate of change" requires, for many people, thinking in new and unfamiliar ways (Thompson, 1996). This begs the question, what other components of complex systems may cause trouble? Students at lower levels (and maybe some at higher levels) have trouble deciding whether to use additive reasoning or multiplicative reasoning. This would be a key issue in understanding relationships in systems. Also, do students have difficulty thinking about relationships rather than about objects? Models of complex systems include time delays and variable rates of change. How do students make sense of these things as causes, and of their effects? Notably, the feedback loop is a fundamental structure in models of systems. How do students understand the behaviors of feedback loops? What is required to make sense of their implications? Al Bartlett has said that "mankind's greatest shortcoming is our inability to understand the exponential function".
Another huge issue in science education is the role of context in reasoning. People tend to reason from concrete contexts. When students seem to understand some particular topic, a seemingly slight change in context can significantly influence how students think (Bao, 2002). What kinds of contexts are involved in thinking about complex systems? How do students negotiate different contexts in the study of systems, and in particular how much experience do they need before they can they distill or apply general principles or properties of systems in varied situations?
I hope to learn something about these and other issues at this conference, and I hope that ideas from physics education research can be useful in teaching about complex systems.
Bao, L., K. Hogg, et al. (2002). "Model analysis of fine structures of student models: An example with Newton's third law." American Journal of Physics 70 (7): 766-779.
Carey, S. (1988). Reorganization of Knowledge in the Course of Acquisition. Ontogeny, Phylogeny, and Historical Development. S. Strauss: 1 - 27.
Dykstra, D. (1992). Studying conceptual change: Constructing new understandings. Research in Physics Learning: Theoretical Issues and Empirical Studies Proceedings of an International Workshop at University of Bremen. R. Duit, F. Goldberg and H. Niedderer. Kiel, Germany, IPN: 40-58.
Posner, G. J., K. A. Strike, et al. (1982). "Accommodation of a Scientific Conception: Toward a Theory of Conceptual Change." Science Education 66 (2): 211-227.
Thompson, P. and A. Thompson (1996). "Talking about rates conceptually, Part II: Mathematical Knowledge for teaching." Journal for Research in Mathematics Education 27 (1): 2-24.