| This research seeks to contribute to the task of cataloging how students and teachers spontaneously reason about everyday systems. Using a post-test only design (Tuckman, 1999), I provide preliminary descriptions of participants' "intuitive models" (Perkins, 1986; Resnick, 1996) of targeted system dynamics and their use of homological reasoning. Participants included 29 sixth-grade students and 11 teachers from two California middle schools. One student/teacher group experienced an intensive ecosystem curriculum while the other group experienced a normal curriculum. During one-on-one, semi-structured interviews, participants were asked to reason through: (a) six natural/social system "dilemmas," ranging from simple predator/prey relationships to road building programs; (b) six questions designed to surface homological reasoning; (c) three questions to probe participants' ability to differentiate between types of feedback patterns; and, (d) two questions related to systemic policy analysis. All seventeen probes were designed to surface participants' intuitive models of causal feedback, nonlinear behaviors and structures, time horizons/time delays and stock and flow structures. A coding guide was developed and student and teacher answers are coded according to a five-stage progression.; Participants used a rich variety of terms---such as "cycle," "chain reaction," and "spiral"---to describe complex system dynamics. One-fourth of the students and half of the teachers made observations of deep, structural similarities, or homologies, that cross a wide variety of systems---from ecosystems and families to global politics and the Internet. A closer look at the findings shows a more sobering picture, however. The majority of students and teachers did not describe feedback processes when feedback processes existed. While some of the phrases used, such as "it goes in a circle" were aptly descriptive; others appear to cloud important conceptual distinctions related to the structure and behaviors of complex systems. When reasoning through complex system scenarios, both students and teachers tended not to reference time and frequently transgressed fundamental relationships between stocks and flows, including conservation of matter. Distinct levels of closed-loop reasoning, time dimension awareness, feedback recognition and homological reasoning were found.; Implications for educational systems, professional development, and educational curricula---particularly curricula designed to strengthen students' natural abilities to recognize and utilize dynamic behaviors and structures common to both our natural and social worlds---are discussed. |
