Abstract: Discrete dynamical systems have been used to theoretically model the complex dynamics of classrooms. While time-series analyses of these models has yielded some insights, state space analyses can yield additional insights; this paper will explore state space analyses and their application to classroom situations. One benefit of state space analysis is that it allows simultaneous exploration of multiple time-series, and so can more easily provide information about divergence and convergence of paths. Additionally, state space analysis, more easily than time-series analysis, can provide information about the existence of multiple paths leading toward a desired state. Further, state space analysis can identify different regimes of behaviors, finding boundaries near which there may be divergent behaviors, and also using those regimes to define a (sometimes) relatively small number of archetypical behaviors. This is particularly useful in tracking behaviors at a microgenetic level, since multiple initial conditions may get to the same (or very close) final states, but in dramatically different ways, and these different routes may have implications for future classroom experiences. Because of these advantages, state space analysis can be used to inform attempts at differentiated instruction in a classroom, assist modelers in identifying appropriate parameter scales, and provide guidance for empirical studies of classroom learning. These ideas will be illustrated through state space analysis of an existing model of teacher-student interactions, identifying four regimes of behaviors, and leading to several implications for classroom practice and research.

Abstract: Typically, studies of teaching on student test scores produce coefficients of determination less than 10% after SES is controlled. We propose that this may be attributable to common assumptions that people contribute to organizational outcomes through their individual characteristics, skills or attitudes. Yet even casual observers have seen interacting individuals ?feed off? one another such that individual and group characteristics are amplified beyond mere accumulation of individual skills. Therefore, we ask, ?Do teachers who are key agents in school networks promote higher test scores than teachers who are not key agents?? We performed analyses in seven elementary schools in a single district. Data came from all professional and support staff in those schools. We first conducted network analyses for each school to calculate network measures, or the degree to which each staff member was engaged in group dynamics. Approximately 30 measures for trust, advice, and social relationships were identified; these included such things as betweenness centrality (the degree to which an individual influences communications between groups) and Simmelian ties (engagement in 3-way reciprocal relationships). Measures for teachers who taught math, ELA, reading, social studies, and science (which had end-of-year test scores) were then combined across schools, and HLM was conducted on the resulting dataset. Predicted test scores were calculated by entering the school identifier with a random intercept, and by controlling student ethnicity and SES. We performed stepwise regression on predicted test scores with network measures as independent. Between 45% and 72% of variation was explained for the various tests. Specific results varied by subject, but measures for trust and advice were the strongest variables, and social engagement only explained science and social studies scores. The types of engagement most explanatory were those in which teachers were sought out for their trustworthiness or the apparent quality of their advice.

Abstract: How real-time classroom interactions in 35 secondary education classes unfold in time was observed to study to which extent teacher and class behaviors in interaction interpersonally adapt to each other; to which extent do students follow the teacher?s behavior? We used Sadler?s joystick method to observe interpersonal teacher and student behavior, in terms of agency and communion (Sadler, Ethier, Gunn, Duong, & Woody, 2009) during the lesson start (the first 10 minutes of the lesson). We used spectral analysis to cyclical patterns in each individual teacher-class interaction. To determine the degree of synchronization between teacher and class behavior, we calculated coherence and phase (Warner, 1998). The results of the study will be illustrated and explained into depth by zooming in on the specific results of Teacher-class 16;Who is a 24 year old male chemistry teacher with 2 years of teaching experience at the beginning of our study in 2010. His results will be compared to the general findings of the 35 teachers in the study. For Teacher-class 16 coherence values were .65 for communion and .78 for agency; indicating a considerable degree of synchronicity between interpersonal teacher and class behavior. Teacher-class 16?s phase values were -.01 for communion and .46 for agency. These values show that the teacher only slightly tends to follow the students in communal behavior and leads the students in agentic behavior. Further analysis of the coherence and phase values of the 35 teacher showed that differences in coherence and phase are related to the quality of the teacher interpersonal style.

Abstract: Ecologies in nature are complex adaptive systems and complex adaptive systems learn. Learning is essential for all living systems. Learning ecologies are comprised of many diverse, interdependent agents, continually self-organizing in surprising ways as systems adapt to shifting environments. System-wide patterns emerge and interact across multiple levels of organization. The Ecology of learning provides an evocative and useful metaphor for powerful teaching and learning systems. Natural ecological systems and learning ecologies share at least three characteristics for transformational complex change (learning): 1. Open, permeable boundaries that allow information, energy, and resource to flow freely; 2. Diverse agents hold tension, generating energy to move the system. 3. Nonlinear exchanges serve as feedback for iterative, continuously, transforming systems. Three different education programs spanning K-12, university writing and post-graduate health professions education are described as ecologies of learning and teaching that share practice and theory in Human Systems Dynamics including: 1. A broad understanding of interconnected knowing different than superficial short-term, sequenced disconnected bits of information; 2. Pattern logic of the whole rather than data logic of individual items; both co-embedded in complex landscapes of socially organized learning. 3. The ability to see, understand, and take action to influence conditions that lead to complex patterns. How we continue to establish conditions to sustain deep learning ecologies for teachers and learners is embedded in an iterative educational process of planning and action: What do we know about complex systems? How do we use what we know to shape conditions for learning ecologies in educational systems? How do we establish and sustain inquiry? These questions frame deep reflection and professional conversation. They set conditions for an ecology including expectations, experiences, and emergent structures that support a praxis of deep learning.

Abstract: Since its boom in the late 20th century, network science has become ever-more relevant to people's everyday life. Knowledge about networks can help us to make sense of this increasingly complex world, making it a useful literacy for people living in the 21st century. Network science offers a powerful approach for conceptualizing, developing, and understanding solutions to complex social, health, and environmental problems; and it also provides opportunities to develop many of the skills, habits of mind, and core ideas that are not currently addressed in extant elementary/secondary education curricula and teaching practice. There is a need for curricula, resources, accessible educational materials, and tools about networks. In this talk, we present a summary of the NetSciEd (Network Science and Education) initiative that we have been running over the last several years to address the educational need described above. It consists of (1) NetSci High educational outreach program (2010--2015) that connects high school students and their teachers with regional university research labs and provides them with the opportunity to work on network-science research projects, (2) NetSciEd symposium series (2012--present) that bring network-science researchers and educators together to discuss how network science can help and be integrated into school education, and (3) Network Literacy: Essential Concepts and Core Ideas booklet (2014--present) that was created collaboratively and subsequently translated into more than 15 languages by a large number of network-science researchers and educators worldwide.

Abstract: Integrated water resource management (IWRM) is a contested goal for landscape sustainability, with proponents offering the possibility of viewing catchments as complex social-ecological systems (CESs), and embracing concepts such as resilience and adaptive management; and detractors arguing for the pragmatic utility of silo?s and more linear management processes. A group of transdisciplinary researchers in South Africa have engaged in several projects over the past five years. We adopt an understanding of catchments as CSESs, and aim to use co-learning and the co-development of knowledge as pathways for deepening democracy, through increasing knowledgeable catchment resident participation in catchment management institutions. We would like to share our experience of four case studies. The first is within a well-developed catchment management institution ? the Inkomati-Usuthu Catchment Management Agency (IUCMA), exposed to CSES thinking since in?s inception in 2004. There, in the Crocodile River sub-catchment, industry partners and municipalities co-operated to develop and initiate implementation of an integrated water quality management system. The other three are within an emerging CMA (Mzimvubu-Tsitsikamma), each with an opportunity to contribute to the catchment management strategy. Within the MTCMA: 1) the Lower Sundays River Valley has no primary water scarcity, and an efficiently irrigated export citrus industry ? but a lack of potable water in many homes; 2) in the sub-catchment of the Makana Muncipality a civil society organisation emerged and we traced practice and learning in facilitating water supply to homes; and 3) in the rural Tsitsa River sub-catchment, proposed dam construction triggered the question: ?How can state-sponsored landscape restoration investment be leveraged to ensure wetland seep protection and improved livestock livelihoods through a co-learning process? Each of these case studies illustrates our ?learning about learning?, which as has embedded our commitment to the CSES concept.