Abstract: We discuss here conceptual change and the formation of robust learning outcomes from the viewpoint of complex dynamic systems (CDS) [1]. The CDS view considers students? conceptions as context dependent and multifaceted structures which depend on the context of their application [1,2]. In the CDS view the conceptual patterns (i.e. intuitive conceptions here) may be robust in a certain situation but are not formed, at last not as robust ones, in another situation. The stability is then thought to arise dynamically in a variety of ways and not so much mirror rigid ontological categories or static intuitive conceptions as assumed by traditional views on conceptual change. We discuss here a computational model based on CDS, in which the learning process is modelled as a dynamical system in order to study the generic dynamic and emergent features of conceptual change [3]. The model is highly simplified and idealized, but it shows how context dependence, described here through structure of epistemic landscape, leads to formation of context dependent robust states representing learning outcomes, kinds of attractors in learning. Due to sharply defined nature of these states, learning appears as a progression of switch from state to another, giving thus appearance of conceptual change as switch form one robust state to another. These states that correspond the intuitive conceptions of the traditional views, are in CDS, however, dynamical epiphenomena arising from the interaction of learning dynamics and targeted knowledge as coded in the instructional design. Finally, we discuss the implications of the results in guiding attention to the design of the learning task and its structure, and how empirically accessible learning outcomes might be related to these underlying factors. References[1] I. T. Koponen and T. Kokkonen (2014) Frontline Learning Research 4, 140-166.[2] I. T. Koponen (2013) Complexity 19, 27-37.[3] I.T. Koponen, T. Kokkonen and M. Nousiainen (2016) Complexity (in print).

Abstract: Recent methodological developments have shown the applicability of nonlinear frame work (i.e. catastrophe theory, nonlinear time series analysis) in science education research and in relevant psychological theories, such as the neo-Piagetian framework, achievement goal theory or conceptual change theories. In this presentation we are reviewing recent investigations in science education research that concern learning at both, the individual-level and at the group-level processes, which ultimately showed the Complex Dynamic System?s meta-theoretical power. Applications of Catastrophe Theory in problem solving and conceptual understanding in chemistry and physics, opened a new area of investigations by implementing cognitive variables, such as, information processing capacity, logical thinking, field dependence/independence and convergent/ divergent thinking as controls explaining students? achievement [1], [2]. The crucial role of certain factors, acting as bifurcation variables, shed light on phenomena associated with surprising effects and students? failure. The catastrophe theory associates the underling cognitive processes with nonlinear dynamics and self-organization. The nonlinear phenomenology, that is discontinuity in mathematical sense, implies that the leaning outcomes are emergent phenomena [3]. Thus, the complex dynamic systems perspective challenges the existing conceptual change theories, which investigate learning through mechanistic and reductionistic approaches. Analogous investigations applied to cooperative learning settings bring up the issue of learning as an emergent phenomenon resulting from the nonlinear interactions among students working in groups. Students? discourses on explanation of physical phenomena analyzed by orbital decomposition method appeared to possess nonlinear characteristic, which are more pronounced in the more effect sessions [4]. The power law distribution of utterances evolving in time denotes the underlying self-organization processes that lead to the emergent learning outcomes. The merit of the new investigations is three-fold. First, they set the basis of the application of new methods and tools to educational research; second, they have provided rigorous explanations and a better understanding of the phenomena under investigation; and third, they signify a paradigm shift in science education and the rising of the new epistemology that embraces research and practice [3]. References[1] Stamovlasis, D. (2006). The Nonlinear Dynamical Hypothesis in Science Education Problem Solving: A Catastrophe Theory Approach. Nonlinear Dynamics, Psychology and Life Sciences, 10 (1), 37-70.[2] Stamovlasis, D. (2011). Nonlinear dynamics and Neo-Piagetian Theories in Problem solving: Perspectives on a new Epistemology and Theory Development. Nonlinear Dynamics, Psychology and Life Sciences, 15(2), 145-173.[3] Stamovlasis, D. (2016a). Catastrophe Theory: Methodology, Epistemology and Applications in Learning Science. In M. Koopmans and D. Stamovlasis (Eds), Complex Dynamical Systems in Education: Concepts, Methods and Applications (pp. 141-175). Switzerland: Springer Academic Publishing. [4] Stamovlasis, D. (2016b). Nonlinear Dynamical Interaction Patterns in Collaborative Groups: Discourse Analysis with Orbital Decomposition. In M. Koopmans and D. Stamovlasis (Eds), Complex Dynamical Systems in Education: Concepts, Methods and Applications (pp. 273-297). Switzerland: Springer Academic Publishing.

Abstract: In my contribution, I develop a new more complex view of learning and education. The focus is on opening and enlarging new spaces of the possible around what it means to educate and be educated. To open and enlarge the spaces of the possible for education, new thinking in complexity is needed to describe learning and development as complex processes of generative change. These may facilitate the opening of so-called ?Spaces of Generativity?, as an extension of Vygotsky?s Zone of Proximal Development. Generativity is the very complex human capability of ?knowing how to go on?. These complex spaces are linked to the generative process of learning and development. Learners may achieve their individual and collective generativity through individual and collective activity. Learners may actually co-create and co-generate each other?s learning and development, with potential non-linear, emergent effects. Learning, then, may be viewed as generative, emergent learning. Learners may even bootstrap each other within communities of learners. This may foster the development of the learner as a whole within his/her multi-dimensional Space of Generativity. New thinking in complexity is needed to design education in a new way, by fostering the scaffolding relations among learners. It is through relations that the complexly generative processes of learning and development of these learners can actually be triggered. The quality of these relations determine the quality of interaction and vice versa. The complexity involved may be taken as the fount of new possibilities for education, with effects hitherto unknown. It shows how new thinking in complexity may be taken as foundational for good education, by complexifying education. This complexifying may be viewed as opening the wondrous world of the possible for education. It may show that human beings are able to develop themselves as whole self-realizing human beings through generative processes of becoming. Complexifying education, then, is a way of humanizing education.

Abstract: The Question: How do children before nine years of age actually learn about significant conceptual meanings, solve problems, and develop self-regulation? Educators who care to address this question--and are not content with rote memorization and children who parrot concrete verbalisms--can find some support in considering the dynamic, non-linear processes by which young children learn. Therefore, it makes sense to apprehend how young children learn in order to choreograph and coordinate how to teach in harmonious ways that do no harm. The Response: A complex dynamical systems theory perspective can help to better understand the generative process of early childhood play and learning in human development. It is relevant to envision the non-linearity of sensitive dependence on initial conditions; the equivalence of different surface manifestations with underlying processes; dynamic phase transitions that become a template for? young children's play and learning processes; and their interface with a content-rich, meaning-based dynamic-themes system of curricular implementation.? Throughout the strands of play dynamics, cognitive dynamics, and curricular dynamics, there appear to be similar non-linear dynamical systems functioning within children?s brains. There is discussion of the confluence of research on brain functions; a body or research that informs the characteristics of young children?s play and imagination; and the ways in which young children acquire fresh perceptions and cognitions.? Focus on the spaces among components of physical and interpersonal relationships can illuminate the processes of these non-linear, complex, dynamic systems.

Abstract: The current literature in educational psychology strongly emphasizes that learners are intentional agents pursuing their personal goals and that they self-regulate their actions in educational contexts. But how do these intentionally regulated learning processes develop over time? The complexity approach in education entails the study of how one condition changes into another, and how the short term and long term time scale of development and learning are interrelated (Van Geert, 1998; Van Geert & Steenbeek, 2005; Thelen & Smith, 1994). Complexity research investigates real-time processes and captures development as it unfolds through multiple interactions between a child and the environment. The approach makes use of microgenetic methods to investigate the interaction between child and environment in real time, and to describe and test its change over time.?But what kind of tools can be used to link these microgenetic measures with long term change ? in processes of learning and skill acquisition - in a meaningful way? In the presentation, we will describe our dynamic interaction model in which teaching-learning processes get their form in the interaction between student and teacher as autonomous, intentional agents. Secondly, several empirical examples will be given in which longitudinal microgenetic measures are combined, such as case studies of the interaction dynamics in student-teacher pairs during individual instruction sessions in arithmetic lessons and during science education (Van der Steen, Steenbeek, Van Dijk, & Van Geert, 2014; Steenbeek, Jansen, van Geert, 2012). In addition, we will discuss state space analysis and other techniques for describing the structure of observational time series as a means to visualize changes in individual teacher-student interaction dynamics, over several time frames. This way the effectiveness of educational interventions can be made visible, in a way that does justice to the complexity and dynamic aspects of the teaching-learning process.

Abstract: In the United States, high school attendance and drop-out are important policy concerns receiving fairly extensive coverage in the research literature. Traditionally, the focus in this work is on the summary of dropout rates and mean attendance rates in specific schools, regions or socio-economic groups. However, the question how stable those attendance rates are over time has received scant attention. Since such stability may affect how long individual students stay in school, the issue deserves attention. We therefore need to investigate the periodic and aperiodic patterns in students? attendance behavior. The school districts that have begun to keep record of daily attendance rates in their schools over multi-year periods, such as those in New York City, have created an opportunity to do so. This presentation will describe how time series analysis can be used to estimate time sensitive dependencies in daily attendance trajectories, distinguishing random fluctuation therein from cyclical patterns (regularity) and aperiodic ones (unpredictability). After showing simulated examples of each of these three scenarios, I will show their occurrence in the attendance plots of actual schools, based on the attendance trajectories in three schools in the course of the 2013-14 school year (N = 187 in each), and in a fourth one from 2004 to 2011 (N = 1,345). A stepwise modeling process is described to statistically confirm the presence of regular and irregular patterns in the series, and it is illustrated how irregular patterns may suggest self-organized criticality (a tension ? release pattern) in the fourth school.The findings discussed here are meant to address a need in educational research to get a statistical handle on the dynamical processes proposed in the literature, and to illustrate the new insights gained from a temporal perspective on the collection and analysis of educational data in general, school attendance in particular.

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.