Recent research on what students know about complex systems shows that they typically have challenges in understanding particular system ideas such as nonlinearity, complex causality, and decentralized control. Yet this research has yet to adopt a systematic approach to learning about complex systems in an ordered way in line with the Next Generation Science Standards’ call for learning pathways that guide teaching and learning along a developmental continuum. In this paper, we propose that learning progressions research can provide a conceptual framework for identifying a learning pathway to complex systems understanding competence. As a first step in developing a progression, we articulate a sequence of complex systems ideas, from the least to most difficult, by analyzing students’ written responses using an item response theory model. Results show that the easiest ideas to comprehend are those that relate to levels or scales within systems and the interconnected nature of systems. The most difficult ideas to grasp are those related to the decentralized organization of the system and the unpredictable or nondeterministic nature of effects. We discuss implications for this research in terms of developing curricular content that can guide learning experiences in grades 8–12 science education.
Does creating small high schools have a beneficial impact on daily attendance? This question was addressed using time series analysis to examine the case of one urban transfer high school that serves students who previously dropped out of school. This analytical approach is uniquely suitable to examine the dynamical processes characterizing stability and transformation in the system. This school reduced its size from enrolling approximately 900 students up to and through the 2009-2010 school year to about 250 students afterward. We looked at whether attendance was higher after the intervention and whether it was more stable. It turns out that the attendance trajectories over a seven-year period show high volatility prior to the reduction in school size but are more stable afterward. The initial increase in daily attendance at the onset of the intervention is not maintained, but increases are observed later. The study illustrates the relevance of time series analysis for educational policy research as well as the use of complexity theory to fully appreciate the nature of the post intervention changes.
As complex systems approaches to research gain a foothold in educational research, educational researchers may be faced with unique study design challenges. Studies that do not target appropriate levels of analysis or do not capture variable change over time at a fine enough granularity run the risk of missing complex, dynamic, and emergent properties that are the hallmark of complex system behavior. By taking into account context, multiple levels of analysis, and change over time complex systems approaches generate evidence for dynamic processes in education. This paper draws upon three example areas from educational psychology to illustrate important design considerations for conducting complex systems research in education. We discuss how complex systems designs can generate new insight for areas of study such as how psychological constructs influence learning, classroom dynamics, and teacher-student interactions.
Our educational systems must prepare students for an increasingly interconnected future, and teachers require equipping with modern tools, such as network science, to achieve this. We held a Networks in Classroom Education (NiCE) workshop for a group of 21 K-12 teachers with various disciplinary backgrounds. The explicit aim of this was to introduce them to concepts in network science, show them how these concepts can be utilized in the classroom, and empower them to develop resources, in the form of lesson plans, for themselves and the wider community. Here we detail the nature of the workshop and present its outcomes - including an innovative set of publicly available lesson plans. We discuss the future for successful integration of network science in K-12 education, and the importance of inspiring and enabling our teachers.
Our purpose is to provide an exploratory statistical representation of initial teacher education as a complex system comprised of dynamic influential elements. More precisely, we reveal what the system looks like for differently-positioned teacher education stakeholders based on our framework for gathering, statistically analyzing, and graphically representing the results of a unique exercise wherein the participants literally mapped the system as they perceived it. Through an iterative series of inter-related studies employing cluster analysis and multidimensional scaling procedures, we demonstrate how initial teacher education may be represented as a complex system comprised of interactive agents and attributes whose perceived relationships are a function of nested stakeholder-dependent simplex systems. Furthermore, we illustrate how certain propositions of complexity theory, such as boundaries, heterogeneity, multidimensionality and emergence, may be investigated and represented quantitatively.
There is considerable variation in the dynamical literature in how the term 'complexity' is used. While there have been several attempts to describe from an educational perspective what complexity encompasses, the term is frequently used without an explicit definition. To forge a shared understanding of what complexity means, the purpose of this article is to define the term for the field in a way that acknowledges the variety of use that is encountered in the education. Four perspectives on complexity are offered: 1) Information theory, 2) Cybernetics and general systems theory, 3) The use of complexity to describe scenarios of transformation and 4) Complexity as a metatheory. The implications of each of these four conceptualizations for educational research and practice are discussed.
This article differentiates approaches to school-based teacher education. It contrasts the pervasive apprenticeship model, to a "naturally integrated" school-based teacher education program that we describe as a complex learning system. Rather than view teacher education as fragmented by separating educational theory (physically based on a university campus) and teaching practice (based in a school and resembling an apprenticeship), we favor an approach where all coursework is integrated with practice in a host school while maintaining close connections to the university. The latter model highlights learning as contextualized in school, focussed on the whole school, yet also informed by progressive educational thought. All participants in the school environment (not just university students) are at once both learners and teachers. Just as university-based aspects of teacher education suffer from a lack of practical relevance, we anticipate that any model of school-based teacher education will have to address the effects of context overwhelming theoretical learning, philosophical understandings, and generalization to other contexts. We claim that a complex learning system model is better able to mitigate these contextual effects. We propose an approach to address this issue through both "reduction" and "complexity".
This article concentrates on the question what kind of model - conceptual and statistical - can serve as a good working model for the study of learning and teaching processes qua processes. We claim that a good way of answering this question is to begin by observing a teaching and learning process as, where, and when it occurs. In addition, a conceptual model of intertwined learning-teaching processes is discussed, and dynamic modeling as an approach to theory formation about teaching-learning processes. The focus lies on the evolution term, the timescale of interaction processes, state space as a perspective on teacher-student interaction dynamics, and the principle of agency. Finally, an empirical approach to studying teaching-learning processes is illustrated by means of a case study, focusing on the use of cluster analyses techniques. In the Conclusion and Discussion section, further perspectives on theory building and empirical research are discussed.
In the present study, complex dynamic systems theory and interpersonal theory are combined to describe the teacher-student interactions of two teachers with different interpersonal styles. The aim was to show and explain the added value of looking at different steps in the analysis of behavioral time-series data (i.e., observations of teacher and student behaviors) that are described by Warner (1998): (1) the general level and overall coordination, (2) the presence of linear, quadratic and cubic trends in behavior, (3) the coherence and phase in cyclical trends that are superimposed on the linear, quadratic and cubic trends, and (4) the residual fluctuations, when studying the fit between teacher and student interpersonal behavior. Interactional fit is conceptualized, and described in each step of the time-series analysis, using the principle of complementarity (e.g., Kiesler, 1996). Results showed that the teacher-student interactions of the teacher with the most desirable interpersonal style largely followed the complementarity principle, whereas the interactions of the teacher with the less desirable interpersonal style did not. These results are discussed in light of the hypotheses and limitations of the study.
In the United States, high school attendance and drop-°©‐‑out are important policy concerns receiving 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 instability in attendance may affect how long individual students stay in school, the issue deserves attention. Theschool 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 investigate the temporal dimension of daily attendance, and thereby explore its stability. This paper will focus on its long-term characteristics, specifically the following: self-similarity, meta-stability or pink noise, and the impact of sudden departures from the central tendency of the series. Such departures can be used to estimate the impact of exogenous influences on the behavior of the system. The findings illustrate the importance of describing the dynamical patterns underlying attendance that remain concealed in traditional summary measures.
Reinventing education is the ultimate aim of this contribution. The approach taken is a radical new complexity-inspired bottom-up approach which shows complexity as the fount of creativity and innovation. Organizing complexity accordingly may be the foundation for a new complexified vision of education. It all starts with new thinking in complexity about how complexity is actually generated in the real world. Such thinking offers new kinds of complexity like generative and emergent complexity. The approach taken is very much inspired by the genius of Vygotsky, as a visitor from the future. His focus was not only process-oriented, but also very much possibility-oriented. His method was bottom-up, and opened new spaces of the possible, like the Zone of Proximal Development. Yet he was not able to deal with the problem of complexity in his days. He 'simply' lacked an adequate causal framework, which showed causation as a generative bottom-up process, to be linked with potential nonlinear effects over time. He could not explain what he saw as possible: the turning points and upheavals of learning and development. In this contribution the focus will be on the link between the new thinking in complexity and the causal, generative nature of complexity in the real world. This link may show the ontological creativity of the entire world in general, and of human learning and development in particular. It may show the power of generativity to unleash this creativity by a new way of theorizing on education. The complexity-inspired theory of development as generative change, as thriving on the generative power of interaction, is fundamental and foundational for this new theorizing.
There are similar, non-linear complex dynamical systems that underlie the epigenetic development of young children. This paper discusses 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, dynamical systems. Particular implications are relevant for educational practices.
We discuss here conceptual change and the formation of robust learning outcomes from the viewpoint of complex dynamic systems (CDS). The CDS view considers students' conceptions as context dependent and multifaceted structures which depend on the context of their application. In the CDS view the conceptual patterns (i.e. intuitive conceptions here) may be robust in a certain situation but are not formed, at least not as robust ones, in another situation. The stability is then thought to arise dynamically in a variety of ways and not so much to mirror rigid ontological categories or static intuitive conceptions. We use computational modelling to understand the generic dynamic and emergent features of that phenomenon. The model is highly simplified and idealized, but it shows how context dependence, described here by an epistemic landscape structure, leads to the formation of context dependent robust states that can be viewed as attractors in learning, and how owing to the sharply defined nature of these states, learning appears as a progression of switches from one state to another, giving thus the appearance of conceptual change as switches from one robust state to another. Finally, we discuss the implications of the results in directing attention to the design of learning tasks and their structure, and how empirically accessible learning outcomes might be related to these underlying factors.
This paper discusses investigations in science education addressing the nonlinear dynamical hypothesis. Learning science is a suitable field for applying interdisciplinary research and predominately for testing psychological theories. It was demonstrated that in this area the paradigm of complexity and nonlinear dynamics have offered theoretical advances and better interpretations of empirical data. Research showed that besides linear modes of behavior, sudden transitions occur in cognitive performance and this has questioned basic theoretical and epistemological assumptions. The neo-Piagetian framework and motivational theories offering constructs for serving as predictors in various model are the local theories which are embraced by the CDS meta-theory. Sudden transitions are modeled by catastrophe theory (CT) the analyses of which reveal the crucial role of certain variables, namely the bifurcation factors. Beyond a critical value of the bifurcation factor, the state variable splits into two-attractor regions and becomes bimodal. The bifurcation effect induces uncertainty and unpredictability in the system, which oscillates between two states entering the regime of chaos. Then in state variables such as learning outcomes and achievement, sudden transitions from success to failure are expected. Catastrophe theory explains unexpected phenomena associated with school failure, dropouts, illicit behaviors, sudden attitude change, and creativity. Moreover CT could contribute in elucidating theoretical debates and conflicting empirical evidences.
This short article presents a summary of the NetSciEd (Network Science and Education) initiative that aims to address the need for curricula, resources, accessible materials, and tools for introducing K-12 students and the general public to the concept of networks, a crucial framework in understanding complexity. NetSciEd activities include (1) the NetSci High educational outreach program (since 2010), which 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) the NetSciEd symposium series (since 2012), which brings network science researchers and educators together to discuss how network science can help and be integrated into formal and informal education; and (3) the Network Literacy: Essential Concepts and Core Ideas booklet (since 2014), which was created collaboratively and subsequently translated into 18 languages by an extensive group of network science researchers and educators worldwide.
This paper utilizes the theoretical framework of complexity theory to compare and contrast leadership and educational change in two urban schools. Drawing on the notion of a complex adaptive system—an interdependent network of interacting elements that learns and evolves in adapting to an ever-shifting context—our case studies seek to reveal the complexities, tensions, characteristics, and related implications for school leadership derived from using this heuristic to understand adaptive change. In particular, we highlight the need to disrupt the status quo as a precursor to adaptive change, the power generated by distributing authority through decentralized networks, the importance of relational trust, and the impact of school culture.
