Toward a Learning Progression of Complex Systems Understanding

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.

NiCE Teacher Workshop: Engaging K-12 Teachers in the Development of Curricular Materials That Utilize Complex Networks Concepts

Our educational systems must prepare students for an increasingly complex and interconnected future, but teachers facing this task are not equipped to prepare students to succeed. Network science–the study of how biological, social, physical and technological systems interconnect, how the structure of those connections evolve over time, and how those structures and behaviors inform our understanding of them–is a pathway to deepening engagement with the kinds of complex problems these students will have to deal with as adults in the workforce. We recently held the Networks in Classroom Education (NiCE) workshop for a group of 21 K-12 teachers with various disciplinary backgrounds. The explicit aim of the workshop 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 using these concepts, in the form of lesson plans, for themselves and for the wider community. Here we detail the nature of the workshop and present its outcomes, including a set of publicly available innovative lesson plans. We also discuss the future development of the successful integration of network science in K-12 education and its importance in inspiring and enabling our teachers.

Exploring the Effects of Creating Small High Schools on Daily Attendance: A Statistical Case Study

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.

Design Considerations for Education Scholars Interested in Complex Systems Research

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.

The Socially Situated Dynamics of Children’s Learning Processes in Classrooms: What Do We Learn from a Complex Dynamic Systems Approach?

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.

Phase Transitions: In the Brain, Socio-­dramatic Play and Meaningful Early Learning

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.

Complex Dynamic Systems View on Conceptual Change: How a Picture of Students’ Intuitive Conceptions Accrue From Dynamically Robust Task Dependent Learning Outcomes

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.

On Reinventing Education in the Age of Complexity: A Vygotsky-­inspired Generative Complexity Approach

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.

Nonlinear Processes in Time-Ordered Observations: Self-­Organized Criticality in Daily High School Attendance

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.