Designing a Complex Curriculum – The Case of Innovation and Reform 2 – a possible complexity

‘Sense making is often about creating a whole out of fragments.’ Burns (2007:2)

This post sets out some of the basic conceptual foundations of complexity as a basis for considering its use in education in the next post in this series. Over the past 30 to 40 years complexity science has developed rapidly from its origins in physics, chemistry, biology and cybernetics to offer new insights within the social sciences. The use of a complexity lens within social contexts has started to create a different way of seeing the social world as well as suggesting new approaches to researching it. Defining complexity itself is difficult as there is no single, unified theory. As Cilliers (2010: vii) argues,

‘….there is a growing realisation that there is no single coherent ‘complexity theory’ which will unlock the secrets of the world in any clear and final way. Instead, we are beginning to understand more about exactly why complex things are so difficult to understand. We really have no choice but to acknowledge that we have to take complexity seriously, even if it does not guarantee perfect solutions.’

To demonstrate some of the different perspectives which have grown from a consideration of complexity, some of the contrasting approaches and typologies are given here. Morin (2008) distinguishes between:

  • restricted complexity – complexity as an emergent product between simple agents. Such a view allows for rules-based, agentic modelling (i.e. modelling of the parts to give a sense of the whole), which is ultimately reductionist in character, i.e. leads to the idea that by modelling the parts, even though difficult, we can gain an understanding of the whole system;
  • general complexity – within this definition the system of interest is not merely the sum of the parts/agents as when they interact they give rise to new properties which are themselves emergent and which resist modelling. Indeed Morin suggests that this shows that we are limited in our understanding of complex systems regardless of the approach we use, that we must accept this, and search for a new language in describing and explaining such systems.

Richardson and Cilliers (2001) alternatively classify complexity through three contrasting approaches to study:

  • hard complexity – computational modelling and quantitative approaches, generally used within the sciences;
  • soft complexity – employed in the social sciences and often seen as offering a ‘metaphor’;
  • complexity thinking – an approach which focuses on the lack of full understanding of systems. This inherently partial perspective is due to multiple factors operating across a number of scales. However, by focusing on emergence (the way systems develop through numerous interactions) as a central process, coherent change can be discerned and studied.

Whilst Cilliers (2010) rightly points to the breadth of approaches to complexity, calling into question the idea of a single ‘theory’, Byrne and Callaghan (2014;8) argue that we should see complexity less as a traditional theory and more as a ‘framework for understanding’, based on the notion that ‘much of the world and most of the social world consists of complex systems…if we want to understand it we have to understand it in those terms.’. They quote Castellani and Hafferty (2009:34) to differentiate a traditional theory from a frame of understanding:

‘social complexity theory is more a conceptual framework than a traditional theory. Traditional theories, particularly scientific ones, try to explain things. They provide concepts and causal connections (particularly when mathematicised) that offer insight into some social phenomenon….. Scientific frameworks, in contrast, are less interested in explanation. They provide researchers effective ways to organise the world; logical structures to arrange their topics of study; scaffolds to assemble the models they construct. When using a scientific framework ‘theoretical explanation’ is something the researcher creates, not the other way round.’

Complexity is explained on an ontological basis starting from a foundation of seeing much of social reality as complex (as opposed to either simple/linear or random).

Taken ontologically, complexity rests on a number of basic concepts.

non-linearity: non-linear systems are those in which cause and effect relationships are disproportionate, i.e. small causes may have very large impacts and vice versa. There are different forms of non-linearity, including ‘threshold effects’, where a system might act in a linear and predictable way until it hits a certain threshold beyond which it acts in the non-linear manner, commonly referred to as a ‘bifurcation point’, and ‘general deterministic chaos’ where very small variations in initial conditions give very different outputs (the so-called ‘Butterfly effect’). What non-linearity stresses is an inability to accurately model or predict a complex system. Where mathematical modelling is used to explain and characterise such systems, it makes use of ‘qualitative methods’ which generate approximate descriptions as it is not possible to create exact and accurate simulations of complex, non-linear systems. This is not to suggest that quantitative approaches to complexity have no utility, they do. However, they are best used in mixed methods approaches with qualitative approaches.

Emergence: non-linear systems have the potential to create new properties from the interactions of the multitude of elements within them, properties which are not predictable given the known starting-points within the system. Deacon (2007) argues that three ‘levels’ of emergence exist.

  1. First order emergence is characterised by an aggregate of elements to give a ‘simple’ higher-order property which occurs through statistically or stochastically determined behaviours. It is the relationships between the lower-order elements/properties which give rise to the higher-order properties, a relationship referred to as ‘supervenience’. This form of emergence is perhaps most closely aligned to Morin’s (2008) definition of restricted complexity.
  2. Second order emergence introduces the impact of time on the processes involved. First-order emergence may retain self-similarity in the relationships over time. Second-order emergence shows change and development of both ‘micro and macro-properties over time.’ (Deacon, 2007:99). This means that prior states in the system become irreversibly replaced and superseded by new states/system characteristics.
  3. Third order emergence has an evolutionary character. Here, there can be amplification of global influences on parts which can lead to recursive amplification (positive feedback) or degradation (negative feedback) across all scales of the system. Hence, initial complex states can become amplifiable initial conditions for later states.

Therefore, the basis for understanding emergence is the interplay of many properties over time and across scales which can lead to new, unpredictable states and properties.

Far from equilibrium systems: Systems can exist in a number of states. Those in equilibrium tend to be isolated with no exchange of energy with the environment beyond. In many cases the lack of interaction with the wider environment leads to decay and death. Much more common are systems which are close to equilibrium, called ‘closed’ systems where there is limited interaction with the environment beyond. Here, any move away from equilibrium tends to lead to damping effects to bring it back towards the near equilibrium state. In other words closed systems tend to be driven by negative feedback loops. Finally, there are ‘open’ systems of which most human systems are examples. These can be impacted by negative feedback but may also be impacted by positive feedback which can move the system further away from equilibrium. It is the introduction of elements from beyond the system which keep these systems in a state of flux and disequilibrium. One specific type of open system is the ‘adaptive’ system, commonly referred to in complexity theory as a Complex Adaptive System. Here, change is in part the result of experience with constant exchange of information between the system and the wider environment. Such systems have a number of features, the most important of which are discussed by Cilliers (1998) who identifies them as characterised by:

  1. a large number of elements with many interactions;
  2. interactions which are non-linear, i.e. large-scale causes can have small-scale impacts and vice versa;
  3. interactions which lead to feedback loops, both negative and positive;
  4. an ‘open’ system, having interactions with elements in external environments beyond the immediate system;
  5. elements which interact with their environment making the identification of boundaries difficult;
  6. a system which is far from equilibrium and therefore needs a constant energy flow for it to operate;
  7. the importance of history, past processes playing a role in forming the present, often unpredictably;
  8. each element only acting on local information rather than information from the whole system.

Cilliers (1998: 13) goes on to argue that such systems are so complex that any total representation of them would have to be as large as the system itself – a practical impossibility;

‘In building representations of open systems, we are forced to leave things out, and since the effects of these omissions are nonlinear, we cannot predict their magnitude.’

Consequently, Richardson et al (2007) refer to CASs as ‘incompressible’, and argue that to understand them, at last in part, we need to use different perspectives to build ever richer, if incomplete, models of the system we are interested in. To some, this might be an excuse not to bother; why research something we cannot understand in its entirety? For others, there is the temptation to use experimental approaches which isolate single variables and assume they operate in the same way in a complex context. But in both cases, the complexity of the system is lost and in many experimental approaches interactive processes are assumed to have little, or no, impact.

Final thoughts

The characterisation and understanding of complexity, particularly in social research, is still very much in its infancy. We have to accept that there is no single, accepted body of theory which is unchallenged, but whilst these restrictions exist, the basic building blocks and ontological underpinning of complexity as a ‘framework for understanding’ seem to me to be worth pursuing. Methodologically, complexity accepts that research will never ‘see’ an ultimately reality (however, I accept the epistemological perspective of ‘complex realism’ developed and advocated by Reed and Harvey (1992 and 1996) and Byrne and Callaghan (2014)). As Richardson and Tait (2010: 92-93) state,

‘Just because a complex system is incompressible it does not follow that there are (incomplete) representations of the system that cannot be useful – otherwise how would we have knowledge of anything, however limited? Incompressibility is not an excuse for not bothering.’



Burns, D. (2007) Systemic Action Research: A strategy for whole system change. Bristol: Policy Press

Byrne, D. & Callaghan, G. (2014) Complexity Theory and the Social Sciences: The state of the art. Abingdon: Routledge.

Castellani, B. & Hafferty, F. (2009) Sociology and Complexity Science. Berlin: Springer.

Cilliers, P. (1998) Complexity and Postmodernism: understanding complex systems. London: Routledge

Cilliers, P. (2010) ‘Acknowledging Complexity: A Forward.’ In D. Osberg & G. Biesta (eds) Complexity Theory and the Politics of Education. Rotterdam: Sense Publishers. vii-viii

Deacon, T.W. (2007) ‘Three Levels of Emergent Phenomena.’ In N. Murphy & W.R. Stoeger (eds) Evolution and Emergence: Systems, Organisms, Persons. Oxford: Oxford University Press. 88-110

Morin, E. (2008) On Complexity. Cresskill, NJ: Hampton Press.

Reed, M. & Harvey, D.L. (1992) ‘The New Science and the Old: Complexity and Realism in the Social Sciences.’ Journal for the Theory of Social Behaviour, 22, 356-79.

Reed, M. & Harvey, D.L. (1996) ‘Social Science as the Study of Complex Systems.’ In L.D. Kiel & E. Elliott (eds) Chaos Theory in the Social Sciences. Ann Arbor: University of Michigan Press. 295-324.

Richardson, K. A., & Cilliers, P. (2001). What is complexity science? A view from different directions. Emergence, 3, 5–22.

Richardson, K.A.; Cilliers, P. & Lissack, M. (2007) ‘Complexity Science: A ‘Gray’ Science for the ‘Stuff in Between’ in Thinking Complexity: Complexity and Philosophy volume 1, Cilliers, P. (ed.). Mansfield, USA: ISCE Publishing, 25-35. (an original version of the paper can be found at

Richardson, K.A. & Tait, A. (2010) ‘The Death of the Expert?’ E:CO, 12(2), 87-97.


Some Initial Thoughts on Pedagogic Literacy – Contextualising Scholarship of Teaching and Learning

All humans have the capacity to both learn and teach. Children teach each other games, parents teach their children how to tie their shoe laces, how to behave and how to ride a bicycle. Teaching is as ubiquitous as learning; it is part of what it is to be ‘human’. In pre-history, humans taught and learned through mimetic and experiential learning and teaching. However as societies become more complex and individuals begin to specialise in the jobs they do, one pursuit which emerges is that of teaching children. Whilst some have responsibility to look after animals, to harvest crops, or build computers, etc, others become expert in teaching others. This is the obvious extension of the formalisation of the act of education. In specialising in pedagogy (here taken to mean the process of bringing together teaching, learning, curriculum and assessment to enable others to extend their experience of the world) teachers move from an informal process of teaching, i.e. trial and error, often implicit and subconscious, to one which is made explicit, problematic, and around which can be built structures and processes to enable better, more efficient, more creative ways of helping others to learn.

By seeing pedagogy as a process which all people have ability in it becomes a continuum rather than something that some of us have and others do not. Instead, what distinguishes teachers is a heightened awareness, understanding and pursuit of better pedagogy. The elements and processes involved in developing pedagogic skill and insight is what we term pedagogic literacy.  Pedagogic literacy is constituted of a wide repertoire of teaching-related knowledge, skills, values, dispositions and attributes. Figure 1 gives a summary of some of the main features involved.

PL outline

Figure 1. Outline of some of the main features of pedagogic literacy

Pedagogy is a complex process, where complexity should be understood by its scientific meaning of being nonlinear, incompressible, and emergent. Taking each of these ideas in turn, nonlinearity emphasises that teaching and learning do not occur in simple cause-and-effect relationships; by teaching X, I cannot universally predict that student Y will learn Z. Sometimes major interventions will have little effect, at other times the smallest of interactions may have profound impacts. The work of teachers is also incompressible in that any attempt to boil down and summarise the complexity of pedagogy into a simple list is doomed to curtail the depth and breadth of the reality of the pedagogic environment (see this post on complexity and graded observation as an example). Finally, associated with the incompressibility of teaching is the notion that pedagogy has features which are beyond the sum total of factors which come together to make it possible, in other words the act of pedagogy is itself emergent and as such is highly unpredictable at any level other than the most general. It must be stated that by accepting that pedagogic literacy is a complex adaptive system, and hence is incompressible, any model of its characteristics such as that in figure 1 can only ever hope to be a guide rather than a totality. It is given as partial description as opposed to a definitive explanation.

For those teachers who become expert at their job there is a career long investment in engaging in understanding the detail of their chosen profession. The complexity of pedagogy is such that we must continue to develop our understanding over the course of many years; in fact it is a truism that we will have neither a perfect understanding of the processes of teaching and learning nor ever teach the perfect lesson over the course of our career’s span. As a medium for understanding the ways in which individual teachers develop, pedagogic literacy is constituted of a wide (though not exhaustive) repertoire of teaching related knowledge, skills, values, dispositions and attributes.

Figure 1 highlights two important features of the concept of pedagogic literacy. Firstly, we see pedagogic environments as complex adaptive systems in which teachers move between the different levels constantly; they ‘level jump’ as they experience pedagogic events and develop pedagogic expertise. As an example, if a student does not understand a concept or area of knowledge, the values of the individual will work with their professional skills and understanding (personal growth) whilst also operating within the organisational and societal contexts to develop pedagogic solutions to aid understanding. The act of pedagogy is a complex interplay between these different levels and processes. Secondly, given the wide range of knowledge, skills, values and contexts inherent in the pedagogic environment, the development of teachers is emergent, and by extension, pedagogic literacy is an emergent process. Teachers’ developing expertise is more than the sum total of the constituent parts, it has extra value and meaning in its own right. However, pedagogic literacy as an emergent process is not deterministic, in other words emergence does not ensure positive change and expertise.

Over several future posts we’ll develop different aspects of pedagogic literacy to illustrate the ideas, concepts and processes which constitute the pedagogic network. Two limitations must be stressed immediately however. As suggested earlier, due to the incompressibility of pedagogic literacy any treatment can only hope to be a partial description, but is nonetheless useful for it. Secondly, the same problem exists in writing about this concept as Deleuze and Guattari (1987) had in writing The Thousand Plateaus, in that writing is a linear construct which is attempting to describe and explain a networked concept. Therefore, whilst we attempt to make links between ideas and posts, this cannot be exhaustive. However, one advantage in this is that we encourage anyone reading these posts to make links and networks of their own.