Chaos Theory, Fractals, Knowledge and Learning – Part 1

This post is devoted to explore and reflect on Chaos Theory, Fractals, Knowledge and Learning.

How to describe knowledge and learning at this digital age?

One way is to describe knowledge as a network phenomena, under Connectivism.

How is learning achieved in MOOCs?

If people want to learn simple factual information (and content and procedural knowledge), best practice, go to school, or attend the xMOOCs.  In this xMOOC movement:

The potential is boundless, according to some educational specialists, they see it as a way of providing students in the developing world with access to the international educational ladder.

But while they also allow students to interact with each other, is this online experience a step too far and is there an opportunity for universities to try more for a mix of teaching methods?

If people want to learn complex, emergent knowledge and practice, they could join the online community, and immerse in the open, digital, vibrant cMOOCs.  In a connectivist MOOC, the best interactive lectures are un-lecture (through shifting preaching or “one-way lecturing” to dialogues, critiques, and conversation), and best learning comes from networked learning action, reflection cycle, with focus on metacognition integrated and embedded in each learning experience. Best practice is contingent to the actual needs of the engaging agents, to collaborate and cooperate in solving problems, where each one’s interests are catered for.  This is where complex pattern could be boiled down to simple heuristics, easy to understand and mutually agreeable language patterns.

What I have been thinking of is the use of Fractals in understanding knowledge and learning.

If we were to conceive knowledge as conversation, & that a set of connections (the engagement), I could also interpret this as a development like the fractals, where such fractal would repeat itself but its shape would be based on initial conditions of agents, with “spirals” & re-birth or re-configuration of different fractals (patterns) emerging in different forms.  Such fractal formation would be dependent on feedback and looping back into other posts, via the linkage, and thus could be amplified or dampened as the pattern developed.

Another application of fractals would be to conceive the footprint of emergence as a pattern that relates to fractal development in emergent knowledge and learning development.

The role of organising emergent learning ‘scapes is an engaged curatorial role, rather than a teaching, facilitating, or even moderating one. Curating the topography of learning requires the course convenor to step back at times; it not only invites but requires self-organization, self-motivation, and creativity.

Refer to Learning across Cultures (R Williams, J Mackness, S Gumtau –

Emergent learning is likely to occur when many self-organising agents interact frequently and openly, with considerable degrees of freedom, but within specific constraints; no individual can see the whole picture; and agents and system co-evolve (3).

The properties of emergent learning – based on interaction would then form the basis of fractals, where such interactions repeat in various forms, as in the case of rhizomatic learning, or in connectivist learning all based on interaction and connectivity.


15 thoughts on “Chaos Theory, Fractals, Knowledge and Learning – Part 1

  1. In my previous post:
    I see MOOCs as the perfect platform to illustrate the importance of “the instructors or facilitators must dampen negative emergence and amplify positive emergence” under an emergent learning environment (Williams et al, 2011).

    If we were to analyse the interactions among Twitterers, what sort of negative constraints would need to be defined? Up till now, I don’t think there are any rules set up on Twitter sharing and conversation yet. The trolling and plagiarism behavior might be some of the negative constraints that one would like to define, as they would likely destroy the cooperative and collaborative spirit of the networkers or practitioners of the COPs.

    Trolling and cheating behavior in MOOCs are surely annoying.

    Trolling in Twitter happened when those followers on Twitter make intimidating remarks or simply flaming the conversations on a strong and destructive emotional level.

  2. ok, I think I understand now. Specific constraints are NOT required for emergent learning to occur. Constraints are required when emergent learning might violate the norms of the instructors or facilitators. So nothing really changes with a MOOC; classroom control is still required by the instructor.

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  4. MOOCs are perfect examples of fractal learning and the attempt of making sense through the chaos of knowledge; or rather, applying knowing and knowledge in a chaotic world. But then again, I am biased – I tend to see learning and knowledge as fractals 🙂

  5. @Ulop. In a typical classroom environment, especially one where the instructor and facilitator is responsible for the management of the classroom discipline, there is a need to establish ground rules, and direction upon which the learning outcomes could be achieved, by exercising appropriate controls to maintain discipline and order. That seems to be challenging though, in open space and forum, as in MOOCs, when certain behavior (like trolling, flaming, accusing and negative criticisms based on personal attacks, or cheating, plagiarism) occurs, or being perceived as a threat to the learning conversation or activity.

    Would these also be a form of emergent learning? Yes, but this would also lead to unpredictable consequences, chaos, with some participants feeling confused, upset, and or leaving the course, or lost in the edge of chaos. The order out of chaos could be restored simply by constraining those spammers or trollers from interfering the conversation or learning activities. The negative emergence is then dampened using a behavioral approach, though the tool used could be “troll filters”, either manually, or automatically, or the typical counselling or conflict resolution approach.

    “So nothing really changes with a MOOC; classroom control is still required by the instructor.” If MOOC is treated as a classroom, yes, but if it is an open platform that goes beyond the classroom, then I reckon the classroom control may not be easily exercised, as witnessed in lots of MOOCs.

    The different voices and “noises” arising out of the discourse on xMOOCs could be viewed as wonderful examples of how different people would behave under an open learning environment. Without some forms of disruption (if MOOC is perceived as an innovative disruption), there wouldn’t be much changes to the traditional practices of classroom management. Does it explain why some institutions insist on formal teaching, with more and more structured course planning, based on risk management approaches? Not too many in the authorities would like to see a chaotic education environment, as that doesn’t always lead to stability in “best-practice” learning and good educational experience.

    I don’t see much researches carried out on this extreme behaviors, at PhD level, as I think most teaching schools (especially behavioral schools) have been teaching all these using a closed approach – with rules and regulations to ensure compliance with education policies. The use of Young People and Child Protection Acts and regulations, Anti-discrimination Acts and regulations, and Social Media Policies are just some of the relevant regulations based on laws of society. Could we consider such rules and regulations as fractals which are also repeating in smaller forms – in communities, schools, classroom, etc?

  6. @Ana. That’s resonating. We all see patterns of fractals, in both artificial and natural world, just perceived differently under different lens. The educational landscape is changing rapidly with these MOOCs and no one could predict or foresee what these would lead to. But in hindsight, they are all fractals embedded in fractals of change and transformation, in the evolution of education, and history 🙂

  7. Well, you can them fractals if you like, but I’m not what purpose that serves. Rules and regulations are social constructs, but that doesn’t necessarily equate to naturally occurring self-replicating patterns. does it?

    I thought that chaotic activity was an ingredient of emergent learning? Is it the amount of chaos that you think should be controlled in your instructivist system? Or do you wish to eliminate chaos entirely?

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  9. Under an institutional framework, yes. Under an open education platform like xMOOC, the professor or his/her TA would likely moderate the discussion forum. So, that’s why prescriptive learning where only “formal canonical knowledge” is accepted as the formal response to questions. Take a look the rubrics – on assessment of both discussion forum and peer -reviewed assignments. They all would likely encourage positive emergent learning, not negative ones. John

  10. Hi Ulop,
    May I share my previous post here? Instead of relying on an instructivist approach towards teaching in MOOCs, here I have discussed different pedagogies and learning strategies that would achieve learning in MOOCs.

    Here is part of it:

    The real revolution that we might anticipate in education would be a paradigm shift where education is about encouraging and supporting learners to develop themselves into creative, autonomous, independent and critical learners who could initiate their own questions, and to explore and implement their own solutions to their questions, in study, and life.

    This would then truly transform education, based on an inverted pyramid of education structure, where learners are situated at the pinnacle of their learning. This is premised on that “learners who find the answers for themselves, retain it better than if they’re told the answer.” as reinforced by Sugata.

    Indeed, this is also underpinned in the wisdom that learners would learn better when they are active in their learning journey, based on authentic learning.

    Being knowledgeable is about knowing the stuff. Knowledge able is being able to find, sort, analyse, criticize and able to create and share new information and knowledge. (Michael Wesch)

    Future education and learning is no longer restricted to the “learning of facts and knowledge out there in the books, artifacts, information networks, and internet”. Any one who could access the internet, webs and social networks, Google and wikipedia etc. could easily get the answers and solutions to their basic questions. Learning is more about knowing what questions are important to the learners, and searching for responses to those questions in the quest of knowledge, and the creation of new knowledge and wisdom in a world of change. It is the critical lenses that learners wear that would allow them to perceive the world differently, and to change, adapt and transform where necessary in their pursuit of knowledge and upgrade of skills and abilities.

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