Rhizome (biology definition): a horizontal underground stem that sends out both shoots and roots. It may act as a storage organ in plants, especially when situated underground (Rhizome – Definition and Examples – Biology Online Dictionary).

Rhizomatic learning is an educational theory and approach that emphasizes the interconnected and non-linear nature of knowledge and learning. It draws inspiration from the concept of rhizomes, which are root structures in plants that grow horizontally and create a complex network of connections.

Rhizomatic learning was first introduced by the educational theorists Deleuze and Guattari in their book “A Thousand Plateaus: Capitalism and Schizophrenia,” published in 1980. They used the rhizome as a metaphor for understanding knowledge and learning as a decentralized, interconnected, and ever-evolving process.

Cormier argues that knowledge is created through the collaboration of many people who contribute to a particular field. This process of knowledge creation can be seen as a negotiation (Farrell, 2001). According to Brown and Adler (2008), online communities demonstrate the possibilities of participatory social learning, where knowledge is actively negotiated and explored in groups. Yet, social constructivist and connectivist pedagogies still rely on a fixed body of knowledge with a beginning and an end that can be verified and determined by a curriculum. In contrast, the concept of the rhizome metaphor is useful in dynamic curriculum development as knowledge is constantly changing and so might the curriculum itself. “Knowledge is changed to the extent that reality also moves and changes. . . . It’s not something stabilized, immobilized” (Horton & Freire, 1990, p. 101).

The rhizome metaphor suggests that knowledge is a dynamic and interconnected system. In this context, social learning practices are important for discovering knowledge through discussions and negotiations.

Cormier (2008) writes: “If knowledge is to be negotiated socially, then the idea of individual intellectual property must be renegotiated to reflect the process of acquisition and the output constructed by that process. What is needed is a model of knowledge acquisition that accounts for socially constructed, negotiated knowledge. In such a model, the community is not the path to understanding or accessing the curriculum; rather, the community is the curriculum.”

According to the concept of rhizomatic learning, knowledge is not a fixed and predetermined structure but rather a dynamic and continuously evolving network. It suggests that learning should focus on exploration, connectivity, and adaptability rather than rigid hierarchies and linear progression.

In rhizomatic learning, learners are encouraged to explore diverse sources of information, make connections between different ideas and perspectives, and actively participate in the co-creation of knowledge. The emphasis is on fostering critical thinking, collaboration, and the ability to navigate and contribute to complex and ever-changing knowledge landscapes.

Rhizomatic learning challenges traditional notions of education that are based on linear curricula, fixed syllabi, and predefined learning outcomes. Instead, it promotes a more flexible and learner-centered approach that embraces uncertainty, creativity, and the capacity to learn and adapt in a rapidly changing world.

Cormier (2008) states that “[k]nowledge seekers in cutting-edge fields are increasingly finding that ongoing appraisal of new developments is most effectively achieved through the participatory and negotiated experience of rhizomatic community engagement. Through involvement in multiple communities where new information is being assimilated and tested, educators can begin to apprehend the moving target that is knowledge in the modern learning environment.”

Culture, a concept foundational to anthropology, has been defined by notable scholars. Tylor, an English anthropologist, offered one of the earliest comprehensive definitions. In his influential work “Primitive Culture” (1871), Tylor defined culture as “that complex whole which includes knowledge, belief, art, law, morals, custom, and any other capabilities and habits acquired by man as a member of society.” Tylor’s definition underscores the broad scope of culture, encompassing various aspects of human society. Building upon Tylor’s work, Kluckhohn defines culture as “the shared patterns of behaviours and interactions, cognitive constructs, and affective understanding that are learned through socialisation” (Kluckhohn, 1952), emphasising the social nature of cultural transmission. Additionally, Evans-Pritchard views culture as “the total way of life of a people, the social legacy individuals acquire from their group” (Evans-Pritchard, 1951), highlighting culture’s comprehensive influence on social organisation, beliefs, customs, and material artefacts. Geertz, an influential anthropologist, employed the metaphor of a “thick description” and a “tapestry of meaning” to describe the intricate and layered nature of culture and social interactions. In his seminal work “The Interpretation of Cultures” (1973), Geertz emphasises the importance of understanding the deeper, symbolic meanings embedded within cultural practices and symbols, which collectively form a rich and complex tapestry of meaning within a certain context. These diverse definitions contribute to our understanding of culture as a multifaceted and evolving phenomenon.

Spierings (2023) defined “culture as a constantly evolving and interconnected system of knowledge, practices, and beliefs that spreads and grows in a non-linear, decentralised manner. Similar to the rhizome, which represents a root structure with multiple entry points and interconnected nodes, culture is characterised by its fluidity, adaptability, and absence of a fixed canon. It thrives through discursive interactions, negotiations, and participatory processes among individuals and communities, allowing for the continuous creation, transformation, and dissemination of knowledge across diverse contexts and perspectives. Interaction is a socio-cognitive process in which we not only consider the other person but also the surroundings and social situations. In this perspective, culture is not limited to specific domains but permeates all aspects of human existence, shaping social relationships, identities, values, and understandings of the world.”

The holomovement brings together the holistic principle of “undivided wholeness” with the idea that everything is in a state of process or becoming (David Bohm calls it the “universal flux”) and a dynamic interconnected process, a kind of art — a movement of fitting together — is what is universal, both in nature and in human activities, also called the ‘artamovement’, which he defines as the “movement of fitting”. The concept is presented most fully in Wholeness and the Implicate Order, published in 1980.

The boundaries of context might therefore be visible only in hindsight and therefore rootedness of curricular design practice can only occur dynamically in Shared Cultural Heritage in a “spirit of dialogue, [and] the ability to hold many points of view in suspension, along with a primary interest in the creation of common meaning” (Bohm, 1987). The future of education is to be as broad as the endlessness of points of view in suspension and “if the digital future is to be our home, then it is we who must make it” (Zuboff, 2014), but we must always be aware of its rhizomatic, infinite nature. It is “only on temporary platforms that we weave our tapestry of meaning” (Spierings, 2023). A 4-D model including time therefore is the only model we can use to mimic the classroom, what goes on there, and the node-vector principle the siplest didactic and pedagogical principle for a teacher to use in a practical way. After all, what goes on in the classroom is what matters.

In a classroom, “every utterance is context-bound, but every context is context-boundless” which means that every statement or utterance is influenced and shaped by its specific context, such as the speaker, the audience, and the social, cultural, and historical circumstances. However, the context itself is not limited or fixed, but rather extends infinitely, as it is connected to a network of other contexts and factors that can influence meaning and interpretation. In essence, while each utterance is situated within a specific context, the potential range of contexts that can affect its interpretation is limitless (Culler, 1997).

Seen in this way, the langugae acquisition process and instructional conversation (IC) might be considered as being at the heart of language teaching. According to Saunders and Goldenberg (2007), instructional conversation has the following components:

INSTRUCTIONAL ELEMENTS

  1. Thematic focus. The teacher selects a theme or idea to serve as a starting point for focusing the discussion and has a general plan for how the theme will unfold, including how to “chunk” the text to permit optimal exploration of the theme.
  2. Activation and use of background and relevant schemata. The teacher either “hooks into” or provides students with pertinent background knowledge and relevant schemata necessary for understanding a text. Background knowledge and schemata are then woven into the discussion that follows.
  3. Direct teaching. When necessary, the teacher provides direct teaching of a skill or concept.
  4. Promotion of more complex language and expression. The teacher elicits more extended student contributions by using a variety of elicitation techniques—invitations to expand (e.g., “Tell me more about that”), questions (e.g., “What do you mean?”), restatements (e.g., “In other words,”), and pauses.
  5. Elicitation of bases for statements or positions. The teacher promotes students’ use of text, pictures, and reasoning to support an argument or position. Without overwhelming students, the teacher probes for the bases of students’ statements, for example. “How do
    you know?” “What makes you think that?” “Show us where it says __.”

CONVERSATIONAL ELEMENTS

  1. Fewer “known-answer” questions. Much of the discussion centers on questions and answers for which there might be more than one correct answer.
  2. Responsivity to student contributions. In addition to having an initial plan and maintaining the focus and coherence of the discussion, the teacher is also responsive to students’ statements and the opportunities they provide.
  3. Connected discourse. The discussion is characterized by multiple, interactive, connected turns; succeeding utterances build on and extend previous ones.
  4. A challenging but nonthreatening atmosphere. The teacher creates a “zone of proximal development,” where a challenging atmosphere is balanced by a positive affective climate. The teacher is more collaborator than evaluator and creates an atmosphere that challenges students and allows them to negotiate and construct the meaning of the text.
  5. General participation, including self-selected turns. The teacher encourages general participation among students. The teacher does not hold exclusive right to determine who talks, and students are encouraged to volunteer or otherwise influence the selection of speaking turns. Topics are picked up, developed, elaborated.… Strategically, the teacher (or discussion leader) questions, prods, challenges, coaxes—or keeps quiet. He or she clarifies and instructs when necessary, but does so efficiently, without wasting time or words. The teacher assures that the discussion proceeds at an appropriate pace—neither too fast to prohibit the development of ideas, nor too slowly to maintain interest and momentum. The teacher knows when to bear down and draw out a student’s ideas and when to ease up, allowing thought and reflection to take over. Perhaps most important, the teacher manages to keep everyone engaged in a substantive and extended conversation, weaving individual participants’ comments into a larger tapestry of meaning. (Goldenberg, 1991, pp. 3–4)

These concepts relate to dynamics in various fields such as sociology, cultural and literary studies, psychology, language studies, physics, biology, systems theory, and complexity science. They highlight the dynamic nature of systems, the interactions between their components, and the patterns that arise from their behavior over time. These additional concepts shed light on the dynamics of systems, including their ability to adapt, exhibit emergent properties, undergo transitions, and interact within complex networks. They capture various aspects of dynamic systems and provide valuable insights into their behavior, organisation, and evolution. highlighting the influence of feedback, coevolution, and sensitivity, as well as phenomena like fractals and path dependence. They delve into the complex interplay between stability and change, adaptation and inertia, and the capacity of systems to self-organize and respond to perturbations in their environment. They further explore the dynamics of complex systems, addressing topics such as emergence, resilience, chaos, synchronization, and percolation. They also delve into the role of memory, hierarchy, and sensitivity analysis in understanding and analyzing system behavior. As Cormier (2008) writes: “The rhizome operates by variation, expansion, conquest, capture, offshoots.”

  1. Emergence: The phenomenon where complex systems or patterns arise from simple interactions or components.
  2. Feedback: The process of information or signals being returned to a system, affecting its behavior or output.
  3. Adaptation: The ability of a system or organism to adjust and change in response to its environment or circumstances.
  4. Equilibrium: A state of balance or stability in a system, where opposing forces or influences are equal.
  5. Resilience: The capacity of a system to recover or adapt in the face of disturbances or changes.
  6. Interdependence: The mutual reliance and interconnectedness between different elements or parts of a system.
  7. Self-organisation: The spontaneous formation of order or patterns within a system, without external control.
  8. Nonlinearity: The property where a system’s output or behavior does not vary proportionally with its inputs or causes.
  9. Hierarchy: A structure or organisation in which elements or components are ranked or arranged in levels or tiers.
  10. Attractor: A stable state or pattern toward which a dynamic system tends to evolve or be drawn.
  11. Chaos: The state of apparent randomness or unpredictability in a system, often associated with complex behavior and sensitive dependence on initial conditions.
  12. Self-regulation: The ability of a system to maintain stability or balance through internal mechanisms or processes.
  13. Dissipative structures: Dynamic systems that maintain their organisation and functionality by exchanging energy and matter with their environment.
  14. Phase transition: The abrupt or gradual change of a system from one state or phase to another, often associated with critical points or thresholds.
  15. Synchronization: The alignment or coordination of rhythmic or oscillatory patterns in different components of a system.
  16. Perturbation: A disturbance or disruption introduced into a system, which can lead to changes in its behavior or dynamics.
  17. Bifurcation: The splitting or divergence of a system’s trajectory into multiple possible paths or outcomes.
  18. Coevolution: The reciprocal influence and adaptation between two or more interacting systems or entities.
  19. Oscillation: The periodic or rhythmic motion or variation of a system around a central point or equilibrium.
  20. Fractal: A complex geometric or mathematical pattern that exhibits self-similarity at different scales or levels
  21. Network: A system or structure composed of interconnected elements or nodes, allowing for the flow of information, resources, or interactions.
  22. Feedback loop: A self-regulating mechanism in a system where the output or effects of a process are fed back into the system, influencing its future behavior.
  23. Instability: The condition of a system that is prone to change or disruption, often associated with sensitivity to initial conditions or external influences.
  24. Disequilibrium: A state in which a system is not in balance or equilibrium, characterized by ongoing changes and adjustments.
  25. Self-assembly: The spontaneous organisation or formation of a system or structure through local interactions or rules, without external intervention.
  26. Convergence: The tendency of different elements or processes in a system to come together or move toward a common point or pattern.
  27. Divergence: The spreading apart or differentiation of elements or processes in a system, leading to diverse outcomes or trajectories.
  28. Hysteresis: The dependence of a system’s behaviour on its history or past conditions, where its response may differ depending on previous states.
  29. Coherence: The state of a system or its components being synchronized, aligned, or in harmony, often resulting in enhanced performance or efficiency.
  30. Phase space: A multidimensional space that represents all possible states or configurations of a system, allowing for the visualisation and analysis of its dynamics.
  31. Non-equilibrium: A condition in which a system is far from or continuously transitioning between equilibrium states, characterised by ongoing activity and change.
  32. Self-organisation: The spontaneous emergence of order or structure in a system, arising from local interactions or processes without external control.
  33. Stochasticity: The presence of randomness or probabilistic behavior in a system, introducing variability and unpredictability into its dynamics.
  34. Synergy: The cooperative interaction or combined effect of different elements or processes in a system, resulting in a greater outcome than the sum of their individual contributions.
  35. Robustness: The ability of a system to maintain its stability or function even in the presence of perturbations, variability, or uncertainties.
  36. Dissipation: The process by which a system loses or dissipates energy, resulting in changes in its dynamics or state.
  37. Self-optimisation: The ability of a system to autonomously adjust or optimise its performance or behavior to maximise desired outcomes.
  38. Path dependence: The influence of previous events or decisions on the current trajectory or development of a system, leading to a limited range of possible future outcomes.
  39. Sensitive dependence on initial conditions: The property of some dynamic systems where small changes in initial conditions can lead to significantly different outcomes or trajectories.
  40. Robust decision-making: The process of making choices or decisions that are resilient and effective across a range of possible scenarios or conditions, considering uncertainties and risks.
  41. Equifinality: The principle that different initial states or paths can lead to the same outcome or final state in a system, suggesting multiple ways to achieve a particular result.
  42. Resilience: The ability of a system to absorb disturbances, adapt, and recover to maintain its structure, function, or performance in the face of changing conditions or external shocks.
  43. Self-regulation: The capacity of a system to monitor and adjust its own behavior or processes to maintain stability, balance, or desired states.
  44. Threshold: The point or level at which a system undergoes a significant qualitative change or transition in its behavior, often leading to new states or properties.
  45. Synchronisation: The coordination or alignment of the behaviour, rhythms, or dynamics of different components or entities in a system, resulting in collective patterns or coherence.
  46. Percolation: The process by which information, influence, or phenomena spread or propagate through a network or system, often involving a critical threshold or connectivity.
  47. Oscillation: The repetitive or cyclic motion, fluctuation, or variation of a system’s state or variables, often characterised by regular patterns or periodic behavior.
  48. Power law: A mathematical relationship or distribution that describes the frequency or magnitude of events or phenomena in a system, where the occurrence of rare or extreme events is more likely than in a normal distribution.
  49. Self-similarity: The property of a system or pattern that exhibits similar structures, forms, or properties at different scales or levels of observation.
  50. Nonlinearity: The property of a system where the relationship between inputs and outputs is not proportional or additive, often resulting in complex and non-predictable behaviour.
  51. Network effects: The phenomenon where the value, influence, or utility of a system or platform increases as more participants or nodes join or interact with it, leading to exponential growth or benefits.
  52. Cascading effects: The propagation or amplification of effects or changes through a system, where the impact of an initial event or disruption spreads and influences subsequent events or components.
  53. Phase transition: The abrupt or qualitative change in the properties or behavior of a system as it crosses a critical point or threshold, resulting in the emergence of new states or phenomena.
  54. Attractor: A stable state, pattern, or configuration toward which a dynamic system tends to converge or settle over time, often associated with certain attractor basins or regions in phase space.
  55. Self-assembly: The process by which components or entities in a system autonomously organise or arrange themselves into ordered structures or patterns, driven by local interactions or rules.
  56. Dissipative structures: Complex, self-organising patterns or structures that emerge in open systems far from equilibrium, sustained by a continuous flow of energy or matter through the system.
  57. Adaptation: The process of adjusting, modifying, or changing the behaviour, structure, or characteristics of a system to better fit or respond to its environment or changing conditions.
  58. Interdependence: The mutual reliance or interconnectedness of different components, entities, or systems, where changes or interactions in one part can affect the behavior or outcomes of others.
  59. Hysteresis: The phenomenon where the current state or behaviour of a system is influenced by its past states or history, causing a delay or lag in response to changing conditions.
  60. Feedback: The process by which information or signals from the output or result of a system are fed back to the input, influencing or modifying the system’s behaviour or dynamics.
  61. Coevolution: The mutual influence or reciprocal adaptation between two or more interdependent systems, where changes in one system can lead to adaptations or responses in the other system.
  62. Fractal: A geometric pattern or structure that exhibits self-similarity and repetition at different scales or levels of magnification, characterised by intricate and detailed structures.
  63. Disequilibrium: A state of imbalance or instability in a system, where the current conditions or variables deviate from the system’s optimal or desired state.
  64. Non-equilibrium: The condition of a system that is far from a state of thermodynamic equilibrium, often associated with dynamic, dissipative, and self-organising systems.
  65. Sensitivity: The degree of responsiveness or susceptibility of a system to changes or perturbations in its environment or inputs, indicating its capacity to detect and react to external stimuli.
  66. Inertia: The tendency of a system to resist changes in its state or motion, maintaining its current behaviour or trajectory unless acted upon by external forces.
  67. Bifurcation: The point or event in a system’s dynamics where it splits into different branches or alternative paths, leading to the emergence of multiple states or behaviours.
  68. Self-organisation: The spontaneous emergence of order, structure, or patterns in a system through local interactions, without the need for external control or central coordination.
  69. Robustness: The ability of a system to maintain its stability, function, or performance in the face of internal or external disturbances, variations, or uncertainties.
  70. Path dependence: The idea that the current state or trajectory of a system is influenced by its previous history or the specific path it has followed, leading to outcomes that are not easily reversible.
  71. Perturbation: A temporary or sudden disturbance or change in a system, often used to study its response or sensitivity to external inputs or shocks.
  72. Adaptability: The capacity of a system to adjust, modify, or reconfigure its structure, behavior, or strategies in response to changing conditions or new challenges.
  73. Robustness: The ability of a system to resist or recover from failures, errors, or disruptions, maintaining its functionality or performance even under adverse conditions.
  74. Emergence: The phenomenon where new properties, behaviors, or patterns arise from the interactions and collective behaviour of simpler components or entities within a complex system.
  75. Resilience: The ability of a system to absorb shocks, disturbances, or perturbations and recover its original state or adapt to a new state while maintaining its essential functions or structure.
  76. Network dynamics: The study of how networks of interconnected elements or nodes change and evolve over time, considering factors such as connectivity, information flow, and influence propagation.
  77. Chaos: The unpredictable behavior exhibited by certain deterministic systems, characterized by extreme sensitivity to initial conditions and the absence of long-term predictability.
  78. Phase transition: A sudden qualitative change in the behaviour or properties of a system as it crosses a critical threshold, leading to a transition from one phase or state to another.
  79. Self-assembly: The process by which individual components or entities autonomously come together and organise themselves into a larger, more complex structure or pattern.
  80. Synchronization: The coordination or alignment of rhythmic or periodic behaviours among different elements or subsystems within a system, leading to collective behavior or emergent patterns.
  81. Attractor: A stable state or pattern towards which a dynamic system tends to converge or settle, representing an equilibrium or preferred behaviour in its phase space.
  82. Feedback loop: A circular relationship or causal chain in which the output or effects of a system’s behaviour are fed back as input, influencing subsequent iterations of the system’s dynamics.
  83. Percolation: The process by which a substance or influence spreads through a network or medium, gradually connecting different components or regions and leading to system-wide changes.
  84. Dissipative structures: Self-organising patterns or structures that emerge and are sustained in systems that are far from equilibrium, characterised by the continuous exchange of energy and matter with their environment.
  85. Hierarchy: A system or organization characterised by nested levels or tiers, where each level has different properties, functions, or scales of operation, contributing to the overall dynamics and functionality.
  86. Sensitivity analysis: A method for quantifying and understanding the sensitivity of a system’s behaviour or outputs to variations or uncertainties in its inputs or parameters, providing insights into its robustness and stability.
  87. Memory: The capacity of a system to retain or store information about past states, events, or experiences, influencing its future behaviour, decision-making, or adaptation.
  88. Nonlinear dynamics: The study of systems and processes in which the relationship between inputs and outputs is not proportional or additive, often characterised by complex, non-sequential, or non-reversible behaviours.

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