On the Three or Four Problems of Connectivism

Marc Clarà and Elena Barberà have advanced at least two articles now where they argue that there are three problems with connectivism. One of these is Learning online: massive open online courses (MOOCs), connectivism, and cultural psychology (Distance Education, 34:1, 129-136). The other, behind a paywall, is Three problems with the connectivist conception of learning (Journal of Computer Assisted Learning. DOI: 10.1111/jcal.12040).

Matthias Melcher was good enough to point out some of the problems with the latter article, including some noteworthy misquotations. In this post I would like to respond to the substantive criticisms, of which there are four:

• connectivist ideas have been widely and rapidly disseminated, but without the academic control procedures which the development of a learning theory needs to ensure rigour and systematicity in its postulates
• the 'learning paradox.' This paradox, first posed by Socrates (Plato, 2002), can be applied to connectivism as follows: How do you recognize a pattern if you do not already know that a specific configuration of connections is a pattern?
• connectivism underconceptualizes interaction and dialogue, by understanding it as a learner’s connection to a human node in the network.
• connectivism is unable to explain concept development... if a concept consists of a specific pattern of associations, how can it be explained that the concept develops but the pattern of associations remains the same?

To address the first issue, it seems to me there are two ways to respond to such a criticism: first, to embrace the requirement, but then to point out that it has been met; and second, to reject the requirement. I would like to do both.

Specifically, I would argue that literature related to connectivism has undergone peer review. According to Google Scholar I have an H-index of 22 and i10-index of 31. This listing does not include my work published in academic books (for example, 'The Role of Open Educational Resources in Personal Learning', in Open Educational Resources: Innovation, Research and Practice, published this year by Athabasca University Press). It's true that I mistreat my publications terribly, and that I should maintain my publications page a lot more carefully, but it's false to say that my work has not been subject to academic scrutiny.

But I would also argue that the requirement that this work be subject to (the traditional) peer review process is misplaced. It is arguable that this process could be replaced with a much more effective process of post-publication review. The idea is that academic and other works are published openly, and then weighed not by an anonymous panel of two or three referees, but by the whole academic community. As Jane Hunter writes, "Open, post-publication refereeing removes barriers for readers and authors alike, and it refocuses the role of peer review from, at its worst, a behind-the-scenes variety of censorship to, at its best, the process of expert criticism and advice."

Finally, there is the undercurrent to the authors' remarks to the effect that connectivism would be in some important way different if it were subject to the peer review process, to the effect that it would ensure rigour and systematicity in its postulates. This is precisely one of the reasons I am cautious (if not to say outright sceptical) of the process of review and revision in academic journals. While I seek clarity and precision in all I write, I do not see connectivism (or any other theory) as a set of postulates, entailments and confirmations. Systematicity is for robots.

Now let us address the second issue, specifically, the suggestion that you cannot recognize a pattern if you do not already know that a specific configuration of connections is a pattern. In 'Learning Online' Clarà and Barberà tie it to a serious issue specific to connectivism: "This theoretical problem causes an important learning problem in cMOOCs: Many learners, especially those who do not have high self-regulation skills, feel lost and without any direction and support.

The argument as originally posed in Meno and elsewhere in Plato's writings does not attach to patterns specifically but to the forms of matter (such as, say, a triangle), colours, and even intangible properties such as justice and virtue. How could we recognize them, if we are not taught? But if they are not taught, do they cease to exist? Obviously not, therefore, the forms, colours, justice, virtue, and everything else we perceive must exist in what we have come to call a 'platonic' or ideal state. 

In the 'Three Problems' paper Clarà and Barberà argue there are "two basic solutions to the
paradox":

• Either, first, to follow Kant, and accept that we have access to these concepts innately, as argued recent theorists such as Jerry Fodor and Jean Piaget. 
• Or second, to follow Hegel, and "accept that a representational means can be shared by two or more people, so they can use it together." Thus we reach Vygotsky's zone of proximal development, based on the idea that "while one of the participants in the agency may not be able to use the means on their own, they are able to use it in the joint activity, in collaboration."

This statement of the dilemma may appear intuitive, because it seems to suggest that we must learn of a concept internally or externally. That does seem to cover all the options.

Philosophy, though, does not reduce to a choice between Kant and Hegel (thank goodness). The two options provided by Clarà and Barberà can be supplemented with many more possibilities. I will adduce two, one internal, and one external.

• Internally, we can appear to examples of self-organization. Simple systems composed of interacting entities can form and reform into patterns. Consider, for example, the computational model called 'the game of life', which shows how complexity can develop out of simple rules.
• Externally, we can learn through direct perception or recognition. For example, consider J.J. Gibson's theory of direct perception."The neural inputs of a perceptual system are already organized and therefore do not have to have an organization imposed upon them."

The point here is that there are many ways for concepts to arise in the mind; they don't need to be delivered fully formed either by innate knowledge or through shared representations. This is a good thing, for if we learned of concepts only through the two mechanisms proposed by Clarà and Barberà, then we would be faced with a problem of infinite regression, for there would be no means through which these concepts could be discovered in the first place.

In connectivism we talk quite a bit about how (what Clarà and Barberà call 'concepts') arise in the mind (and in networks generally). Learning theories, ranging from simple Hebbian mechanism to complex Boltzmann engines, create and modify connections between entities. There is a vast literature devoted to learning rules. I think we can regard 'the learning paradox' as definitively solved.

The claim made by connectivism in this regard is that learning is a process of pattern recognition, nothing more or less. The warning inherent in connectivist theory is that there is no apriori privileged set or type of pattern that may be learned: so while you may think that you are presenting shapes to learners, they may be learning to recognize colours. And that any pattern inherent in your teaching - including bad habits, prejudice, whatever - will also be learned by the people watching you.

Finally - to be clear - talk about "recognizing" a pattern does not involve some homunculus inside our head doing some conceptual work. The phenomenon of pattern recognition is a well-known property of neural networks. The point I make is epistemological: what makes something a 'pattern' is the fact that it is recognized by neural nets. There is no apriori set of entities, 'patterns' (or 'concepts', or whatever) that must somehow acquired and placed in the mind.

The third issue raised is based on the contention that connectivism underconceptualizes interaction and dialogue.

To set up this discussion, Clarà and Barberà first offer a simplified action in a network, then offer the following critique (as quoted from the Three Problems paper):

• [first] the connectivist scheme of the network does not permit any (human) node to which the learner connects to be conceptualized as part of learning but not part of the connective pattern of which knowledge consists,
• [second]  a binomial conceptualization is too simple to characterize the complexity of connection states in a network, especially if human nodes (interactions) are involved, [and]
• [third] the problem is not only the simplicity involved in characterizing the state of interaction, but the very fact that interaction is thought of as a state.

In all of these it is apparent that Clarà and Barberà are confusing the concept of a connection with the concept of an interaction. The two are very different.

A connection is a state. Roughly speaking, it is a communications channel that exists between two entities such that a change in the state of one entity can result in a change in the state of the other entity. Usually, we depict these channels as physical, for example, the axons of a neuron, or a telephone wire carrying signals.

Connections can be extremely complex; there is no requirement whatsoever that they be two-state on-off types of things. Connection strength can vary, the frequency of signals can vary, the nature of signals can vary, there may be multiple strands and different types of connection between two nodes (hence, I can send George an email and a Tweet). The nature of the states of the nodes can be variable as well. A signal from one node to another may have a cumulative effect, triggering a reaction only after a tipping point is reached, for example.

An interaction is the actual event where a change of state in one entity takes place with the result that a change of state in the second entity takes place. We may also think of an interaction as a mass noun, referring to a set or a series of such changes of states. Again, we usually think of an interaction as something physical, for example, a signal sent down a communications channel.

So there's no sense in which connections and interactions are simple, but that does not address the problem posed by Clarà and Barberà, because there is something else they're after. We have to tease it out a bit.

When we look at the first objection, "as part of learning but not part of the connective pattern of which knowledge consists," what they appear to be appealing to is the lack in connectivist theories of learning of a sense of aboutness. When one person teaches another person about France, we interact only with the other person, and not with France. But in learning, we are not learning about the other person, but about France.

So the criticism is essentially that connectivism doesn't have a built-in semiotics. It doesn't have a sense in which a communication between two entities is about a third entity. And it's true that representation in communication doesn't work this way in connectivism. Rather, connectivism works according to two principles: direct representation, and distributed representation.

• Direct representation is the idea that the signal is its own message (think of it as a corollary to Gibson's direct perception). We can think of this along the lines of the concept of content addressable memory in computer science. The message is its own content. True, we as a sender may intend the message to refer to or represent some object or entity, but what is in fact received is only the sentence itself, which must carry all its representational content with it.

• Distributed representation is concepts (for lack of a better work) are stored not as single entities in the mind, but as sets of connections between entities, so they exist not just in one place, but in many places. What's significant here is that the same set of connections is used to store not one but many concepts (indeed, all concepts). So when the set of connections defining one concept is changed, so also is the set of connections defining many other concepts.

The combination of direct representation and distributed representation together do the same job that semiotics does: it explains how we can learn one thing through reference to another. A person says the word 'Paris' to me; the sound of this word stimulates a part of my neural net, initially, that part associated with the word 'Paris' but ultimately, that part associated with a variety of other concepts ('City', 'France', etc.) all of which are composed (partially) of the same connections.

Communication and interactivity are useful in learning because they enable us to make connection s between entities we might not have made through direct experience. A person may never visit Paris in a lifetime, and no that the Louvre is located in Paris only through the repeated association of 'Louvre' and 'Paris' in sentences uttered by others.

The claim made by connectivism is that communication is non-semantical. Or as McLuhan would say: the medium is the message. It doesn't 'stand for' something else; it is what is being communicated. The warning in connectivism is this: we cannot assume that the person receiving the message embodies the same intent (the same mental world of objects and concepts and ideas) as the person sending it. Communication is a complex process because, in order for anything to (if you will) 'mean' anything, a great deal of background needs to be in place. So much so, in fact, that it's doubtful that any two people ever mean exactly the same thing by any two instances of the same word.

We won't say the question of meaning and messaging are definitely solved. But there is certainly a story here; connectivism is not silent on the issue, as Clarà and Barberà suggest, but makes some assertions that can (and should) be investigated and empirically tested.

Let me now turn to the fourth issues, which is essentially, that connectivism cannot explain concept development. "If a concept consists of a specific pattern of associations, how can it be explained that the concept develops but the pattern of associations remains the same?"

For example, write Clarà and Barberà, consider "Piaget’s work on the matter in question, in which he established four basic stages, the sensorimotor stage, the preoperational stage, the concrete operational stage and the formal operational stage."

In the first instance, I would respond that Clarà and Barberà have confused naming with identity. Their question is analogous to asking, "how can you explain how a river develops, and is yet the same river?" For example, they might expand, "we can identify the tributary stage, the feeder stage, the meandering stage, and the delta stage."

Looking more intently at their objection, we can see the problem built into the formulation: when they state that "a concept consists of a specific pattern of associations" they suggest that it can never change. It is as though a 'river' were defined as the water in it at any given point in time, which while strictly true (for it would not be a river without the water) is nonetheless a definition of 'river' that would be unworkable.

But there is nothing in connectivism that asserts that a concept consists of a specific pattern of associations. Quite the opposite. What we consider a 'concept' is instantiated in one person by means of a completely different set of associations than in another person, and in that person the same concept may be instantiated by changing associations over time. What makes a set of associations, say, the concept 'Paris' is simply (and only) the fact that it is this set of connections that is activated when the person hears or reads the word 'Paris' (or visits the city, etc).

So how does our understanding of the world evolve over time? In the 'Three Problems' paper, Clarà and Barberà offer three alternatives (and again I quote): either

• concept development occurs because of the biological maturation of computational structures, [or]
• some processes are maturational, such as decentering, and others are educational, such as equilibration, [or]
• learning drives or causes development, so that learning in a ZPD becomes development when psychological functions become autonomous.

And they write, "If a concept is a set of associative connections, how can it be explained that the psychological nature of the concept changes but the pattern of the associative connections
of which the concept consists does not?"

The simple explanation for concept change is plasticity. This is the phenomenon whereby the nature and number of neural connections changes over time as a consequence of experience. But while explaining conceptual change, plasticity by itself doesn't explain what Clarà and Barberà are trying to describe.

Their concern is more metacognitive. It has to do with the attitudes and perspectives surrounding a concept, rather than the concept itself. This comes out when they describe a person's relation to their family. "the concept is not the same when I am 4 as it is when I am 20; psychologically, it functions in a very different way." Note that this isn't simply a case of the family changing; the family may grow by several more children and still be the same family, but that's not the problem. Rather, it has to do with the role the concept plays in the person's life, and consequently, their varying attitude toward it.

Having made this observation, it becomes evident that the three alternatives offered by Clarà and Barberà are all unattractive. What are the causal mechanisms that lead one to regard a family from a sensorimotor perspective when young, and from an operational perspective when older? Indeed, what does that even mean?

But connectivism does explain these things, and it does so in a manner that does not leave us wondering about the underlying causal structures. Concepts evolve because concepts do not exist in isolation in the mind; they are interwoven with other concepts. The concept itself may be entwined with one set of associations at a younger age, and a very different set of associations at an older age, so the concept's role changes - it is implicated in different thoughts, different ideas, different actions.

The claim made by connectivism is that concepts are plastic; that the associations implicated in a concept at one time will be different from those at another time, as the entire network of connections grows and changes. The warning offered by connectivism is that these changes inform our own understanding as well as our students, so that (for example) what is intuitive and obvious to us, is murky and mysterious to another, or what is important and urgent to them may be seen as trivial and irrelevant to us. And further, that while this represents change, it does not necessarily represent progress or development.

To wrap up, Clarà and Barberà conclude their paper with some surprising assertions. These are worth commenting on briefly.

First, they write, the problems "should warn scholars and educators against uncritically assuming the theoretical postulates of connectivism, and encourages the search for a stronger theory of learning (which does not necessarily mean a completely new theory) to explain and foster network based learning."

Nowhere is it asserted that anyone should uncritically "assume the theoretical postulates of connectivism." Quite the opposite; it is iterated on numerous occasions that these are offered tentatively, that they are subject to empirical verification, and that they should be questioned and challenged. Connectiovism is not a religion; it requires neither faith nor belief.

If by "stronger" they mean "better", then if such a theory is found, then by all means people should embrace it. But researchers should be cautioned against embracing a theory simply because it makes wider or more sweeping explanatory claims. "The devil made me do it" is a theory that is much stronger than connectivity, explaining as it does all evil in the world, but it would serve poorly as a basis for learning research. The parameters for explanatory success are well-known, and the maximization of parsimony is only one such.

Second, they write, "Downes’s four defining characteristics of a MOOC (autonomy, connectivity, diversity and openness) and the eight principles proposed by Siemens(2005a) are pedagogical in nature and fully assumable by a large number of learning theories."

Nowhere in connectivism is this denied. There is no requirement for one theory to be completely different from its predecessors; that would be an odd (and inconsistent) view of science and research. Indeed, it should be clear that the four principles I describe were borrowed liberally from a talk by Charles Vest in 2005; he was describing the principles for the success of the American university system, and I employed the same terminology for networks. It is also worth nothing that some of these are also employed by James Surowiecki in The Wisdom of Crowds.

They cite a number of places where some of these concepts arise, and specifically reference Ivan Illich, and then say, "Connectivism emerged later as an attempt to theoretically explain why and how those principles work." While Siemens can speak for himself, I can only say that my own motivations for pursuing this line of thought had nothing to do with Ivan Illich. This is not to say I do not respect his work tremendously; I do. But my motivations and foundations can be seen quite clearly in my PhD dissertation proposal, and Illich is nowhere to be seen in it.

Finally, they argue, "MOOCs and their pedagogical principles should therefore be regarded as an object of study, independent of connectivism, which, in turn, should be regarded as an
approach (one among others) that tries to explain what happens in a MOOC."

People should feel to stuidy MOOCs however they wish. It is a matter of empirical fact that MOOCs have evolved beyond their original roots as instantiations of connectivist theory; many of them (for example, the video-and-test offerings found in Coursera) are developed along explicitly instructivist lines. Suggesting MOOCs should only be understood from a connectivist perspective makes no conceptual or empirical sense, and nobody would argue for it.