Monday, April 21, 2014

Connectivism as Learning Theory

I think the students in the Building Online Collaborative Environments Course has an almost impossible task. Here is their effort to prove that connectivism is a learning theory.
"Connectivism has a direct impact on education and teaching as it works as a learning theory. Connectivism asserts that learning in the 21st century has changed because of technology, and therefore, the way in which we learn has changed, too.

"Not too long ago, school was a place where students memorized vocabulary and facts. They sat in desks, read from a textbook, and completed worksheets. Now, memorization is not as prevalent because students can just “Google it” if they need to know something."

Though this is not very accurate, in fairness it was an impossible task because of the readings they were assigned (Verhagen’s criticism of connectivism and Siemens’ response to Verhagen) and because the context appears to be the application of learning theories in the classroom.

Verhagen's criticism is an early and not particularly well-informed criticism, which Siemens does a reasonable job refuting. But if the sort of perspective of connectivism that you're given is one where 'you look up answers through your network instead of remembering them' then your understanding of connectivism will be significantly limited.

What is a Learning Theory

So in this post, let me clear, first, about what a theory actually is, and then let me outline the ways in which connectivism can be thought of as a learning theory.

To start then: theories explain. They're not handbooks or best-practices manuals. They're not taxonomies, in which a domain of enquiry is split into types, steps or stages. Theories answer why-questions. They identify underlying causes, influencing factors, and in some cases, laws of nature.

Explaining why learning occurs has two parts: first, describing what learning is, and second, describing how it happens (or what causes it to happen). Both parts are important. Theories may be as deeply divided about what something is as they are in how it happens.

A learning theory, therefore, describes what learning is and explains why learning occurs. It is not a teaching manual or a set of pedagogical best practices. You don't 'apply connectivism in the classroom' (though you might apply an understanding of connectivism in the classroom).

What is Learning?

According to connectivism, learning is the formation of connections in a network. The learning theory, therefore, in the first instance, explains how connections are formed in a network.

But think for a moment about how this contrasts with the theories of learning offered by other theories. For example:
  • in behaviourism, learning is the creation of a habitual response in particular circumstances (or as Gilbert Ryle would say, to learn is to acquire a disposition).
  • in instructivism, learning is the successful transfer of knowledge from one person (typically a teacher) to another person (typically a student).
  • in constructivism, learning is the creation and application of mental models or representations of the world.
As you can see, these are very different stories about what learning is. This is why it's diffiocult to compare theories of learning. The vocabularies are different, and they are talking about different things. Thomas Kuhn called this the incommensurability of theories.

As you can see, connectivism says that learning is something very different from what is described in other theories. This is one reason we say connectivism is a learning theory: the vocabulary of learning it employs is in some ways importantly incommensurate with that of other theories.

When I say of connectivism that 'learning is the formation of connections in a network' I mean this quite literally. The sort of connections I refer to are between entities (or, more formally, 'nodes'). They are not (for example) conceptual connections in a concept map. A connection is not a logical relation. It is something quite distinct.

In particular, I define a connection as follows (other accounts may vary): "A connection exists between two entities when a change of state in one entity can cause or result in a change of state in the second entity."

Why is this important? Because it captures the idea that connections are something that we can observe and measure (they're not a black box), and because it captures the idea that networks are not merely structures, but also that they enable (what might be called) signalling between entities.

How Does Learning Occur?

The question of how learning occurs is therefore the question of how connections are formed between entities in a network. There is a deep and rich literature on this topic, under the heading of (not surprisingly) 'learning theory', though most of it is published outside the domain of education. The first chapter available here provides a good overview.

The literature describes either actual networks of neurons ('neural networks', such as human or animal brains) or simulations of these networks ('artificial neural networks'), which are created using computers. In both cases, these networks 'learn' by automatically adjusting the set of connections between individual neurons or nodes.

This is a very different model of learning from that proposed by other learning theories.
  • In behaviourism, learning takes place through operant conditioning, where the learner is presented with rewards and consequences.
  • In instructivism, the transfer of knowledge takes place through memorization and rote. This is essentially a process of presentation and testing.
  • In constructivism, there is no single theory describing how the construction of models and representations happens - the theory is essentially the proposition that, given the right circumstances, construction will occur.

To be fair, a long discussion here would be required to talk about constructivist accounts of model or representation formation. This is a weakness of constructivist theories - there's no particular means to determine which constructivist theory is actually correct.

And this points to an underlying weakness of all three approaches: they all involves, ultimately, some sort of black box beyond which no further explanation can be provided. How does reward stimulate behaviour? How is transferred information stored in the brain? What is a model and how is it created?

In my talks I've presented four major categories of learning theory which describe, specifically and without black boxes, how connections are formed between entities in a network:
  • Hebbian rules - 'what fires together wires together' - neurons that frequently share the same state then to form connections between each other
  • Contiguity - neurons that are located near to each other tend to form connections, creatinhg a clustering effect
  • Back Propagation - signals sent in reverse direction through a network, aka 'feedback', modify connections created by forward propagated signals
  • Boltzmann - networks seek to attain the lowest level of kinetic energy 
The actual physical descriptions of these theories vary from network to network - in human neurons, it's a set of electrical-chemical reactions, in social networks, it's communications between individual people, on computer networks it's variable values sent to logical objects.

These are the actual learning theories. Connectivism essentially collects these theories together into a single package as a mechanism for explaining how connections are formed in a network.

Building on the Theory

These are the foundations of connectivism as a learning theory.

As you can see, it has nothing to do with 'looking up the answer on Google' or any of the surface characteristics commonly associated with it.

A connectivist view of the world is very different from one found in other theories.

For example, to the question what is knowledge a connectivist will talk about the capacity of a network to recognize phenomena based on partial information, a common property of neural networks.

Connectivism proposes therefore what might be called 'direct knowledge', following the work of people such as J.J. Gibson. This is very different from what might be called 'indirect knowledge', which is based on the creation of models or representations using an internal (and possible innate) language or logic.

Consequently, a connectivist account of literacy will be very different from that found in other theories. These theories are essentially language-based and are concerned with the coding and decoding of information in such a language. Major principles will revolve around syntax (aka grammar) and meaning and truth (aka semantics).

A connectivist account of literacy reinterprets both syntax and semantics, looking well beyond rules and meaning. In my 'Speaking in LOLcats' presentation, I propose a six-element connectivist account of literacy, one that also includes elements of cognition, context and change.

Additionally, the question of how we evaluate learning in connectivism is very different. Rather than focus on rote response, or on manipulations inside a model, a connectivist model of evaluation involves the recognition of expertise by other participants inside the network.

In connectivism, the principles of quality educational design are based on the properties of networks that effectively respond to, and recognize, phenomena in the environment.In various works, I have identified these as autonomy, diversity, openness, and interactivity. These are very different from standard accounts of quality.

With each of these aspects of connectivism being identified and developed, it becomes increasingly apparent that a connectivist sees learning very differently from those who follow other theories.

They see a person learning as a self-managed and autonomous seeker of opportunities to create, interact and have new experiences, where learning is not the accumulation of more and more facts or memories, but the ongoing development of a richer and richer neural tapestry.

They understand that the essential purpose of education and teaching is not to produce some set of core knowledge in a person, but rather to create the conditions in which a person can become an accomplished and motivated learner in their own right.


  1. What I have not been able to see previously in your work on Connective Knowledge is how it sheds light on the 'quality' of connections. By that I mean that some connections may be better than others in particular learning situations. Is this related to Hebbian rules and/or contiguity? I am not just thinking at the neuronal level here but at a broader view of entities in a network.

  2. To my mind there isn't an observable property of connections called 'quality'.

    Connections vary from each other according to a value typically called a 'weight'. The weight impacts the signal strength between the two entities. In learning theories such as back propagation connections are usually adjusted by adjusting weights (rather than severing and creating connections).

    There is a large literature on weights. See

  3. I'm commented in a blog post, "The Incompleteness of Connectivism."

  4. I've replied with a post on my blog, "The Incompleteness of Connectivism" -

  5. I really appreciated this succinct and thorough post.
    I am in the middle of trying to document what happened in a blended kind of learning situation with 8th grade Life Science students. When I look at how they worked and what they accomplished, I become more and more convinced that the situation itself was conducive to certain students (many, in fact) increasing the size and robustness of their networks, and therefore having more learning take place.
    I have been struggling with how to determine the weight of each node, so the literature you cite is helpful.

  6. Please bear with my simple approach ;) I can see how synaptic weight applies to neurones and even computational models. What I can't see is how this applies to connections such as Facebook likes, reviews of books on Amazon, social connections between people in a PLN.

  7. @Frances Bell: Commonly the weight of sociotechnical connections between entities refers to their direction (bidirectional connections might be considered double-weighted) and their frequency (individual contacts load on a weighted edge). So speaking, a facebook like (or maybe even just having a focused look at a post) is a unidirectional one-time contact between you and an object. From my understanding network theory doesnt distinguish between high-quality and low-quality edges, it's just weak or strong. (but of course subjective perceptions of edge quality are another story)

  8. @Frances Bell: Commony the weight of connections between sociotechnical entities refers to their direction (bidirectonal edges may be considered double-weighted) and their frequency (individual contacts "load" on a weighted edge). So speaking, a Facebook like, or maybe even just a focussed look at a fb post, is a one-time unidirected connection between you and an object. From my understanding there is no such thing as a normative quality of edges, they are just weak or strong. Of course subjective perceptions of connection quality are another story.

  9. Subjective perceptions of connection quality are of great interest to me. I think that there is a lot more to say about connections than their weakness / strength in the way that you describe. You apply the term sociotechnical to entities but that term is used in Science and Technology Studies. And my view of sociotechnical goes beyond weakness/strength of connections.

  10. I am interested in subjective perceptions of quality eg I could make a fair attempt at distinguishing between joke Amazon reviews and genuine ones - I wouldn't just rely on an average score.

  11. One of the reasons this theory is so important (or will be recognized as such) is that networks are creating new ways for people to learn that are not accounted for in other theories. Just look at Duolingo, for instance, a recent study showed that students, using this highly networked game, are learning languages in 1/3 the time as in conventional college classes. And okay, I am just going to say it - I find the definition of the learner in this article inspiring and a good part of the reason I got into education in the first place.

  12. Stephen, a learning theory is supposed to provide an explanans to an explanandum within the domain of learning phenomenons. So let's put connectivism, as a learning theory, to the test with this simple explanandum:

    A student responds to the equation "1+1 = ?" with "2" - this type of knowledge can be learned, right? I hope you agree with me, that this observable phenomen can readily be explained with theories from behaviorism and cognitivism (If so desired, I can supply suitable explanans, but I hope it's fairly evident that an explanation is possible within those frameworks).

    I'd like you to explain within your connectivist approach
    (1) how such knowledge is acquired and
    (2) how performance is accomplished.

    Please do so, by stating the required theorems.

  13. > I hope it's fairly evident that an explanation is possible within those frameworks

    I think it's far from evident but you're welcome to try.

    > this observable phenomen can readily be explained with theories from behaviorism and cognitivism

    Why 'theorems'? What exactly do you mean by theorems? Are you offering a deductive-nomonological model where explanations come exclusively in the form of general principle+initial conditions?

  14. Yep, that's pretty much, what I meant by theorems: If-Then-statements or principles. If you can, please provide a deductive-nomological account of any one learning phenomenon (e. g. the one I stated or one of your choice) using connectivist thinking (or theorems/statements/principles, whatever you may want to call it). If such an account is not possible, then please provide the most stringent explanation for any learning phenomenon (or the one i mentioned) you can come up with.

    I'm primarily looking for specific (and simple) instances of explanations here that employ connectivist statements (theorems/principles/etc). I'd like to see its explanatory power demonstrated.

    I'll provide a rough sketch of an explanation for my example using behaviorist and cognitivist thinking, just to give an idea of what I mean by an explanation. I'd like to see an analogous account of the phenomenon using connectivist ideas.

    A behaviorist account could be something along these lines:

    The response "2" can be thought of simply as a conditioned response to the stimulus "1+1=?". When presented with that stimulus, the response "2" is triggered.

    This kind of stimulus-response-coupling can be acquired by the mechanism of operant conditioning as mentioned in your article above.

    A cognitivist account of the phenomenon could be something like this (deploying ideas from John R. Andersons ACT-R cognitive architecture, without some knowledge about ACT-R this is probably hard to understand):

    A student reads the statement "1+1=2" (for example in a text book), this information thus is enters the visual module (note: the cognitive system is made up of specialized modules in ACT-R) and is then encoded as a chunk in declarative memory that can be retrieved later on.

    When the student is presented with "1+1=?" this information enters the visual modules buffer. ACT-Rs pattern matching capability then compares this partial chunk in the visual buffer to the chunks available in declarative memory and finds a partial match (utilizing ACT-R's spreading activation mechanism for memory search) to the "1+1=2"-chunk stored there during the acquisition phase. Other production rules then map the "?" in the presented stimulus/chunk to the corresponding part in the memorized chunk (i. e. "2") and generate the (let's say written) response using the manual module.

    No matter how incomplete and crude these explanations may be (I happily concede that, but more detailed and stringent explanations can be found in the literature), please try to sketch out an explanation using connectivist thinking that is at least as crude an incomplete for this very simple learning phenomenon.

  15. What you describe as a very simple learning phenomenon is actually a very complex learning phenomenon.

    Moreover, it is complicated by the fact that there is no single event that constitutes "A student responds to the equation "1+1 = ?" with "2""

    If you wanted I could give you a very rough connectivist account:
    - a student is presented with n instances of a training set with input '1+1=' and output '2'
    - in instance n+2 the student is provided with input '1+1='
    - the student responds '2'

    The connectivist literature is full of examples like that. But of course this does not (except in a very trivial sense) represent the understanding of numbers of of addition that is implies with 1+1=2

  16. "They see a person learning as a self-managed and autonomous seeker of opportunities to create, interact and have new experiences, where learning is not the accumulation of more and more facts or memories, but the ongoing development of a richer and richer neural tapestry."

    Does this mean that learning is the accumulation of connections, rather that facts or memories?

  17. "They see a person learning as a self-managed and autonomous seeker of opportunities to create, interact and have new experiences, where learning is not the accumulation of more and more facts or memories, but the ongoing development of a richer and richer neural tapestry."

    Does this mean that learning is the accumulation of connections, rather than facts or memories?

  18. No it doesn't, Ken. More is not better when it comes to connections. For any given set of nodes, there is a 'sweet spot' of connectivity. Learning is the management of the connections around that sweet spot, organizing them optimally.

  19. So I am thinking that rather than 'apply' connectivism in a classroom, a teacher might better 'permit' or 'foster' an environment wherein the network properties (autonomy etc.) would thrive, thus permitting the emergence of the sweet spot and optimal organization.

  20. So I am thinking that rather than 'apply' connectivism in a classroom, a teacher might better 'permit' or 'foster' an environment wherein the network properties (autonomy etc.) would thrive, thus permitting the emergence of the sweet spot of connectivity and optimal organization of the nodal connections. Does this sound accurate?

  21. Ken: yes. That would be accurate.

  22. I appreciate that theory is not a set of instructions, a theory of learning is not a method of teaching. I wish that idea were more widely accepted. It's not even entirely accepted in the very course of assuming it we see above.

    The version of connectivism offered here seems oddly physicalist: learning is entirely different now that students don't memorize vocab sheets or sit facing a blackboard. (A) many still do, and (B) even memorization in the past was not the be-all end-all of learning.

    Presumably, learning has always been the same, it's only teaching practices that differed. So the theory of learning being detailed here through teaching methods is oddly out of sync with the very key assumption with which the presentation starts.

    It also seems like a weak point that there's no such theory as "instructivism." It seems to be offered here as a straw man. "Instructivism" is required here to make it seem like BC (Before Constructivism) no one ever thought knowledge was a a mental model, a network, and whatever else connectivism might want to say.

    In short, it seems to make more sense to say "our social arrangements and communication technologies have changed" than it does to say 'now we know that learning is the construction of mental models' or 'now we know that knowledge is a network.' (And people have been saying that learning involves building mental models long before constructivism, so that does not seem to distinguish constructivism as a theory, if indeed it is a theory, of learning.)

    When writing was more strongly linear, a line seemed like a good model for knowledge. And now that our communication technologies are structured like networks, it seems more sense to think of knowledge as a network. But these are displaced physical descriptions of the material form knowledge takes projected onto some 'underlying' idea of what knowledge is.

    Perhaps that is why the explanation of connectivism as a theory of learning needs constantly to refer implicitly to methods: the network model is doing double duty on both sides, and so the very effort to maintain a theory of learning/method of instruction distinction keeps collapsing.

    It still may be useful to say 'knowledge' is a network or to get learners to work in groups.

    But then no special theory is required to do this.


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