Thinking out loud about Connectivism

I’ve been reading George’s writing on the unique ideas in connectivism. Two assertions leap out at me in his list of how connectivism is different from other approaches.

First is the statement that “the same structure of learning that creates neural connections can be found in how we link ideas and in how we connect to people and information sources. One scepter to rule them all.”

This sounds almost exactly like the claim made in John Anderson and Lael Schooler’s 1991 Reflections of the Environment in Memory, which I consider one of the finest pieces of research in our field:

Availability of human memories for specific items shows reliable relationships to frequency, recency, and pattern of prior exposures to the item. These relationships have defied a systematic theoretical treatment. A number of environmental sources (New York Times, parental speech, electronic mail) are examined to show that the probability that a memory will be needed also shows reliable relationships to frequency, recency, and pattern of prior exposures. Moreover, the environmental relationships are the same as the memory relationships. It is argued that human memory has the form it does because it is adapted to these environmental relationships. Models for both the environment and human memory are described. Among the memory phenomena addressed are the practice function, the retention function, the effect of spacing of practice, and the relationship between degree of practice and retention.

Anderson and Schooler provide solid empirical data from multiple domains, strong analysis of that data grounded in their theoretical framework (that the environment is reflected in memory), and mathematical models that accurately embody the relationships they observe. Whether you consider yourself a behaviorist or not, I don’t think a reasonable person can disagree with their conclusions. They’ve simply done too thorough a job clarifying their theoretical framework, gathering relevant raw data from multiple domains, analyzing those data, and arguing their interpretation.

I would be absolutely delighted to see this kind of empirical work done to shore up the nascent theoretical framework called connectivism. I expect that if we put our brains to it for a while we could figure out how to do this. Without any kind of strong empirical grounding, connectivism will be forced to dwell in a “thought experiment” realm with the unfortunate majority of educational research that argues from “obvious” first principles and apparently needs no rigorous validation. This kind of disdain for empirical data is a large part of what is wrong with education more broadly. (Please note that I’m not accusing George of this disdain! I think he would also love to see this kind of work done on connectivism.)

The second statement that leaps out at me is “knowledge is defined as a particular pattern of relationships and learning is defined as the creation of new connections and patterns.”

I understand that it’s hip to downplay the importance of nodes and claim that all the action in a graph is in its edges. However, it’s a very valid epistemological concern to ask questions like “what are the entities that exist in relationship to each other in connectivism?” “What are the entities that, when observed, can be interpreted as existing in patterns?” In other words, “what are the nodes that are connected in connectivism?”

If we’re allowed to talk about extremely impoverished networks in connectivism (I get the sense that many of the people on this train are only interested in very complex / rich networks), let’s consider a very simple graph: a graph with only two nodes and one edge linking them. Set that graph to the side for now, we’ll come back for it in a moment.

Next let’s consider the most basic kind of learning, the kind that you’ve been taught to mock and scorn: memorizing facts. This is sometimes called paired associate learning, because you’re trying to associate two items with each other (a vocabulary word with its definition, a country with its capital, a historical event with its date, etc.) It’s also appropriate to talk about this kind of learning in terms of stimulus-response: you’re supposed to learn that when I say “France” you should say “Paris.” When you reminisce about those good old S-R approaches to learning, you realize that the popular abbreviation S-R almost looks like a very simple graph. A graph with one node labeled S and another labeled R, with a link between them.

Now, I haven’t answered the question “what are the nodes in connectivism” I posed three paragraphs ago. But I believe I just demonstrated that old-fashioned, behaviorist, S-R learning is a simplest case of, and is completely subsumed by, the connectivist framework (as I understand it). Perhaps that’s an interesting enough assertion to hit “publish” and go home for the day on.

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  • This is the same John R. Anderson who wrote ‘Human Associative Memory’ with Gordon Bower, which describes the associative structures fundamental to my own work and also to associationist reasoning generally. http://act-r.psy.cmu.edu/people/ja/ja_bio.html (another Canadian, too).

    In other words, this sort of work *is* the “empirical work done to shore up the nascent theoretical framework called connectivism.” I suppose more of it can be done; I cite it when I come across it. I can’t speak for George, but it’s not like I just made some stuff up and called it a theory.

    Related to this, when you ask questions like, “what are the nodes that are connected in connectivism?” I refer you, not to hand-waving generalities, but to things like Boltzmann engines, which draw upon the thermodynamics inherent in the gradual build-up and release of electrical changes in neurons. http://en.wikipedia.org/wiki/Boltzmann_machine There’s plenty of solid empirical research here, some solid mathematics, and even a spiritual dimension if your so inclined (my various references to ‘harmony through diversity’ are directly grounded in the Boltzmann machine). The average human is more complex than the average neuron, of course, and different mechanics apply. But within some bounds, the same sort of descriptions that apply to neurons also apply to humans – the phenomenon of a ‘propensity to respond after repeated stimuli’, for example, can be observed in both.

    That said, what seems to be important is the set of connections, rather more than the particular physical make-up of the nodes being connected. There is not any evidence that find that stipulates that only certain kinds or essences of nodes can be connected (Thomas Nagel notwithstanding). That said, there is a requirement that the entities be in some sense *physical*, because the nature of a connection (as I’ve often stated) is that a change of state in one results, via the connection, in a change of state in the other (that’s why graph theory, nodes and edges, constitutes only a virtualization, and not an instantiation, of network learning).

    For while I realize that good-old SR looks like paired associate learning, you can’t substitute words, like ‘Paris’ or ‘France’, for two nodes. A word, in and of itself, has no causal property; only the tokening has a property. This is important because a word has no discrete token inside a human mind, and therefore, while we can *represent* an association between ‘Paris’ and ‘France’, we cannot *instantiate* it. *That* is why we prefer complex networks (and what accounts for the generally anti-cognitivist stance of my own work).

    Now I am perfectly happy to talk about simple networks. One node, a connection (not merely an ‘edge’), and another. We can represent nodes as simply as possible – on/off (though in reality many more states are possible).

    We can represent different networks of this sort. A connection as simply as possible (on/off) such that if node A is on and connection is on, node B turns on (that’s an excitatory (or Hebbian)connection). A connection as simply as possible (on/off) such that if node A is on and connection is on, node B turns if (that’s an inhibitory connection). Etc. What are the mechanisms for these? Could be electric switches, could be chemical reactions, could be dominos. If you look at Rumehhart and McClelland’s ‘Jets and Sharks’ experiment, you see we can create pooling and differentiation with these kinds of connections.

    If the nodes aren’t simply on/off, if the connection is represented with a probability function, etc., based on different properties, you get different types of networks.

    All of this is known, old, well-proven. It doesn’t need to be proven all over again, just for education. Quite the opposite. Education should, for once and at long last, learn from what has already been proven.

  • If we understand the knowledge as the ability to solve problems by way of creating patterns based on previous experiences stored, the memory is a central element that allows human and artificial reasoning.

    So, in my view, the nodes act as parts or fragments an external memory that is used as an extension of our memory in a process activated by the need or wish to receive a stimulus (information, answer, …) and not by its emission.

  • Hi David,

    You’ve caught me in a bad week for tackling the big topics your put forward! I will have a bit more time next week to do justice to the important points that you address.

    For now, a couple of quick thoughts.

    In CCK08, discussion partly addressed the behaviourism/connectivism distinctions: http://ltc.umanitoba.ca/moodle/mod/forum/discuss.php?d=926 – this thread runs a bit long, and as you can tell, largely fails to resolve the concerns for either party. But, sometimes the conversation itself is the outcome :). If anything, this discussion reveals the opportunities for research that you state, David.

    In CCK09, the topic was revisited, but this time with an emphasis on connectIONism/connectivism: http://ltc.umanitoba.ca/moodle/mod/forum/discuss.php?d=2248 (this time, complete with a diagram tracing one individual’s view of the behaviourist foundations of connectivism).

    To directly address your questions:

    1. Yes, connectivism needs more minds with a research slant. I would welcome your request to “put our brains to it for a while”. Connectivism is particularly amenable to empirical research evidence, especially as conversations, interactions, and conceptual development are made explicit in online environments. Our interactions are captured and can then be analyzed. This, in turn, gives rise to the need for educational analytics – a topic that you’ve been addressing from the perspective of open education, but would provide a strong basis for evaluating connectivist claims as well.

    2. What is a node? Without sounding glib – a node is a pattern of connections. Networks are nodes in other networks, as we scale up. For example, if I have the conceptual understanding of why we have seasons, I have connected a sequence of nodes that in themselves breakdown into their own networks. We have, for example, the sun, the earth, rotation, space, atmosphere, heat, cold, seasons, etc. To form an accurate conceptual understanding of seasons, we need to bring these individual nodes in relation to each other. And, if we decide to break down the node “son”, we find it too is a network of entities: gases, heat, size/mass, gravity, etc.

    George

  • Greetings David, Stephen, George, and Dolors –

    Just a quick note to say I appreciate the dialog. I am doing a small connectivism-related survey project at the moment.

    I have some background in the neuroscience of behavior but have catching up to do in the other areas of empirical research you’ve discussed. I have read (or am reading) several publications by George and Stephen. So I consider my overall understanding of connectivism rather shallow thus far.

    The angle I am pursuing at the moment, though, is something that perhaps (I flatter myself to think) you might find interesting. Here is an excerpt from a teaching philosophy statement I submitted here at the University of Georgia (where I serve as a lecturer in the Learning, Design and Technology program):

    “As a paradigm for learning and knowledge, connectivism articulates what many professionals have already been putting into practice in their day-to-day professional routines. Effective practitioners, including many of those in the programs in which I teach, are gathering together the tools that will help them effectively connect from day to day with the rapid changes that are occurring in their professional worlds.

    My goal as an instructor is to connect with my students as human beings and to help them be successful. Building personal connections with students has been a strength of my teaching. However, recently I reached a tipping point in my teaching philosophy relating to the confluence of this new paradigm for learning and knowledge – connectivism – and new networking tools for individuals to harness in building connections. Specifically, the last few years have seen the advent of a new kind of personal console or portal. Previous portals were provider-driven. Now, a user can build a personal portal virtually from the ground up using tools such as Netvibes, iGoogle, and Zooloo.

    Thus I am sharing with my students the concept of being an effectively networked professional who has current professional information as well as connections with professional people at his or her fingertips as part of the fabric of day-to-day work. The practical expression of this perspective is the use of the personal portal. Via a custom-built personal interface I created using the tool Netvibes, I have begun modeling for my students an approach to accessing professional information that is as close to seamless as possible. The kind of professional work we are preparing students for, in the programs in which I teach (Instructional Design and Development and School Library Media) is a good fit, in both cases, for this concept.”

    The survey project we are doing (I and two graduate students) is a simple exploration of the tools professionals use to stay connected to their professional (and personal) world, along with some basic questions about their concepts of learning and knowing and about creativity (this is also related but I haven’t gone into it in this post).

    I hope to present the results of this survey at AECT in the fall, and we already have some ideas about where to take this line of inquiry next.

    In the end, after typing this, I fear I may be a bit off-topic. But I guess I’m sort of standing up to be counted among those interested in exploring and researching connectivist concepts (each in our own way). I tip my hat to George and Stephen for initiating this area of inquiry!

    Best regards,

    Greg

  • > What is a node? Without sounding glib – a node is a pattern of connections.

    OK, that was way too glib, but it does touch on an important point.

    Nodes may have properties inherent to themselves, and be in one or another state. They may have the physical form of a neuron, for example, they may have (at any given time) an inherent electrical potential, etc.

    But what distinguishes one neuron from another is not some property or some description of its internal state. We do not, in other words, identify neurons individually, as if by name.

    Rather, what distinguishes one neuron from another – and hence, from a connectionist perspective, one node from another, is the set of connections it has with other neurons. It is not ‘the neuron at location 2b’ or ‘the neuron with potential +2v’ or even ‘the neuron named fred’ but rather ‘the neuron connected to these three other neurons’.

    Again, this isn’t something just made up and speculated upon, but rather, it is something that has been the subject of considerable research. A system structured this way is styled as having “content addressable memory” (see http://en.wikipedia.org/wiki/Content-addressable_memory ) and computers built this way are called “associative computers”.

    Content addressability – associative memory – Anderson – see how it all hangs together?

  • So Stephen, are you defining nodes to be neurons? Are there other forms of nodes? If so, can you name some?

  • From what I have read most recently, I concur with what I understand Stephen and George to be saying, that nodes are actually *not* neurons, or, more to the point, individual neurons are not nodes. Any “unit of meaning” in the brain (to the extent that there is such a thing) consists not in a single neuron but in a pattern of connections between many neurons.

    Greg

  • Ok – I see where Stephen said “They [nodes] may have the physical form of a neuron.” But even then, it’s “the neuron connected to these three other neurons” (or more likely these 10,000 other neurons).

    So the node doesn’t consist in the single neuron itself but in a pattern of connections.

    Greg

  • Thanks Greg. So a neuron is not a node until it is connected, and it is the connected entity that is the node then, is that what you understand Stephen to be saying? Is one connection sufficient to be classified as a node? Upon connection, does the state of the neuron thus change, from (standalone) neuron to (connected) node?

  • Hi,

    Stephen said: “Rather, what distinguishes one neuron from another – and hence, from a connectionist perspective, one node from another, is the set of connections it has with other neurons.”

    Exactly. While a node may have some attributes of its own (keeping in mind that nodes can often be broken down into sub-networks), what defines a node is its relationships to other nodes. Which is why, in connectivism, emphasis on “pattern recognition” is so important. What is a concept but a pattern of connectedness? What is a memory but a pattern of connections? As David highlighted in his post: “the same structure of learning that creates neural connections can be found in how we link ideas and in how we connect to people and information sources.”

    The point that Stephen is making – and that I generally agree with – is that a rich body of research is available to support claims being made under the umbrella of connectivism. Where we have not done original research, the claims being made are supported by research in other fields. (this reminds me of Don Swanson’s concept of “undiscovered public knowledge”)

    Translating established research into education is an important challenge. I imagine studies are available that support the transference of a concept from one domain to another. Language changes in the process. “Strong and weak ties” in sociology have different terms in different fields (even though the concept is the same). Edges, nodes, connections – each field as their twist. In education, the concept of networks will need to be researched within the domain, setting the stage for creating new software or new models of instruction. It’s fine to accept that neuroscience offers a certain view of learning…and this is valuable research. How this view of learning translates into software design, teaching, and learning is the task of educational research.

    I’ll be bold and make two claims (actually, one claim and one prediction):

    1. The core assertions of connectivism, in relation to learning, are better supported by empirical evidence than those of constructivism.

    2. Learning theory will progressively trend toward connections and connection analysis. In a decade, researchers will be predominantly exploring learning from a connections perspective simply because of how this view intersects with trends in numerous disciplines: neuroscience, sociology, philosophy of mind, and connectIONism (neural networks). Additionally, as our use of technology makes more of our actions explicit, connections can be traced through visualization and data analysis.

    btw – a call for papers on a special IRRDOL issue of connectivism is out: http://www.irrodl.org/index.php/irrodl/announcement/view/6

    George

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  • Well George, I would like to ‘think out loud’ myself on this matter. For one, is it not a little presumptous to suggest that

    >a rich body of research is available to support claims being made under the umbrella of connectivism?

    Besides the JR Anderson research referred to above, what is this ‘rich body’? Could you point me to it?

    I am really hesitant to grant that connectivism is the umbrella theory for all learning. It is but one perspective, n’est ce pas? It may have utility in explaining the ‘connection’ aspect of learning, but again, I hesitate to yield to the idea that learning is only about connection, particularly when I don’t have a clear understanding of what a node is, given that nodes seem to be the fundamental atomic unit in the connection, when reduced, within the connectIONIST neural network, as you have indicated. Am I to understand that the process of learning is different in the connectIONIST neural network than in the connectIVISIT social network? How is it different?

  • Ken, generically, the object of the connections is to mantain the system balance. For it is requires an organization that implicates a subdivision in specialized domains and a system of internal and external communication.

    There are natural connections (neurals, environmental, …) and others that only are possible through technology (internet, …) and that are research object.

  • Hi Dolores. I wonder if S-R learning is at the heart of the connections, as suggested by David Wiley above. I am also interested in knowing more about the nodes involved in these connections; perhaps the S-R learning (connecting)is contingent upon or at least affected by node state/type/location etc.

    Perhaps there is a research project in this, if one could focus in on a proper question(s). If learning = connecting, how wide-spread is S-R learning in connectivist learning?

    Given that the same sceptre covers the micro (connectionist neural network) and the macro (connectivist social network) one could probably extrapolate principles from the micro (Boltzmann engines?) to the macro as Stephen has suggested, and research/analyze the S-R learning at the social network level. Any suggestions on how this might be done?

  • Further on my ‘thinking out loud’

    I wonder if Connection can be defined as S-R learning?

    i.e Connection (C) = Stimulus-Response (S-R)

    where stimulus is thought of as a proximal association (coming into contact with) and response is thought of as a change of state (a causal relationship or instantiation) in the connecting entities (call them nodes if you like)

  • Hi Ken,

    In a process of learning the key is the apprentice. It is he who decides what imputs interest you and which do not.

    Therefore, not all stimuli gets an answers, but, instead, there are always arising consequences, whether by act or omission.

  • Andy Van Schaack

    Three items:

    1. “The value of a psychological theory is judged not only by its explanatory and predictive power, but also by its operational power to improve human functioning.” (Bandura, 1986)

    2. And here is a question and answer from an interview with Educational Researcher. (Note: Gene Glass developed the research technique of meta-analysis.)

    Educational Researcher: If you could offer educational research one suggestion to improve its standing, what would that be? And/or what specifically could we educational researchers begin doing to improve our field?

    Gene Glass: It’s not a popular suggestion, I predict, and it surely goes against the grain to some extent, but educational research would do well to regard itself not as a science seeking theory to explain such phenomena as classroom learning, teaching, aptitude and the like, but as a technology designing and evaluating lessons, programs, and systems. Some will regard this as a comedown from the search for grand theory. I regard it as a productive advance to a level of relevance and contribution not yet experienced by educational researchers.

    Finally…

    I offer you a relatively quick read (one of those unpublished grad school throw-away papers) that *applies* the findings of Anderson and Schooler’s research toward a practical educational purpose:

    AN ADAPTIVE, AUTOMATED INSTRUCTIONAL SYSTEM TO SUPPORT THE LEARNING OF FACTUAL INFORMATION

    http://andrewvs.blogs.com/usu/files/avs_bentley_prosem_paper.pdf

    • I wonder why Gene Glass’s suggestions are unpopular. What are his motivations in suggesting a come-down search for meaning?

      This other business of flash-card memory retention. Does it have legs? What does it have to do with connectivism?

      • Andy Van Schaack

        Hello Ken,

        Gene Glass’s suggestion is unpopular among academics because development of theories trumps development of applications for those on the tenure track. It’s the difference between science and technology. (A gross simplification for sure, but you get the idea.)

        Regarding the flashcard retention stuff. Its connection to connectivism comes from David’s original post where he quotes Anderson and Schooler’s article. They found “reflections” of the environment in human memory. And to quote from the original thread that David was responding to: “Connectivism addresses the principles of learning at numerous levels – biological/neural, conceptual, and social/external.” Biological/neural patterns for encoding information appear to be tuned to patterns of information in the environment.

        Paired-associate learning is one of the simplest forms of learning we know of. A physical representation is a flashcard–look at the front, try recall the back. Repeat as necessary.

        I developed a software application that optimized this type of learning (under the assumption that “optimal” means the most efficient way to acquire and retain paired-associates if long term retention and fluency are your objectives).

        You can download and play with the application here:

        http://andrewvs.blogs.com/factor

        It runs in Flash on Macs and PCs. And yes, it’s Open Source. That’s what happens when Wiley is your dissertation chair. ; )

  • Swint

    Dr. Van Schaack,

    Incidentally, ideas similar to your student’s seem to inform the “science” behind Tokyo-based start-up smartFM

    http://smart.fm/tour

    • Andy Van Schaack

      The “student” that wrote that paper was me. = )

      Good catch: the ideas sound similar to smart.fm’s “science” because I was one of the founders and the Chief Scientist of the company (formerly known as Cerego). You can read my 1999 patent here:

      http://www.google.com/patents/about?id=ACMNAAAAEBAJ&dq=6652283

  • Swint

    Small world. One of my students is interning there this summer.