I think that the concepts of complex networks that I've gleaned so far from Morin and Sporns and of decalcomania that I've taken from Deleuze and Guattari lay two cornerstones for my emerging view of knowledge and learning.
First, complex networks suggest that knowledge is not a single thing, or single think (sorry, I couldn't resist, and I may yet edit this awful wordplay); rather, knowledge is a network of patterns enclosed by larger patterns and enclosing smaller patterns. Any given knowledge pattern is constantly open to the dynamic interactions of all those other various patterns on their various levels. This reinforces Morin's admonition that we define any entity—a cell or a word, say—not from its boundaries inward, but from its center outward. Or better yet, we should define a cell from its center both inward and outward. The center of the cell is not an endpoint of definition; rather, it is the starting point of definition, and to understand the cell, we must move from that center both outward to larger patterns and inward to smaller patterns. The cell must be understood as itself and as a part of an enclosing ecosystem and as an ecosystem for other entities, all dynamically interacting with each other, affecting each other and being affected by each other. Any given knowledge is like this cell: recognizable and addressable as itself, and yet not completely understood without consideration of its constituent parts and its ecosystem and of the ways that it interacts with both those micro and macro scales.
Thus, my knowledge of Connectivism is in fact a pattern of neurons, but that is just a starting point. Moving inward, that pattern of neurons encloses various patterns in different regions of the brain. Each of those patterns encloses individual neurons and individual electro-chemical processes, which enclose individual cells and electrical charges, which enclose other things, and other things, and other things, all the way down to quarks and strings, and maybe beyond that if we ever develop instruments that can see that far in. Back to our starting point and moving outward, the pattern of neurons that is my knowledge of Connectivism is enclosed by my conversation in MOOC CCK11 (among numerous other conversations I'm having—for instance, this blog), which is enclosed by an ecosystem of larger thought about education, which is enclosed by a larger system, and then a larger system, and then the entire Universe, and maybe beyond that if we ever develop instruments that can see that far out. To understand completely my knowledge of Connectivism, then, I must understand everything else.
This, of course, is absurd silliness. It is also our hope for the future. There is no end to learning anything, so we should never be bored. However, in the everyday discourse of common day, we simply can't let a single cell or bit of knowledge bleed into everything else in the Universe, even though it is quite literally connected to everything else in the Universe. A cell or an idea must in some useful way be recognizable and describable and must have potency in and of itself. How do we get out of this predicament?
Perhaps Nicholas A. Christakis and James H. Fowler have an answer for us in their book Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives (2009). In describing how social networks work, they note that the influence of people extends out to about three degrees of separation. In other words, the patterns of our own lives influence our friends, our friends' friends, and our friends' friends' friends. After that, the potency of our patterns of behavior and belief fade and lose their efficacy. Perhaps some mechanism similar to this is at work among the various levels of patterns of any given entity. What do I mean?
Well, consider my knowledge of Connectivism as a single cell. My knowledge is still a recognizable entity with some potency within the context of this blog, though this blog also discusses other things. My knowledge is still recognizable and potent within the context of MOOC CCK11 and the larger discussion about Connectivism, but I think you an begin to see that my unique knowledge is beginning to fade in this larger conversation as it joins to and is overwhelmed by more voices and stronger voices. As my voice moves into a choir, my own unique tone and tenor becomes blended and a different voice emerges, a group voice. Connectivism means something different at this scale. Though my own meaning may still be recognizable, at two or three degrees removed from my single voice—my single understanding—the unique pattern of my knowledge begins to fade into the wider pattern of the general conversation about Connectivism. When we move up to a larger choir—the discussion of education in general—then my voice is quite lost, its identity and potency subsumed by and faded into the cacophony of voices. There are still a few voices potent and identifiable at this scale—Dewey, Piaget, Bloom, etc.—but most voices have long since drowned.
Thus, while I can trace the connections of my single knowledge about Connectivism to infinity and back (assuming I have the time, patience, focus, tools, and skill set), it makes great sense day-to-day to speak of my knowledge of Connectivism as a unique, identifiable entity with its own potency and contours and center. Being an English scholar, I think this entity is something of a convenient fiction, but it makes life much easier to manage.
I'll talk next post about decalcomania.
Friday, March 4, 2011
Wednesday, March 2, 2011
#CCK11: Mapping the Complexity of Knowledge
I spent some of the afternoon trying to create some images that captured my sense of how knowledge and, thus, learning are complex activities. I'd like to share them, though I'm already dissatisfied with them. Still …
I started trying to map my knowledge about Connectivism in Figure 1. Those of you in CCK11 will immediately recognize a heavy debt to Stephen Downes' illustration about the meaning of Paris.
My understanding of Connectivism is represented by the six-pointed star in the middle of the image and is surrounded by people and resources that have contributed in some way to my understanding. My understanding is not one thing, even though the six-pointed star seems to suggest that it is. Rather, it is the dynamic pattern created by the retro-interactions of various people, some of whom know about Connectivism and some who don't, the CCK11 MOOC, readings, some of which are about Connectivism and some which are not, conversations, and my own critical analysis. No one of these things is sufficient to explain my concept of Connectivism; however, all of them are necessary.
It is easy for me to see in this image how just my understanding alone at this level is a complex activity: understanding is the emergence of an idea from the interplay of various patterns of meaning to create a new pattern which takes on intelligibility and a stable core even as it continues to develop and grow in meaning from the center out and even shifts its center from time to time as drastic new patterns occur. In other words, as I keep listening and talking, reading and writing, drawing and thinking, the six-sided star of my understanding of Connectivism defines itself from the core outward, gains its own identity and presence, and begins to interact with the other patterned elements in its field, affecting and being affected, or to use the term of Morin: retro-interactions.
Complex, yes, but really only just the beginning. If I add the concepts of others—for instance, those of you in CCK11, represented by U1 and U2—then you can see how each of your understandings of Connectivism (represented by the four- and five-pointed stars) starts to interact with my own understanding, and the image becomes even more complex.
What immediately impresses me is that none of us can have exactly the same knowledge of Connectivism. We all come at the concept from different angles and with different concepts, different neural pathways, different understandings of teaching and learning, different emotional fields, different connections to others and to other resources. This seems so obvious as almost to be not worth saying, yet our educational system is predicated on all students learning the same things, at the same time, through the same lessons, and monitored by the same tests. This assumption of standardization is simply wrong. Consider U2's understanding of Connectivism in Figure 3.
It looks nothing like my own understanding. Indeed, there is only an overlap where U2 and I share somewhat similar patterns and some common resources, but both U2 and I have lots of patterns, people, and resources that contribute to our understandings that don't directly contribute to each other. U2 and I cannot possibly have the same understanding.
How can we communicate, then? Well, as near as I can see, communication lies on the borders between the miraculous and the impossible, and the best that U2 and I can manage is a functionally similar understanding. We cannot share an exact understanding. There is no chunk of knowledge that we can both swallow mentally and then say, "Yup, you've got it! Exactly!" The best we can do is to continue in dialogue (in all its various manifestations) until we both create functionally similar patterns of knowledge that allow us to say, "Yeah, that's pretty much what I mean."
Then as if this wasn't complex enough, I'm reminded what Sporns says about the various layers of networks: "Networks span multiple spatial scales, from the microscale of individual cells and synapses to the macroscale of cognitive systems and embodied organisms. … In multiscale systems, levels do not operate in isolation—instead, patterns at each level critically depend on processes unfolding on both lower and higher levels" (2). Thus, within my own mind, a similar complex network of patterns is churning and emerging, and this level affects the churning and emergence of knowledge at the wider level of the MOOC, and in turn, the MOOC level is affected by the wider discussions of education, chaos, complexity, and so forth. These wider discussion are themselves part of a larger ecosystem of discussion about society, politics, and economics, which are themselves elements within language and thought throughout the Ages. And on, and on. Worlds within worlds, patterns within patterns, all self-similar at each scale. All dynamic within their own scales and adding to the dynamism of all the enclosed and enclosing scales.
Finally, if I really wanted to capture a sense of this complexity, then I would have made a movie that captured all these patterns at all the various levels growing, fading, clarifying, and fragmenting as they interacted with elements in their own scale and with the other scales. I don't know if I have the technical talent to create that movie, but I definitely don't have the time just now. Maybe later. It'll be impressive, I think.
I started trying to map my knowledge about Connectivism in Figure 1. Those of you in CCK11 will immediately recognize a heavy debt to Stephen Downes' illustration about the meaning of Paris.
 |
| Figure 1: My Concept of Connectivism |
It is easy for me to see in this image how just my understanding alone at this level is a complex activity: understanding is the emergence of an idea from the interplay of various patterns of meaning to create a new pattern which takes on intelligibility and a stable core even as it continues to develop and grow in meaning from the center out and even shifts its center from time to time as drastic new patterns occur. In other words, as I keep listening and talking, reading and writing, drawing and thinking, the six-sided star of my understanding of Connectivism defines itself from the core outward, gains its own identity and presence, and begins to interact with the other patterned elements in its field, affecting and being affected, or to use the term of Morin: retro-interactions.
 |
| Figure 2: Our Understandings of Connectivism |
Complex, yes, but really only just the beginning. If I add the concepts of others—for instance, those of you in CCK11, represented by U1 and U2—then you can see how each of your understandings of Connectivism (represented by the four- and five-pointed stars) starts to interact with my own understanding, and the image becomes even more complex.
What immediately impresses me is that none of us can have exactly the same knowledge of Connectivism. We all come at the concept from different angles and with different concepts, different neural pathways, different understandings of teaching and learning, different emotional fields, different connections to others and to other resources. This seems so obvious as almost to be not worth saying, yet our educational system is predicated on all students learning the same things, at the same time, through the same lessons, and monitored by the same tests. This assumption of standardization is simply wrong. Consider U2's understanding of Connectivism in Figure 3.
 |
| Figure 3: U2's Understanding of Connectivism |
It looks nothing like my own understanding. Indeed, there is only an overlap where U2 and I share somewhat similar patterns and some common resources, but both U2 and I have lots of patterns, people, and resources that contribute to our understandings that don't directly contribute to each other. U2 and I cannot possibly have the same understanding.
How can we communicate, then? Well, as near as I can see, communication lies on the borders between the miraculous and the impossible, and the best that U2 and I can manage is a functionally similar understanding. We cannot share an exact understanding. There is no chunk of knowledge that we can both swallow mentally and then say, "Yup, you've got it! Exactly!" The best we can do is to continue in dialogue (in all its various manifestations) until we both create functionally similar patterns of knowledge that allow us to say, "Yeah, that's pretty much what I mean."
Then as if this wasn't complex enough, I'm reminded what Sporns says about the various layers of networks: "Networks span multiple spatial scales, from the microscale of individual cells and synapses to the macroscale of cognitive systems and embodied organisms. … In multiscale systems, levels do not operate in isolation—instead, patterns at each level critically depend on processes unfolding on both lower and higher levels" (2). Thus, within my own mind, a similar complex network of patterns is churning and emerging, and this level affects the churning and emergence of knowledge at the wider level of the MOOC, and in turn, the MOOC level is affected by the wider discussions of education, chaos, complexity, and so forth. These wider discussion are themselves part of a larger ecosystem of discussion about society, politics, and economics, which are themselves elements within language and thought throughout the Ages. And on, and on. Worlds within worlds, patterns within patterns, all self-similar at each scale. All dynamic within their own scales and adding to the dynamism of all the enclosed and enclosing scales.
Finally, if I really wanted to capture a sense of this complexity, then I would have made a movie that captured all these patterns at all the various levels growing, fading, clarifying, and fragmenting as they interacted with elements in their own scale and with the other scales. I don't know if I have the technical talent to create that movie, but I definitely don't have the time just now. Maybe later. It'll be impressive, I think.
Sunday, February 27, 2011
CCK11: Why Networks?
In my last two posts, I talked about Olaf Sporns' book Networks of the Brain, and I want to continue working with that book. I'm finding it very rich and resonant.
In his Introduction (2), Sporns asks, "Why should we take advantage of modern network approaches to study the brain?" I want to ask why should we take advantage of modern network approaches to study knowledge and learning?
First, because knowledge and learning are network phenomena, and network approaches tell us things about learning and knowledge that we just can't get any other way. Sporns' comments are salient here. "Virtually all complex systems form networks of interacting components" (2). Learning and knowledge are complex systems receptive to network approaches which, says Sporns "can provide fundamental insights into the means by which simple elements organize into dynamic patterns, thus greatly adding to the insights that can be gained by considering the individual elements in isolation" (2). If we consider just a single brain alone, knowledge is the selection and orchestration of many individual neurons into meaningful patterns of interactions. No single neuron alone constitutes a chunk of knowledge; rather, knowledge emerges only when all the relevant nurons fire coherently. As I write each word of this sentence, patterns of relevant neurons are firing in my brain to orchestrate thoughts, motor movements, and memories into (we hope) a coherent expression of knowledge.
We must, of course, keep in mind that it greatly helps to understand "the individual elements in isolation," and I appreciate those physical scientists who dedicate their careers to studying how neurons fire. Knowledge absolutely depends upon the proper firing of individual neurons within our brains, and if we understand this electro-chemical process, then we understand real and crucial facts about knowledge and knowledge creation. But understanding single neurons alone isn't enough. It cannot explain thought, memory, consciousness, and knowledge. Not even complete knowledge of the fundamental physical element of knowledge—the neuron—will explain knowledge. To understand knowledge—to know knowledge—we must understand how individual neurons orchestrate themselves into meaningful patterns. As Sporns says of the brain:
To remove us from the black hole that I just landed us in and to put some bounds on this train of thought, imagine the patterns of neurons that are firing in your brain as you read each word in this current sentence (actually, studies show that you are likely reading clusters of words, but more of that in another post). You have a unique pattern of neurons for each word or word cluster, but each unique pattern of neurons yields precious little knowledge—precious little because each identifiable pattern is precious, or absolutely necessary for your knowing the sentence, but also little, or absolutely insufficient for knowledge. Rather, to understand what I'm writing, you must scale up to a larger pattern of patterns, from individual words and word clusters to sentences. And if you follow this logic, you see that to understand the sentence, you must scale up again to the paragraph. Then you must scale up again from the paragraph to the post. Then again from the post to the entire blog. Then you must scale again to the conversations about Connectivism, CCK11, complexity, rhizomatics, and to awareness that I'm writing all of this on a beautiful Sunday morning in Macon, GA, USA after a wonderful night's sleep and two cups of coffee while my wife across the room watches the television show CBS Sunday Morning about the upcoming Oscars.
Sorry, but I tend to expand outwards. To center my thinking again, consider that to understand any knowledge pattern, we must understand the context, or ecosystem, within which that knowledge pattern exists, and we must accept that no scale level makes complete sense without understanding the scales above it and below it, or to say it better, no scale can be understood without understanding the scales it contains and the scales within which it is contained. To understand any layer of an onion, you must understand both how it functions as a layer by itself AND how it functions with the layers it encloses and the layers that enclose it. In the words of Edgar Morin, your thought—your knowledge—must be complex. Olaf Sporns says it better and more succinctly than I, so I'll end with him:
In his Introduction (2), Sporns asks, "Why should we take advantage of modern network approaches to study the brain?" I want to ask why should we take advantage of modern network approaches to study knowledge and learning?
First, because knowledge and learning are network phenomena, and network approaches tell us things about learning and knowledge that we just can't get any other way. Sporns' comments are salient here. "Virtually all complex systems form networks of interacting components" (2). Learning and knowledge are complex systems receptive to network approaches which, says Sporns "can provide fundamental insights into the means by which simple elements organize into dynamic patterns, thus greatly adding to the insights that can be gained by considering the individual elements in isolation" (2). If we consider just a single brain alone, knowledge is the selection and orchestration of many individual neurons into meaningful patterns of interactions. No single neuron alone constitutes a chunk of knowledge; rather, knowledge emerges only when all the relevant nurons fire coherently. As I write each word of this sentence, patterns of relevant neurons are firing in my brain to orchestrate thoughts, motor movements, and memories into (we hope) a coherent expression of knowledge.
We must, of course, keep in mind that it greatly helps to understand "the individual elements in isolation," and I appreciate those physical scientists who dedicate their careers to studying how neurons fire. Knowledge absolutely depends upon the proper firing of individual neurons within our brains, and if we understand this electro-chemical process, then we understand real and crucial facts about knowledge and knowledge creation. But understanding single neurons alone isn't enough. It cannot explain thought, memory, consciousness, and knowledge. Not even complete knowledge of the fundamental physical element of knowledge—the neuron—will explain knowledge. To understand knowledge—to know knowledge—we must understand how individual neurons orchestrate themselves into meaningful patterns. As Sporns says of the brain:
The collective actions of individual nerve cells linked by a dense web of intricate connectivity guide behavior, shape thoughts, form and retrieve memories, and create consciousness. No single nerve cell can carry out any of these functions, but whenStudying the neural patterns within a single brain seems complex enough, but if we accept the network approach, then we must accept that, as Sporns says, "networks span multiple spatial scales, from the microscale of individual cells and synapses to the macroscale of cognitive systems and embodied organisms. This architecture is also found in other complex systems—for example, in the multiscale arrangement of social networks, ranging from interpersonal relations and cohesive social groups, to local communities and urban settlements, all the way to national economies and global political organizations" (2). Thus, just understanding the pattern created by a single mental concept is not sufficient; rather, we must move up the scale to clusters of concepts housed within other clusters of larger networks, like ecosystems housed within planets, within solar systems, within galaxies, within galaxy clusters, within multiple universes.
large numbers are linked together in networks and organized into a nervous system, behavior, thought, memory, and consciousness become possible. Understanding these integrative functions of the brain requires an understanding of brain networks and the complex and irreducible dynamic patterns they create.
To remove us from the black hole that I just landed us in and to put some bounds on this train of thought, imagine the patterns of neurons that are firing in your brain as you read each word in this current sentence (actually, studies show that you are likely reading clusters of words, but more of that in another post). You have a unique pattern of neurons for each word or word cluster, but each unique pattern of neurons yields precious little knowledge—precious little because each identifiable pattern is precious, or absolutely necessary for your knowing the sentence, but also little, or absolutely insufficient for knowledge. Rather, to understand what I'm writing, you must scale up to a larger pattern of patterns, from individual words and word clusters to sentences. And if you follow this logic, you see that to understand the sentence, you must scale up again to the paragraph. Then you must scale up again from the paragraph to the post. Then again from the post to the entire blog. Then you must scale again to the conversations about Connectivism, CCK11, complexity, rhizomatics, and to awareness that I'm writing all of this on a beautiful Sunday morning in Macon, GA, USA after a wonderful night's sleep and two cups of coffee while my wife across the room watches the television show CBS Sunday Morning about the upcoming Oscars.
Sorry, but I tend to expand outwards. To center my thinking again, consider that to understand any knowledge pattern, we must understand the context, or ecosystem, within which that knowledge pattern exists, and we must accept that no scale level makes complete sense without understanding the scales above it and below it, or to say it better, no scale can be understood without understanding the scales it contains and the scales within which it is contained. To understand any layer of an onion, you must understand both how it functions as a layer by itself AND how it functions with the layers it encloses and the layers that enclose it. In the words of Edgar Morin, your thought—your knowledge—must be complex. Olaf Sporns says it better and more succinctly than I, so I'll end with him:
In multiscale systems, levels do not operate in isolation—instead, patterns at each level critically depend on processes unfolding on both lower and higher levels. The brain is a case in point. We cannot fully understand brain function unless we approach the brain on multiple scales, by identifying the networks that bind cells into coherent populations, organize cell groups into functional brain regions, integrate regions into systems, and link brain and body in a complete organism. In this hierarchy, no single level is privileged over others. The notion that brain function can be fully reduced to the operation of cells or molecules is as ill conceived as the complementary view that cognition can be understood without making reference to its biological substrates. Only through multiscale network interactions can molecules and cells give rise to behavior and cognition. Knowledge about network interactions on and across multiple levels of organization is crucial for a more complete understanding of the brain as an integrated system.Apply this, then, to students and learning: Only through multiscale network interactions can learning give rise to behavior and cognition. Knowledge about network interactions on and across multiple levels of organization is crucial for a more complete understanding of students and learning as integrated systems. Ultimately for me then, we must apply network approaches to learning and knowledge for political and moral reasons: to stop the dreadful reduction of students to test scores. Test scores simply do not capture the complexity of learning and knowledge.
Friday, February 25, 2011
CCK11, Connectivism, and Quantitative Analysis
In my previous post, I walked a long way around to finally say that one of the main reasons I like Connectivism is because it seems to be a vibrant conversation within the context of a much larger conversation about complex network structures. If Morin and Sporns are correct, then science in general is moving away from the closed-system, reductionist science of the past to an open-system, complex science of the future. From my point of view, the people engaged in the conversation heating up about Connectivism are moving in a direction that is complementary to this larger shift. I want to be part of that shift.
However, Sporns' book has opened my eyes to what I suspect may be a gap in the Connectivism community: quantitative research. In the Introduction to his book Networks of the Brain (2011), Sporns points out that "connectivity comes in many forms—for example, molecular interactions, metabolic pathways, synaptic connections, semantic associations, ecological food webs, social networks, web hyperlinks, or citation patterns" (1), and I assume that we can include students and teachers in traditional classrooms, MOOCs, and PLNs. He points out, however, that all these different kinds of connectivity require hard scrutiny from the perspective of network science. He says: "In all cases, the quantitative analysis of connectivity requires sophisticated mathematical and statistical techniques" (1).
Perhaps I have overlooked this pocket of discussion, but I think Connectivism lacks a strong, quantitative voice. I know that I don't have that voice, but I think all our conversations could be a bit more grounded if they were informed from time to time with precise observations and quantifiable measurements. Now, I'm an English teacher, so I am not suggesting that quantitative analysis is the only answer, but it is certainly part of the answer.
What might we investigate quantitatively? Sporns suggest several lines of research for neuroscience that might be enlightening for those of us in education in general and composition in particular. For instance, he notes that "nervous systems are composed of vast numbers of neural elements that are interconnected … [thus, we can] probe for architectural principles that shape brain anatomy" (3). Similarly, MOOCs are composed of vast numbers of people and resources that are interconnected by computer networks; thus we can probe for architectural principles that shape a MOOC's anatomy. The writing specialist might phrase it this way: MOOCs are composed of vast numbers of documents from blog posts, to essays, to Elluminate sessions, to tweets that are propagated and interconnected by computer networks; thus, we can probe for architectural principles that shape the written and recorded conversation.
This last question, of course, is of real interest to me, and I am confident that I could tie any findings back into the scholarly conversation about writing, but I am not confident that I have the "sophisticated mathematical and statistical techniques" to generate those findings. Still, this MOOC is sitting here with all these linked documents. It's a shame to see it go to waste. Anybody with sufficient quantitative skills (and I don't even know enough to know what those are) want to join me in this research? Or is this research already underway? Anyone?
PS: The ink was not dry on this post when I happened on a post by Sui Fai John Mak about quantitative research into Connectivism and MOOCs. He references some studies by Dave Cormier, Rita Kop, and others, which shows that this conversation has been heating up. So it was there all along, and I just didn't hear it until I started thinking about it. Seems that's the way my brain works.
However, Sporns' book has opened my eyes to what I suspect may be a gap in the Connectivism community: quantitative research. In the Introduction to his book Networks of the Brain (2011), Sporns points out that "connectivity comes in many forms—for example, molecular interactions, metabolic pathways, synaptic connections, semantic associations, ecological food webs, social networks, web hyperlinks, or citation patterns" (1), and I assume that we can include students and teachers in traditional classrooms, MOOCs, and PLNs. He points out, however, that all these different kinds of connectivity require hard scrutiny from the perspective of network science. He says: "In all cases, the quantitative analysis of connectivity requires sophisticated mathematical and statistical techniques" (1).
Perhaps I have overlooked this pocket of discussion, but I think Connectivism lacks a strong, quantitative voice. I know that I don't have that voice, but I think all our conversations could be a bit more grounded if they were informed from time to time with precise observations and quantifiable measurements. Now, I'm an English teacher, so I am not suggesting that quantitative analysis is the only answer, but it is certainly part of the answer.
What might we investigate quantitatively? Sporns suggest several lines of research for neuroscience that might be enlightening for those of us in education in general and composition in particular. For instance, he notes that "nervous systems are composed of vast numbers of neural elements that are interconnected … [thus, we can] probe for architectural principles that shape brain anatomy" (3). Similarly, MOOCs are composed of vast numbers of people and resources that are interconnected by computer networks; thus we can probe for architectural principles that shape a MOOC's anatomy. The writing specialist might phrase it this way: MOOCs are composed of vast numbers of documents from blog posts, to essays, to Elluminate sessions, to tweets that are propagated and interconnected by computer networks; thus, we can probe for architectural principles that shape the written and recorded conversation.
This last question, of course, is of real interest to me, and I am confident that I could tie any findings back into the scholarly conversation about writing, but I am not confident that I have the "sophisticated mathematical and statistical techniques" to generate those findings. Still, this MOOC is sitting here with all these linked documents. It's a shame to see it go to waste. Anybody with sufficient quantitative skills (and I don't even know enough to know what those are) want to join me in this research? Or is this research already underway? Anyone?
PS: The ink was not dry on this post when I happened on a post by Sui Fai John Mak about quantitative research into Connectivism and MOOCs. He references some studies by Dave Cormier, Rita Kop, and others, which shows that this conversation has been heating up. So it was there all along, and I just didn't hear it until I started thinking about it. Seems that's the way my brain works.
Thursday, February 24, 2011
The Value of Connectivism and CCK11
In one of our past Elluminate sessions in CCK11, George Siemens mentioned a book by Olaf Sporns called Networks of the Brain (2011). Something about the book piqued my interest, so I'm reading it now. The book addresses the question "What can network science tell us about the brain" (1), and I confess up front that I do not have either the scientific or mathematical backgrounds to follow all of Prof. Sporns' arguments, but as with most conversations that I engage, I'm reading it through the foggy windows of my own interests and biases, so it is still worthwhile.
I'm interested in the book because connectivity and complexity are at the heart of how Sporns is attempting to understand the brain. He says in his Introduction that science in general is informed by the perspective of complex networks:
What does this mean for education? I am not so well read in educational theory as to say reliably, but lack of knowledge does not appear to be a strong deterrent, so I'll make a few observations, hoping that others better informed will correct me. The other three major strains of educational theory—behaviorism, cognitivism, and constructivism—appear to me to focus primarily on the individual. In those theories, knowledge is something in an individual brain or mind or both. Learning is something that happens in that same individual, discrete mind, whether we think of the mind as an inscrutable black box (as in behaviorism) or a translucent computational device (as in cognitivism). Knowledge and learning, then, belong to the individual student and are observable, measurable, and describable only in terms of that individual student. This attitude is reflected in our grading economy, which insists upon an inviolable and sacred correspondence between 1 student and 1 grade. As everyone knows, group grades suck.
This reductionism is precisely what Connectivim tries to overcome, while at the same time respecting the truly impressive achievements of the reductionist theories. Reductionist theories and the schools built upon them largely favor "only knowledge of elementary system components," or the individual student; whereas Connectivism attempts to add "knowledge of the ways in which these components interact and the emergent properties of their interactions." Connectivism does not deny that knowledge and learning occur in individual students; rather, it counters the diminutive and reductionist idea that knowledge and learning occur only in individual students. Connectivism says for me that knowledge and learning are most properly understood in terms of individual students and the interactions of students with their ecosystems and the emergent properties of all that dynamic interaction. This is a radical difference in understanding, a precipitous difference. Really. A school built on Connectivism will not function or look like existing schools.
Now, I am not suggesting that Connectivism has invented complexity or networking theory, nor am I suggesting that cognitivists and constructivists are total reductionists with no understanding of complexity and networking structures. Even as unread as I am, I can think of scholars such as Wenger who have incorporated the interactions within groups into their ideas about education. I'm speaking in this post on a very general level, fully aware that most anyone who reads this could think of numerous scholars from the other camps who have already anticipated many of the insights of Connectivism. I am in no way suggesting that Connectivism is totally new. I'm not sure that a totally new idea has ever existed, and largely, I regard any complaint by curmudgeons that this idea or that theory is not new to be a red herring. Who cares? Rather, I want to ask if an idea or theory is useful.
Connectivism is useful for me. It gives me a conversational space within which to connect with and engage others who are examining and thinking—in light of complex, networked systems—about how we humans create and share knowledge.
I'm interested in the book because connectivity and complexity are at the heart of how Sporns is attempting to understand the brain. He says in his Introduction that science in general is informed by the perspective of complex networks:
Increasingly, science is concerned with the structure, behavior, and evolution of complex systems such as cells, brains, ecosystems, societies, or the global economy. To understand these systems, we require not only knowledge of elementary system components but also knowledge of the ways in which these components interact and the emergent properties of their interactions. … All such complex systems display characteristic diverse and organized patterns [which are] the outcome of highly structured and selective coupling between elements, achieved through an intricate web of connectivity (1).As I have mentioned in an earlier post, Edgar Morin says that this emergence of complex network thinking is a third great paradigm in the development of science, the first being the static, mechanistic universe of Newton and the second being the declining universe of thermodynamics. I hear Sporns agreeing with Morin that the idea of complex networks is radically changing the way that scientists explore and describe (or map, to use Deleuze and Guattari's term) reality. If this is the case, then it seems to me that Connectivism, and the discussion emerging about that concept, is a response to this new and emerging way of viewing the world. Connectivism is an attempt to move beyond the reductionism of Cartesian dualism (despite all its marvelous successes) to a richer, more complex understanding.
What does this mean for education? I am not so well read in educational theory as to say reliably, but lack of knowledge does not appear to be a strong deterrent, so I'll make a few observations, hoping that others better informed will correct me. The other three major strains of educational theory—behaviorism, cognitivism, and constructivism—appear to me to focus primarily on the individual. In those theories, knowledge is something in an individual brain or mind or both. Learning is something that happens in that same individual, discrete mind, whether we think of the mind as an inscrutable black box (as in behaviorism) or a translucent computational device (as in cognitivism). Knowledge and learning, then, belong to the individual student and are observable, measurable, and describable only in terms of that individual student. This attitude is reflected in our grading economy, which insists upon an inviolable and sacred correspondence between 1 student and 1 grade. As everyone knows, group grades suck.
This reductionism is precisely what Connectivim tries to overcome, while at the same time respecting the truly impressive achievements of the reductionist theories. Reductionist theories and the schools built upon them largely favor "only knowledge of elementary system components," or the individual student; whereas Connectivism attempts to add "knowledge of the ways in which these components interact and the emergent properties of their interactions." Connectivism does not deny that knowledge and learning occur in individual students; rather, it counters the diminutive and reductionist idea that knowledge and learning occur only in individual students. Connectivism says for me that knowledge and learning are most properly understood in terms of individual students and the interactions of students with their ecosystems and the emergent properties of all that dynamic interaction. This is a radical difference in understanding, a precipitous difference. Really. A school built on Connectivism will not function or look like existing schools.
Now, I am not suggesting that Connectivism has invented complexity or networking theory, nor am I suggesting that cognitivists and constructivists are total reductionists with no understanding of complexity and networking structures. Even as unread as I am, I can think of scholars such as Wenger who have incorporated the interactions within groups into their ideas about education. I'm speaking in this post on a very general level, fully aware that most anyone who reads this could think of numerous scholars from the other camps who have already anticipated many of the insights of Connectivism. I am in no way suggesting that Connectivism is totally new. I'm not sure that a totally new idea has ever existed, and largely, I regard any complaint by curmudgeons that this idea or that theory is not new to be a red herring. Who cares? Rather, I want to ask if an idea or theory is useful.
Connectivism is useful for me. It gives me a conversational space within which to connect with and engage others who are examining and thinking—in light of complex, networked systems—about how we humans create and share knowledge.
Wednesday, February 9, 2011
Formalism in CCK11
Our CCK11 Elluminate conversation today, 2011 Feb 09, featured guest speaker Neil Selwyn, who said several times that he thought we might lose something valuable if we indeed ever managed to rid our educational selves of formal institutions and practices. I imagine that he meant such things such as universities, school boards, curricula, programs of study, grading scales, and college deans. I think I have a faint appreciation for his point, but first I want to quibble with his use of the term formal.
To my mind, Mr. Selwyn was contrasting the wide open, free, self-directed, personalized, sometimes chaotic connect-and-collaborate informal structures of networks with the closed, restrictive, other-director, depersonalized, usually well-defined command-and-control formal structures of hierarchies. Popular usage of formal suggests that hierarchical structures are formal while network structures are informal, but I disagree. I take formal to mean any structure that is capable of generating a recognizable form on the basis of some regular procedures. If this is so, then a flock of birds is a formal structure: it is recognizable as a structure (a flock) and it is formed on the basis of a few, regular procedures. A fractal image is just as formal as, say, a triangle. A swirling eddy of water is just as formal as, and much more common than, a perfectly executed circle. Some forms are rigid and geometric, while others are flexible and fractal, but all are forms and, in that sense, formal.
That being said, hierarchies are different from networks, or rhizomes (to use my favorite term). Hierarchies are closed, rigid, and authoritative. Networks are open, flexible, and collaborative. Hierarchies are imposed on reality. Networks emerge from reality. I greatly prefer networks over hierarchies, and I suspect that many in CCK11 share this preference and predisposition.
Still, I think that Mr. Selwyn has a point. Hierarchies have built much of human culture for the past few millennia, and perhaps we dismiss them at our peril. It's at least an idea worth contemplating for a few minutes. Of course, in the past, we hardly had any options. If we wanted to build large organizations (churches, states, businesses, universities), then we almost had to resort to hierarchical structures, bureaucracies and such. We did not have the technology to enable one hundred thousand people to spontaneously gather and coordinate their behavior for some effort or play. We needed churches and states for that, so we built them—some big ones, too. In some ways, then, hierarchies have been one of the crowning achievements of humanity. I just happen to believe that they've been rendered somewhat irrelevant by networks, but perhaps not totally irrelevant.
The question, then, is what do hierarchies do well that we should keep them, at least in special cases?
Clay Shirkey posted an essay entitled Ontology Is Overrated that addresses this very issue, I think. What he calls ontological classification is very much like what I refer to by the word hierarchy. They both impose a prescribed order on reality rather than allowing an order to emerge from reality (this is reminiscent of Deleuze and Guattari's distinction between tracing reality and mapping reality). Shirkey makes a strong case that the new technology allows for humanity to largely abandon ontological classification schemes for more flexible tagging schemes for tracking and finding information. However, he notes, classification and hierarchy still have some strengths. Hierarchical classification works best when the domain being organized has:
Even as I write this, something in me rebels. I'll have to think some more.
To my mind, Mr. Selwyn was contrasting the wide open, free, self-directed, personalized, sometimes chaotic connect-and-collaborate informal structures of networks with the closed, restrictive, other-director, depersonalized, usually well-defined command-and-control formal structures of hierarchies. Popular usage of formal suggests that hierarchical structures are formal while network structures are informal, but I disagree. I take formal to mean any structure that is capable of generating a recognizable form on the basis of some regular procedures. If this is so, then a flock of birds is a formal structure: it is recognizable as a structure (a flock) and it is formed on the basis of a few, regular procedures. A fractal image is just as formal as, say, a triangle. A swirling eddy of water is just as formal as, and much more common than, a perfectly executed circle. Some forms are rigid and geometric, while others are flexible and fractal, but all are forms and, in that sense, formal.
That being said, hierarchies are different from networks, or rhizomes (to use my favorite term). Hierarchies are closed, rigid, and authoritative. Networks are open, flexible, and collaborative. Hierarchies are imposed on reality. Networks emerge from reality. I greatly prefer networks over hierarchies, and I suspect that many in CCK11 share this preference and predisposition.
Still, I think that Mr. Selwyn has a point. Hierarchies have built much of human culture for the past few millennia, and perhaps we dismiss them at our peril. It's at least an idea worth contemplating for a few minutes. Of course, in the past, we hardly had any options. If we wanted to build large organizations (churches, states, businesses, universities), then we almost had to resort to hierarchical structures, bureaucracies and such. We did not have the technology to enable one hundred thousand people to spontaneously gather and coordinate their behavior for some effort or play. We needed churches and states for that, so we built them—some big ones, too. In some ways, then, hierarchies have been one of the crowning achievements of humanity. I just happen to believe that they've been rendered somewhat irrelevant by networks, but perhaps not totally irrelevant.
The question, then, is what do hierarchies do well that we should keep them, at least in special cases?
Clay Shirkey posted an essay entitled Ontology Is Overrated that addresses this very issue, I think. What he calls ontological classification is very much like what I refer to by the word hierarchy. They both impose a prescribed order on reality rather than allowing an order to emerge from reality (this is reminiscent of Deleuze and Guattari's distinction between tracing reality and mapping reality). Shirkey makes a strong case that the new technology allows for humanity to largely abandon ontological classification schemes for more flexible tagging schemes for tracking and finding information. However, he notes, classification and hierarchy still have some strengths. Hierarchical classification works best when the domain being organized has:
Shirkey adds that this scheme also benefits from being used with certain types of people, those who are:This is all the domain-specific stuff that you would like to be true if you're trying to classify cleanly. The periodic table of the elements has all of these things -- there are only a hundred or so elements; the categories are simple and derivable; protons don't change because of political circumstances; only elements can be classified, not molecules; there are no blended elements; and so on. The more of those characteristics that are true, the better a fit ontology is likely to be.
- Small corpus
- Formal categories
- Stable entities
- Restricted entities
- Clear edges
If the educational objective fits the above characteristics for both content and students, then traditional hierarchical structures may provide the student and teacher real benefits over a network structure. Thus, the first introduction to a new programming language might benefit from a more formal approach, in the sense that Selwyn was using the term. However, becoming a really good programmer means that eventually we leave the formal behind and move toward the more informal.
- Expert catalogers
- Authoritative source of judgment
- Coordinated users
- Expert users
Even as I write this, something in me rebels. I'll have to think some more.
Tuesday, February 1, 2011
Decalcomania and CCK11
In his blog connectiv: On Connectivism and Learning, Jaap distinguishes between training and learning when we train ourselves to play a piece of music. I think he is capturing the distinction I am trying to explore between tracing and mapping, competence and performance, and working and playing. Jaap's training, then, is tracing and working toward competence, and learning is mapping and playing toward performance. Music provides a wonderful metaphor: to play well enough to bring joy and satisfaction (and perhaps a paycheck) to both herself and her audience, a musician must have competence with music and instrument (which requires ten thousand hours of work), but she must also transcend mere competence into performance in order to play the music on her instrument and to expand and express as an artist. Training/tracing and learning/mapping are not opposing activities, but different ends on a sliding scale of activities, and both are connectivist in nature.
I understand both training and learning as Connectivist through Deleuze and Guattari's concept of decalcomania, one of the six characteristics of rhizomatic structures that they explore in their book A Thousand Plateaus (1988). Decalcomania is the artistic process of transferring an image or pattern from one structure to another, usually by pressing the two structures together. According to ARTTalk, "technical explanations of decalcomania describe the method as geometric shapes--irregular, broken or fractured (rather than smooth and even). The two images created by pressing one area of liquid with a top sheet of paper display a form of 'self-similarity,' appearing similar in scale and magnitude - very nearly exact duplicates. In early production, this meant that the creation of two images was made with each attempt. Infinitely fine detail is immediately apparent yet, when magnified, yields startling accents." The capitalismandschizophrenia.org website defines Deleuze-Guattarian decalcomania as a method of "forming through continuous negotiation with its context, constantly adapting by experimentation, thus performing a non-symmetrical active resistance against rigid organization and restriction."
A class about fractals at Yale University notes that decalcomania can form dendritic fractals, as in the picture below:
To my mind, decalcomania is a process for transferring a pattern from one thing to another, and it describes quite accurately how we create meaning in our minds. In decalcomania, a surface with a potent image or medium is pressed against another surface. After the two surfaces are separated, self-similar images reside on both surfaces. The images can diverge more and more as the two surfaces vary in material, texture, porosity, density, color, and so forth. The images can diverge again given the viscosity and consistency of the intermediary medium being pressed between the two structures, and the images can diverge even more if the pressing is inexact or uneven and smears. Decalcomania, I think, provides a nice metaphor for understanding learning and training: the process of impressing patterns between student and class, person and world, guitarist and guitar, artist and canvas.
But first, let me correct a part of my definition. In decalcomania, pattern is NOT transferred from one thing to another. Transfer is an habitual manner of speaking that obscures a deeper insight. Only in it's most basic and popular form of decals, where an image is removed from a special paper and applied whole and unaltered to a new surface, does decalcomania reduce to mere pattern transfer. Unfortunately, this is the dominant metaphor for traditional learning and all training: a knowledge pattern is transferred whole and unaltered from a source into a new brain which then has that new knowledge pattern. This is fundamentally wrong and leads to all sorts of counter-productive pedagogical strategies and theories.
Rather, decalcomania awakens patterns in both structures. When an artist presses some medium—paint, for instance—between two surfaces—say, cloth and paper—then the act of pressing and releasing the paint creates a pattern on both the cloth and the paper. The two patterns very well may be self-similar, but they are highly unlikely to be exact duplicates. Even in industrial processes which impress images on some surface (on a Coke bottle, for instance), "infinitely fine detail is immediately apparent yet, when magnified, yields startling accents," or variations.
Decalcomania, then, helps me explain my interaction in MOOC CCK11. I have pressed some media between myself and MOOC CCK11—different media: Elluminate sessions, discussions, back channel chats, blog posts, essays, Facebook comments, Youtube videos, etc.—and each pressing has awakened in my mind new patterns or reinforced or changed old patterns. Each pressing has also awakened different patterns in MOOC CCK11. Both I and MOOC CCK11 are different because of the impressions each has made on the other. (Of course, CCK11 is bigger than I am, so the impression I make is smaller on it than the impression it makes on me; however, think of the impressions made by Downes and Siemens to see more clearly how the act of impressing works both ways, changing both the individual and the group.)
This process can be explored more. For instance, I am certain that my learning is slightly different, perhaps radically different, from the learning of others in MOOC CCK11, even when we consider the same media. In strictly physical terms, no two brains are structured alike; therefore, a pressing between my brain and MOOC CCK11 through the medium of a given Elluminate session will create a necessarily different pattern of knowledge amongst my neurons than amongst, say, Stephen Downes' neurons. The surfaces of his brain and of my brain are perhaps similar but still different, even in physical detail and certainly in knowledge detail. I may not even map what I learn in the session in the same area of the brain as he does. I certainly won't map it with the same arrangement of neurons. It takes multiple pressings through different media for the two of us even to begin to approximate consistent knowledge patterns in both our brains and in our interactions. (It's the whole process of getting to know each other.)
This process of decalcomania seems to describe many of the classes I've taken and taught. It also explains to me why the industrial method of education as described by Sir Ken Robinson has become so ineffective. If you haven't seen him speak on this issue, then watch Sir Ken explain why we need a radical shift from the industrial paradigm of education:
I understand both training and learning as Connectivist through Deleuze and Guattari's concept of decalcomania, one of the six characteristics of rhizomatic structures that they explore in their book A Thousand Plateaus (1988). Decalcomania is the artistic process of transferring an image or pattern from one structure to another, usually by pressing the two structures together. According to ARTTalk, "technical explanations of decalcomania describe the method as geometric shapes--irregular, broken or fractured (rather than smooth and even). The two images created by pressing one area of liquid with a top sheet of paper display a form of 'self-similarity,' appearing similar in scale and magnitude - very nearly exact duplicates. In early production, this meant that the creation of two images was made with each attempt. Infinitely fine detail is immediately apparent yet, when magnified, yields startling accents." The capitalismandschizophrenia.org website defines Deleuze-Guattarian decalcomania as a method of "forming through continuous negotiation with its context, constantly adapting by experimentation, thus performing a non-symmetrical active resistance against rigid organization and restriction."
A class about fractals at Yale University notes that decalcomania can form dendritic fractals, as in the picture below:
To my mind, decalcomania is a process for transferring a pattern from one thing to another, and it describes quite accurately how we create meaning in our minds. In decalcomania, a surface with a potent image or medium is pressed against another surface. After the two surfaces are separated, self-similar images reside on both surfaces. The images can diverge more and more as the two surfaces vary in material, texture, porosity, density, color, and so forth. The images can diverge again given the viscosity and consistency of the intermediary medium being pressed between the two structures, and the images can diverge even more if the pressing is inexact or uneven and smears. Decalcomania, I think, provides a nice metaphor for understanding learning and training: the process of impressing patterns between student and class, person and world, guitarist and guitar, artist and canvas.
But first, let me correct a part of my definition. In decalcomania, pattern is NOT transferred from one thing to another. Transfer is an habitual manner of speaking that obscures a deeper insight. Only in it's most basic and popular form of decals, where an image is removed from a special paper and applied whole and unaltered to a new surface, does decalcomania reduce to mere pattern transfer. Unfortunately, this is the dominant metaphor for traditional learning and all training: a knowledge pattern is transferred whole and unaltered from a source into a new brain which then has that new knowledge pattern. This is fundamentally wrong and leads to all sorts of counter-productive pedagogical strategies and theories.
Rather, decalcomania awakens patterns in both structures. When an artist presses some medium—paint, for instance—between two surfaces—say, cloth and paper—then the act of pressing and releasing the paint creates a pattern on both the cloth and the paper. The two patterns very well may be self-similar, but they are highly unlikely to be exact duplicates. Even in industrial processes which impress images on some surface (on a Coke bottle, for instance), "infinitely fine detail is immediately apparent yet, when magnified, yields startling accents," or variations.
Decalcomania, then, helps me explain my interaction in MOOC CCK11. I have pressed some media between myself and MOOC CCK11—different media: Elluminate sessions, discussions, back channel chats, blog posts, essays, Facebook comments, Youtube videos, etc.—and each pressing has awakened in my mind new patterns or reinforced or changed old patterns. Each pressing has also awakened different patterns in MOOC CCK11. Both I and MOOC CCK11 are different because of the impressions each has made on the other. (Of course, CCK11 is bigger than I am, so the impression I make is smaller on it than the impression it makes on me; however, think of the impressions made by Downes and Siemens to see more clearly how the act of impressing works both ways, changing both the individual and the group.)
This process can be explored more. For instance, I am certain that my learning is slightly different, perhaps radically different, from the learning of others in MOOC CCK11, even when we consider the same media. In strictly physical terms, no two brains are structured alike; therefore, a pressing between my brain and MOOC CCK11 through the medium of a given Elluminate session will create a necessarily different pattern of knowledge amongst my neurons than amongst, say, Stephen Downes' neurons. The surfaces of his brain and of my brain are perhaps similar but still different, even in physical detail and certainly in knowledge detail. I may not even map what I learn in the session in the same area of the brain as he does. I certainly won't map it with the same arrangement of neurons. It takes multiple pressings through different media for the two of us even to begin to approximate consistent knowledge patterns in both our brains and in our interactions. (It's the whole process of getting to know each other.)
This process of decalcomania seems to describe many of the classes I've taken and taught. It also explains to me why the industrial method of education as described by Sir Ken Robinson has become so ineffective. If you haven't seen him speak on this issue, then watch Sir Ken explain why we need a radical shift from the industrial paradigm of education:
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