Recently I attended the Orlando Chapter of Creativemornings‘ (CM) August presentation by Dr. Bruce Stephenson, Professor of Environmental Studies at Rollins College in Orlando, FL. Dr. Stephenson highlighted the development of the Creative Village in Orlando as an example of the new urbanism.
I enjoyed the presentation and the interaction with Dr. Stephenson and the other attendees and staff, but, it wasn’t like I had really contributed much of anything to the discussion, altho some people had asked some interesting questions. Like, ‘ I’d love to live in Orlando because we walk the talk of sustainability, but the schools are so much better in the suburbs and I want my kids to get a good education; that’s important to us.’ The answer was ‘sorry, can’t help you.’ Evidently schools were not a priority of the Creative Village people. Maybe that’s just me, but isn’t that something you’d consider if you were serious about attracting young, creative people? In fact, if they were really serious about improving Orlando and attracting creative people to the area, if the schools were good, they would come. What happens when the creative people that move here grow up and start families?
I want to be involved in building a community, but not rubber stamping a real estate project. After all who is really benefiting from it if it doesn’t meet the needs of the whole community of Orlando? I wondered how the rest of the citizens of Orlando would feel, because I’m sure they probably want good schools too. Thanks for having this presentation. If I lived in Orlando I’d want, and I’d want other citizens to be able to be involved, too, in developing community solutions to community problems.
Its too bad that there isn’t a forum for people to talk about issues like this, tho. The current CM format might be a good place to start to think about models. Maybe the current lecture style format could be updated in favor of one that favors more dialogue, question and answer, that gives everyone, opportunities to participate. It could be effective. I mean, suppose people came to CM to get creatives’ opinions, views, etc.? Just a thought.
It might follow the examples of complex learning systems explicated by Davis and Sumara in “Complexity and Education-Inquiries into Learning, Teaching and Research,” and Patricia Shaw’s “Changing Conversations in Organizations, A Complexity Approach to Change.”***
Davis and Sumara explain that over the past 50 years our ideas of “What is knowledge and how do I get it?” have been radically revised. In the past, knowledge was thought to reside inside one’s head; learning was a process of internally representing what is out there, as if “ingesting” knowledge; e.g. “getting things into your head,” “soaking things up.” Teaching was “transmitting” knowledge from the teacher to the student; “banking” or depositing knowledge with the student for later withdrawal. (Unfortunately, this paradigm of education, combined with frequent testing, continues in many, if not most, of our schools, with predictable average results.)
This linear view does not work at all in complex systems that are self-transforming like (wo)man. Learning is not simply a matter of “experience causes learning to happen,” and is not limited to individuals. . A learner is a complex unity that is capable of adapting itself to the sorts of new and diverse circumstances that an active agent is likely to encounter in a dynamic world. From a complexity perspective, learners can include social and classroom groupings, schools, communities, bodies of knowledge, languages, cultures, and species.
Although people individually create their own knowledge, simultaneously knowledge is being created within social groups. The process of knowledge “production” might be described as an ever-expanding space of possibility that is opened and enlarged simply by exploring the space of what is currently possible.
In a complex system the object at the center is never an individual, but an idea, a shared commitment, a common purpose, a collective orientation or an emerging possibility.
In designing complex systems it is impossible to predict the outcomes; one must be principally concerned with preparing the conditions for the emergence of the as-yet unimagined. *
1. CM’s common purpose appears diffuse, undefined. CM originated in New York City as a way to bring together local creative communities that was accessible and free of charge; no involved multi-day conferences, which the founder thought were elitist and not accessible. The first meeting was a coffee and chat that evolved into a recurring lecture series attracting leading thinkers, designers and other types of creative people. Succinctly stating the organizing purpose of CM, (perhaps a monthly topic for each chapter to consider?), will facilitate the group’s self-organization around the purpose, improving functioning and facilitating emergence of the as yet unknown. In other words, CM could transform itself.
2. Taking into account the qualities necessary for a complex system and for emergence,* it may be helpful to conduct monthly meetings more as conversations, as a dialogue among attendees concerning an idea – in October it might have been “What is Urbanism?–with the invited speaker and/or convener playing the roles of ‘director’/facilitator/resource person. (Since in this setting leadership is diffused, the speaker and/or convener may experience this as an acute sense of the paradox of being “in charge but not in control”.) Participants will likely experience a fun, exciting and entertaining environment where new knowledge is created in several levels, including perhaps a scale free network linking the participants.
An example of developing the conditions for emergence of knowledge from group discussions taken from Davis and Sumara’s research is given below:** (Although participants in this case are professionals familiar with the subject matter, similar studies have been carried out with high school students during regular class periods with similar results. It appears appropriate, then, to extend the study results to CM participants who are not necessarily experts in the month’s topic.)
You may also find relevant an excerpt concerning ensemble improvisation from Patricia Shaw’s “Changing Conversations in Organizations, A Complexity Approach to Change.”***
*Researchers have identified several necessary qualities of a complex system:
1. Emergence (self-organization)
Emergence (e.g. ants, birds flocking, human social groups) is a primary quality of a learning system where these collectives develop capacities that can exceed the possibilities of the same group of agents if they were made to work independently; where people that need not have much in common, much less be oriented by a common goal, can join in a collective group that seems to develop a clear purpose.
The conditions for emergence:
- Internal diversity—a source of possible responses to emergent circumstances. One cannot specify in advance what sorts of variation will be necessary for appropriately intelligent action.
- Internal redundancy—the complement to diversity; enables the habituated, moment-to-moment interactivity of the agents that constitute a system.
- Neighbor interaction—the neighbors that must interact with one another are ideas, hunches, queries, and other manners of representation.
- Distributed control—one must relinquish any desire to control the structure and outcomes of the collective; one must give up control if complexity is going to happen.
- Randomness—the structures that define complex social systems maintain a delicate balance between sufficient coherence to orient agents’ actions and sufficient randomness to allow for flexible and varied response.
2. Bottom up
Emergence is an example of “bottom up” organization; it does not require a “leader,” per se. Emergence is a paradox: a manifestation of a collective intelligence, but intelligent group action is dependent on the independent actions of diverse individuals. (“Intelligence” is the quality of exploring a range of possible actions and selecting ones that are well suited to the immediate situation; a repertoire of possibilities, and a means to discern the relative effectiveness of each possibility, not unlike creativity.)
- Non-polarized groups can consistently make better decisions and come up with better answers than most of their members and…often the group outperforms the best member.
- You do not need a consensus in order…to tap into the wisdom of a crowd, and the search for consensus encourages tepid, lowest-common-denominator solutions which offend no one rather than exciting everyone.
- The rigidly hierarchical, multilayered corporation…discourages the free flow of information.
- Decisions about local problems should be made, as much as possible, by people close to the problem…People with local knowledge are often best positioned to come up with a workable and efficient solution.
- The evidence in favor of decentralization is overwhelming…The more responsibility people have with their own environments, the more engaged they will be.
- Individual irrationality can add up to collective rationality.
- Paradoxically, the best way for a group to be smart is for each person to act as independently as possible.
3. Scale-free networks
A so-called scale-free (decentralized) network, which consists of nodes nodding into grander nodes, usually on several levels of organization, is more robust than a centralized network because if a node were to fail, it is unlikely that the whole system will collapse.) A decentralized network will decay into a centralized network under stress. For example, when time is a scarce commodity, the most common organizational strategy is a central network with a leader or teacher as the hub and employees or students at the ends of the spokes. This works against the “intelligence” of the organization by preventing agents from pursuing their own self-interest and obsessions, preventing diversity of experience.
4. Nested organization
An immediate implication of a decentralized architecture is that distinct levels o of organization can emerge.
5. Ambiguously bounded, but organizationally closed systems
- Complex systems are “open”; that is they are constantly exchanging matter and/or information with their contexts. In a situation where a collective is working on a project, it is rarely a simple matter to discern who has contributed what, especially if the final product is at all sophisticated.
- Complex systems usually arise from and are part of other complex systems, even while being coherent and discernible unities. Where does an agent stop and a collective begin? The question is sometimes easily answered. After all the distinction between an ant and an anthill seems relatively straightforward. However, if one considers more complex systems, for example, and individuals personality, the situation becomes much more difficult.
- Distinguishable but intimately intertwined networks can and do exist in the same “spaces.” Consider the relationship between one’s neural system and one’s system of understandings, both of which can be understood in terms of decentralized networks, but neither of which can be collapsed into the other.
Structured-determined behavior is one of the key characteristics used to distinguish a complex unity from a complicated (mechanical) system. The manner in which a complicated system will respond to a perturbation is generally easy to figure out, simply because its responses are determined by the perturbation. For example, if a block of wood is nudged, its response will be quite different than if you nudge a dog. The response will not be determined by you, but by the dog. What is more, not even experience with nudging will provide an adequate knowledge of what will happen if it is repeated—for two reasons. First, a complex system learns. That is, it is constantly altering its own structure in response to emergent experiences. Secondly, systems that are virtually identical will respond differently to the same perturbation. Hence one cannot generalize the results from one system to another…it problematizes the contemporary desire for “best practices” in education—a notion that what works well in one context should work well in most contexts. That only makes sense when talking about mechanical systems.
Complex systems do not operate in balance; indeed, a stable equilibrium implies death for a complex system.
8. Short-range relationships
Most of the information is exchanged among close neighbors, meaning that the system’s coherence depends mostly on agents’ immediate interdependencies, not on centralized control or top-down administration. A “win-win logic”; an agent’s situation will likely improve if the situations of his/her/its nearest neighbors improve. A “we” is usually better than an “I” for all involved.
**An Example of Emergence of knowledge from group discussions:
1. Developing Knowledge
The example that we use to illustrate the discussion in this chapter is based on an extended and ongoing study of practicing teachers’ knowledge of mathematics, conducted by Davis, Simmt, and Sumara. At the time of the writing, the project is entering the fourth year of its six-year duration.
To date, most empirical studies concerned with teachers’ knowledge of mathematics have been oriented by a “deficit” model of personal understanding, whereby teachers are examined according to a predetermined set of competencies. A different approach is taken in the research reported here, which is anchored in the assumption that experienced mathematics teachers enact a certain sort of mathematical knowledge that may never have been an explicit part of their own learning—or, for that matter, of their own teaching. Indeed, much of this knowledge may not be popularly recognized as part of the formal disciplinary body of knowledge. As such, the project which involves a group of 24 teachers, is aimed explicitly at representing teachers’ mathematics-for-teaching—that is, the sorts of mathematics that arise in the actual contexts of teaching.
The cohort is a diverse one, with grades from kindergarten through high school represented. In terms of professional experience, a few of the participants are at the beginning of their careers, several have taught for decades, but two are mathematics specialists. Some teach in small urban centers, some teach in rural locations. The cohort meets for daylong seminars, scheduled every few months. The thread of the discussion that is presented through this chapter is developed around one of these sessions, in which the topic of discussion was “What is multiplication?”
2. Developing Specialized Knowledge
In the study of teachers’ mathematical knowledge, the research sessions with the teachers are regarded in different ways by the various participants. For the most part, the teachers see the meetings as “in-service sessions;” their principle reasons for taking part revolve around their professional desires to be more effective mathematics teachers. In contrast, for Davis, Simmt, & Sumara, these events are “research sessions”—that is, sites to gather data on teacher knowledge. The researchers are explicit in the fact that they are there to try to make sense of teachers’ understandings of mathematics and how that knowledge might play out in their teaching. The common ground, as developed through the course of these discussions boxes, arises in the joint production of new insights into mathematics and teaching. Topics have ranged from general issues (e.g. problem solving) to specific curriculum topics (as in the case of multiplication, developed here).
In regard to the explicit research agenda of assessing teachers’ mathematics, the investigation team often finds that teachers’ first responses to a question like “What is multiplication?”, while usually appropriate, represent just one of many possibilities, and usually a possibility that is redundant to every member of the system—that is, one that is automatized and requires little thought. In response to the “What is multiplication?” prompt, for instance, almost everyone answered “repeated addition” or “groups of”, and was surprised when asked the follow-up question, “And what else?” However, when this same group of teachers is asked to share their responses or explain for others, in general a much greater diversity of responses comes to be presented.
With regard to the redundant elements of the collective, the session that serves as the focus of this discussion unfolded early in the second year of the collaboration, and so there had been ample opportunity to establish routines and expectations. The topic of multiplication had been selected by the teachers themselves in a previous session, and so it represented a matter of shared interest and concern. The researchers’ decision to begin with the question “What is multiplication?” was intended as means to have participants represent their common knowledge on the topic—to explicitly announce the common or redundant elements around the issue-at-hand, as it were.
Participants certainly understood it in this way. What they were not expecting was that follow-up question, “And what else?”—which, as elaborated in subsequent discussion boxes, turned out to be an occasion to represent a diversity of images, applications, and other associations used to give shape to the topic of multiplication at various grade levels. It was in this diversity of responses that new, emergent possibilities for conceptual interpretation began to arise.
3. Developing Trans-Level Knowledge
As noted in the previous discussion box, the teachers’ responses to the “What is multiplication?” prompt were at first limited and seemed to offer little promise for discussion, let alone elaboration. However, when participants were asked to interact and to explore other interpretations, in rather short order they generated several other possibilities.
To enable the interactions of ideas, the researchers asked small discussion groups to prepare lists of their interpretations on posters. After an appropriate time to prepare these posters, the products were put on display at the front of the room. Through a combination of explanation, discussion, and questioning, key points were collected into single summary poster, contents of which follow:
Multiplication has to do with…
- Repeated addition: e.g., 2 x 3 = 3 + 3 or 2 + 2 + 2;
- Equal grouping: e.g., 2 x 3 can mean “2 groups of 3″;
- Number-line hopping: e.g., 2 x 3 can mean “make 2 hops of length 3″;
- Sequential folding: e.g., 2 x 3 can refer to folding a page in two parts and then into 3;
- Many-layered: e.g., 2 x 3 means “2 layers, each of which contains 3 layers”;
- The basis of proportional reasoning: e.g., 3 L at $2/L costs $6;
- The inverse of division—which makes division about repeated subtraction, equal separations, number-line fragmentation, etc.;
- A sort of intermediary of addition and exponentiation—i.e., multiplication is repeated addition, and exponentiation is repeated multiplication;
- Array-generating: e.g., 2 x 3 gives you 2 rows of 3 or 2 columns of 3;
- Area-producing: e.g., a 2 unit by 3 unit rectangle has an area of 6 units;
- Dimension changing;
- Number-line stretching or compressing: e.g., 2 x 3 = 6 can mean that “3 corresponds to 6 when a number-line is stretched by a factor of 2″;
By the end of the lengthy discussion, there was consensus that the concept of multiplication was anything but transparent. In particular, it was underscored in the interaction that multiplication was not the sum of these interpretations. It was some sort of complex conceptual blend. Teachers at all levels of schooling participate in the development and elaboration of the idea.
More significantly, perhaps, through the course of the research activity, it became more and more apparent that the mathematics of individual participants could not be distinguished from the emergent mathematical understanding of the collective itself. It became impossible to attribute authorship of particular understandings to one person or another. Moreover, the final product surpassed the knowledge of any single individual present. Its authorship was decentralized.
And even though the product was clearly a collective one, every participant attested to having learned a great deal about the topic. Several commented that they had learned more about multiplication through the session than they ad learned at any other time. The learning, that is, occurred across at least two different level of organization.
4. Enabling Constraints for Developing Knowledge
During research sessions, teachers are invited to work on shared interpretive and problem-solving tasks. These tasks are developed around mathematical topics that are selected by the teachers themselves and they are designed in ways that allow the researchers to map out some of the contours of their mathematical knowledge.
At first glance, it might seem that some of these tasks are rather narrow. Many of them—like the “What is multiplication?” example that has served as the focus of this linked series of discussions—appear to have immediate and well-established responses. Indeed, in most mathematics assessment-contexts, they would likely be seen as questions as closed-ended, with singular correct answers.
The quality is actually important. The participants need to perceive of the tasks as both relevant and do-able—that is, as coherent. At the same time, there must be sufficient play in the questions to open spaces for broader discussion. In the multiplication example, this quickly proved to be the case as teachers realized that their immediate responses did not reflect the actual conceptual complexity represented by the notion of multiplication. In other words, the follow-up “And what else?” served to flag a certain openness or ambiguity—sort of inherent randomness.
Further to this point, as new interpretations were suggested and others blended, it grew increasingly apparent that not only is there no definitive response to the question, “What is multiplication?”, but that the answer was always a moving target that is subject to endless recursive elaboration as new applications, images and metaphors are tossed into the mix.
So framed, the principle role of the researchers is understood in terms of structuring tasks that are meaningful and appropriate to participants and to organize the settings in a way that allow participants and their ideas to interact. In the context of these discussions, the researchers listen in particular for teachers’ commentaries on how they teach, might teach, and should teach. Embedded in such articulations are profound understandings of not just mathematical concepts, but the manner in which mathematical concepts are developed and learned. In other words, teachers’ knowledge of established mathematics and their knowledge of how mathematics is established are inextricably intertwined. In different terms, for us, the phrase mathematics-for-teaching refers not just o a mastery of content, but also t teachers’ understandings of the development of that knowledge on both individual and collective levels—a truly complex phenomenon. (p. 136-50)
***Ensemble Improvisation—constructing the future together
“…Keith Johnson…has spent a lifetime working with improvisation in the theater, since his days at the Royal Court in London in the 1950s. Each day Keith worked with us to develop wonderfully bizarre, comic and moving scenes in hundreds of brief improvisations involving a handful of us at any one time…Keith would notice when an improviser paused, caught in a silent conversation, and attempt to catch whatever they were in the process of rejecting. Sometimes if he asked quickly enough the person would say something and Keith would say lightly, ‘No, just before that’ and the person might suddenly offer a word or phrase which in one way was ordinary yet would immediately stir something amongst the rest of us. Often such contributions at the moment of the paused improvisation seemed to strike multiple entendres. This stirring in the audience of the rejected next contribution was spontaneous—we were tickled before we could precisely say why. And then immediately we would start making the links and associations, often sexual, irreverent, clever, always apposite at the precise moment. We resonated in various ways with the improviser’s discomfort—we all felt the pull towards and away from the revealing nature of our spontaneous responses, we felt exposed in our knowingness as the webs of associations rippled amongst us.
“Keith made it clear that he was not interested in this phenomenon from a Freudian interpretation of repressed contents of the unconscious individual mind. He was showing us how, as we communicated with ourselves and with one another, we were constrained by our history of relating as social persons. If we did not interrupt the emergence of the next and the next and the next response as they arose in us we delighted and disturbed ourselves in a way we could scarcely bear. Like someone always off balance and continuing to stay upright only by moving, the ensemble evolved. To stop was to fall. As we gestured to one another in the openness of the present engagement, the next spontaneous contribution paradoxically created continuity with the past and transformed its nature by opening a way forward which only became recognizable as it was taken up by the next response. And this creativity was of a very ordinary kind. Blood flowing with a mixture of pleasure and embarrassment, alarm and satisfaction, as we all discovered that our joint action was indeed beyond our individual control. As Keith pointed out, in ‘normal’ life we create conditions together which keep our sense of who we are and what kind of situation we are in much more stable and repetitive. Some conditions include the technologies, ideologies and institutional forms that we sustain together. In the imaginative world of improvisation, and with Keith’s deft encouragement, the constraints became our capacity to accept and move with whatever was happening. It is hard to bear such a degree of rapid evolution either socially, organizationally or personally, such fluidity of individual and group identity. Yet the experience was very instructive. It made it hard to hold on to the humanistic notion of an essential, authentic, unitary self as an inner possession of our subjectivity.” (p. 114-5)