It Makes Complete Sense to Us

8/2/2019 It Makes Complete Sense to Us

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it makes complete sense to usTeaching the Collective

By Craig DwyerLearning, Teaching and Knowing ED6743.87

University of Calgary - M.Ed Mathematics for TeachingApril, 2012

[email protected]@dwyerteacher

www.teachingparadox.edublogs.org


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What is a Learning Collective?

! In a recent talk at the Learning Without Frontiers conference in London, KenRobinson delivered the keynote speech and the made the following comment, We teachchildren ingroups, but not asgroups. This is a profound statement with applications andconsiderations for all levels of education and society; but what does it mean? What is agroup of learners? How do people learn asgroups? How does a teacher accomplishsuch a task? There are no fast and easy answers to these questions. In order to get intothe heart of this matter, we need to delve deeply into very problematic waters that open upseas of possibilities and interpretations. And even then, how do we know where we are?! Teaching is very difficult term to define, as Davis (2004) has suggested by tracingthe cultural and historical webs of association connected to perceptions of what teachingis. Even in present time, if you put a group of twenty teachers into a room and asked themto define teaching, you more than likely get twenty different answers. The common node

between the definitions will more than likely have something to do with learning. Again, weare at an impasse. What is learning? This question again will send us into murky andfoggy waters where are our personal interpretations will guide our definitions. There maybe another common node that learning is something about knowing. Well, what isknowing? These kind of questions have kept people awake late at night for thousands ofyears, and are beyond the scope of this paper.! I would like to begin my journey in a more humble and simple place by starting withan analysis of the two words in the title; learning collective.

Learning

! If we take the dictionary definition of the word learning, we are immediately struckby a couple of interesting ideas. First, it is a verb, or an action, and it has to do withacquiring something, be it knowledge, truth, habits or mannerisms. So, the question is,how do we acquire these things? Where do we go to get them? And, what do we have todo?! Throughout all of these definitions and examples, a common thread exists. There ischange. The person can now ski, when they could not before. They can speak French.They are acquainted with a new idea. They have memorized the poem. She is nowpatient.!

Yet, I feel troubled by these definitions. Can the person ski as well as HermannMaier? Do they speak French as fluently as Dumas? Do they know everythingabout that

verb

learned [lurnd] or learnt, learning.

verb (used with object)1. to acquire knowledge of or skill in by study, instruction, or experience: to learn French;to learn to ski.2. to become informed of or acquainted with; ascertain: to learn the truth.3. to memorize: He learned the poem so he could recite it at the dinner.4. to gain (a habit, mannerism, etc.) by experience, exposure to example, or the like;acquire: She learned patience from her father.


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new idea? Will they be able to recite the poem at a dinner in five years from now? Is sheas patient as her father? The answer to all of these is probably not. So, have theylearned?! The change that occurs during the process of learning (be it an hour, a week, or alifetime) is an ongoing process. We never stop learning. It is inherent to human life, and

to all life on Earth. Change occurs at a rapid pace; the destruction of a habitat due to adisaster, or the transformation of a deeply held belief when confronted with a strongperturbation. Change also occurs at a glacial pace; the transformation of an ecosystemdue to new weather patterns, or the evolution of a persons ways of thinking and seeing theworld through study and reading. In all cases, learning is evolving, and knowledge iscontinually challenged and replaced with new knowledge. Knowing and learning aredynamic.! Davis, Sumara and Luce-Kapler (2007) provide a useful metaphor and visualizationthat I would like to co-opt for a different purpose.

Linear Change

! In this model of change, learning andknowing are gradual, and continually rising.We learn and we gain knowledge in a slopeof line. The knowledge that we had before isimproved on and it gets larger and larger. Wemay travel along the line, up or down(memory and forgetting). In this model, theiris only one way to know, or to learn. The wayof the line. Everything there is to know, existson a straight line with easily defined startingpoints, ending points, and variables that are

tightly controlled. The goal is clear, and withthe right work, it is attainable. In this model,where is innovation? Where is outside the box thinking? Where is the novelty and thedifferent possibilities? It is a problematic assumption. In the 1800s, scientists believedthat they were on the cusp of knowing all their is to know (Capra, 1997). Many believedthat science would provide all the answers, and we would, in essence, know everything.In this worldview, learning would stop at the end of the line.

Spiral Change! This model provides a different set of ideas. Likethe linear line, it is moving upwards, towards a goal.Itcurls back over itself suggesting change and revisiting,

and it gradually gets bigger and wider. Time affects theknowing and learning, yet it is not as neat as thestraight line. Near the bottom of the spiral the partialcircle is small (no knowledge, yet to be learned), but asthe learner grows, the circle and the space in-betweenthe edges of the boundaries grow, suggesting their ismore room to build. The line itself will continue on, andthe space in between will continually get larger andmore expansive. It still, however, suggests growth

towards a known goal, a destination. It makes theassumption that there is only one possibility, and thatpossibilitymoves in this shape. It isstill, at its core, a simple model and simple view of how we know. It is a line.


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Fractal Change! This image is taken from fractal geometry. It starts with a simple seed, in this casea Y. There is only one rule to build this image; at the end of every branch of the Y, buildanother Y. If the rule is allowed to iterate, we get a picture that looks very much like a tree(using this seed, other seeds will cause other images). In our

metaphor, what would the seed be? If we assume the seed tobe knowledge and learning, we can see how a great variety ofpossibilities would arise over the course of a learning life. Thatlife may be one person, one cell, or an entire forest.! The main point with this fractal tree is that there isvariation, there is a multitude of change, and it is unclearwhere the learning will go. You are faced withanextraordinaryamount of choice, either conscious orunconscious, personal or environmental, etc. Do I go this way,or that way? The branches you travel along will bring you to different points, with differentperspectives. This image also continues along a path, but the destination is unclear. In

the other two diagrams, what happens if you were to go backwards on the line or thespiral? Well, it would result you going back on your learning, or your circle getting smaller,your knowledge decreasing. In this case, going backwards should be encouraged,because it opens up more possibilities, and presents different paths and ways of knowing.We can get lost in our own fractal tree and spend a lifetime trying to know and to learn.There is also the possibility to be traveling along multiple points at the same time,suggesting that learning is not held to a single place in time, in a single biological frame.! Think of this from an evolutionary perspective, or from a sociological perspective.What would have happened if the dinosaurs had not died out? Would mammals haveevolved into primates and eventually into humans? Who knows. How about the closing ofthe Silk Road? Would Columbus have set sail to find a new route to Asia and discovered

the Americas? Would the colonization of this new frontier been necessary? Would I havebeen born? Possibilities are embodied in our history, and they are endless. Many greatwriters of science fiction have taken these ideas and created amazingly beautiful alternateuniverse based on simple changes in the past (See; Bradbury, A Sound of Thunder, 1952;and Philip K. Dick, The Man in the High Castle, 1962).! Learning is dynamic. It is changing. It evolves.

Collective

[kuh-lek-tiv]adjective1. formed by collection2. forming a whole; combined: the collective assets of a corporation and its subsidiaries.3. of or characteristic of a group of individuals taken together:the collective wishes of themembership.4. organized according to the principles of collectivism: a collective farm.

noun5. collective noun6. a collective body; aggregate.7. a business, farm, etc., jointly owned and operated by the members of a group.8. a unit of organization or the organization in a collectivist system.


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! A collective is both an adjective and a noun. It modifies, identifies, or quantifiessomething else. It is also used to describe and symbolize groups, or combinations ofthings. The collective assetsis referring to the combination of money and land holdings ofa particular group of investors. Each piece of land, and each dollar they have, still belongsto each individual. It is an aggregate, a collection of items that are gathered together to

form a total quantity. It is a number.! If we parse through this definition a little further, we see a different set of values.The collective wishes of the membership, is referring to a set of something that themembers of the group hold. There is something in commonamong these people that isbeyond a mere number. They are more than just a collective of landholders adding uptheir assets to make a whole. There is something shared among them; a value, or a rule,or a set of ideals or principles that are accepted by each one of them, and that theybelieve in strongly enough to, as a group of individual people, wishfor something. Theyhave culture.! With this in mind, what would be considered a collective? Johnson (2001) suggeststhat collectives are all around us; ants possess collective intelligence, cities are a thriving

form of collectivity, our brains are a collection of individual neurons, video gamers and thecommunities they reside in, and even artificial software. The common thread between allof these seemingly diverse parts is thatthey self-organize, they form a wholethat is more than the sum of its parts,and they are decentralized (or bottom-up) systems. In other words, acollective is a collection of diverseagents that make up a grander whole.! When these elements are addedtogether, emergence is possible. Capra

(2002) defines emergence as Thephenomenon takes place at criticalpoints of instability that arise fromfluctuations in the environment,amplified by feedback loops.Emergence results in the creation ofnovelty, and this novelty is oftenqualitatively different from thephenomenon out of which it emerged.Many other theorists have many otherdefinitions, yet emergence is a term that is embodied in other terms like knowing, learningand collectives.

! If we set back and look at human society and we see that we live in manycollectives that are a major part of our lives. Our families would be an example of acollective group. It is made up of individual parts, yet it has its own unique character andis its own entity. Picture a family sitting around the kitchen table and planning a vacation,or a party. The ideas and conversation spark new ideas as the different members of thegroup contribute their own perspectives and musings, and then a final plan that could nothave been created by a single member arises out of the interactions between themembers. The collective of the family allowed for new ideas to emerge.! Along the same lines, but much larger, an entire country could be a collective.Japan, where I have lived for close to ten years, is a great example. Here, the individual isencouraged to be an active member in their own groups, and to seek identity from those

groups. People here speak openly and proudly of the groups they belong to, be it work,organizations, hobbies, or political. They see it as part of who they are, and it is

Traits of Collectivist Culture

! ! Each person is encouraged to be an activeplayer in society, to do what is best for thenation as a whole

! ! The rights of families, communities, andthe collective super-cede those of theindividual

! ! Rules promote stability, order, obedience! ! Working with others and cooperating is thenorm; everyone relies on each other forsupport

! ! In addition to individual identity, citizens areencouraged to identify as a community


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inseparable from the self. They openly acknowledge that these collectives form theirindividual identity.! More to the point to our current discussion, a classroom would be a great exampleof a collective. If a classroom is left to its own, the students will self-organize and formideas that were not possible as individuals. Emergence will happen, whether you want it

to or not! Teamwork and collaboration between students can create an infinity of differentideas and artifacts. So, if they are a collective, how are they are a learning collective?

Learning Collective!! For a moment let us step back and look into the past of human evolution andconsciousness. Merlin Donald (2001) has suggested that human consciousness hasevolved over the last few million years and has undergone four major stages. It isimportant to note these stages are dynamic in nature, and did not happen suddenly, butrather slowly bubbled to the surface over vast amounts of time.! The first stage was what he called episodic consciousness. In this stage, humanthought was limited to the surrounding environment and was based on short term survival.I need a rock to break open this nut. This is our most primitive technology. Donalds nextstage was Mimeticconsciousness. In thisstage, humans began to copy (learn) fromeach other by miming the people aroundthem. This resulted in tools that took moreskill to make and manufacture, and theholders of those skills showed (taught) others.! Moving along, we come to mythicalconsciousness. This is the stage wherehumans moved beyond just creating artifacts

for survival, and began to create stories andart to explain their existence. This wouldhave surely seen an explosion of language,and the oral-story telling tradition. The stories(cultural knowings) would have been passeddown from generation to generation, andthese memories would have been stored inthe collective cultural. This would haveoffloaded the brain of the burden of recallingdetails, and instead the culture became arepository of learning and knowing. This

would be represented in the cave painting atLascaux, which both served as artifacts of beauty and inspiration, and as warnings, adviceand help for future generations.! Finally, we get to his last stage, which is theoreticalconsciousness. In this stage,we have abstract thinking and ideas. Among the many forms of abstractions we use todaywould have been metaphor, mathematics, and advanced technology. All of theseadvances continued to free the mind to think other thoughts, and store information in theculture.! The purpose of illustrating this theory is that it shows how a collectiveunderstanding through culture evolved. Knowledge did not have be discovered or learnedby each new individual. Rather, it was built into the cultural understandings around us,

and we tap this resource when we need it. It shows how a shared mindset and similaritiesbetween agents would result in increased cognitive capacities. Donald says, Collectivity

Autopoeisis (Maturana and Varela,1987)The authors trace the idea of a systemthat creates itself from a biologicalperspective (the cell and its membraneexist is a world where the two partscreate a whole) up through bodily

systems, to human interactions, tocultural behavior. They define culturalbehaviour as, the transgenerationalstability of behavioural patternsacquired in the communicativedynamics of a social environment. Weare to culture as a fish is to water. Welive in it. Any discussion of knowledgeand knowing that does not includesocial element is flawed.


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has thus become the essence of human reality. Although we may have the feeling that wedo our cognitive work in isolation, we do our most important work as connected membersof cultural networks. Our cultural invades us and sets our agendas.! Put differently, a learning collective is essentially an organization of diverse agents(consciousness in the case of humans) that produce meaning, creating new and emergent

forms. Through the evolution of our consciousness, we have arrived at this branch in thefractal tree of humanness.! There have been many changes in the world since the days of our ancestors in thecaves of Lascaux. Our cave paintings, oral stories, tool manufacturing, and early gods,have been replaced with the internet, twitter and facebook. Advances in communicationtechnologies and networking have made us more connected to our various collectivesthan at any other time is human history. We live in a time of a new and emergent type ofculture.

Participatory Culture

! Henry Jenkins (2005) defines participatory culture as one:1. With relatively low barriers to artistic expression and civic engagement2. With strong support for creating and sharing ones creations with others3. With some type of informal mentorship whereby what is known by the most experiencedis passed along to novices4. Where members believe that their contributions matter5. Where members feel some degree of social connection with one another (at the leastthey care what other people think about what they have created)

! In order to illustrate this point and how it applies to learning collectives and thegeneration of knowledge, I would like to use the examples of Youtube and Wikipedia, and Iwould ask the reader to keep these five points in mind.! Both of these have become cultural mainstays in our modern world, so much sothat each of them is often used as a verb in colloquial language. When one asks aquestion and the recipient does not know the answer, the answer is usually, a) googleit, b)youtubeit, or c) wikipediait (the choice of which platform depends on the person, andpossibly on an inference of the questioners preferred style of media consumption). For theremainder of this section of the paper, I will have all of my references and citations directlyfrom links on either of these platforms. The spirit of sharing will be embodied.

! Wikipedia was founded by Jimmy Wales and Larry Sanger in2001. Wiki is from the Hawaiian word for quick, and it means quickencyclopedia. There are over 21 million articles posted on wikipedia in283 languages (at the time of writing this on March 27th at 22:41Tokyo Time; this number will certainly be higher by the time this paperis finished, and I am certain that this wikipedia entry will reflect thischange). It is not a perfect system of reliable information, but that isbeside my point.! Rather, I would like to discuss this as a point of collectiveintelligence, collaboration, and the passion of various groups of peoplebrought together into a collective they had no idea they were a part of. First, a short tripback in time.! In 1993, Microsoft purchased the rights to several encyclopedias and began tocreate a digital version of an encyclopedia that could be utilized on desktop computers and


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the internet. It was called Microsoft Encarta. They hired top talent, paid top dollar, andspared no expenses in bringing this vision to life. Experts from all areas of academics andculture were consulted and brought on-board to the project. All of this work wascentralized and controlled from the Microsoft offices in Washington state. In 2008, it shutdown after a decade of poor performance in the market. At its zenith, it had over 60,000

articles posted. It was crushed by a model where no one was paid, no one was in charge,and where people did it for fun.! Wikipedia was created by people who were working for free because they enjoyed it(Pink, 2009). However, it was more than that. It was the collaboration that drove people tocontribute. Right before their eyes, a tangible product was being created that they weredeeply invested in. Where else but the internet can you find a group of people who areinterested in updating and maintaining a website based on Towel Day? Or tracking thevisual history of Handsome Dan, the Yale Bulldog? In fact, the basic idea of unusualwikipedia articles is itself a massive entry! It is not just focused on the bizarre or theunusual. The entry for the Moon gives a detailed analysis of its physical structure, bothinternal and external, its relationship to Earth, the history of scientific space exploration,

and conspiracy theories associated with it (among many, many others). If you wanted tosit down and read all of the links and side entries connected with the Moon, it would takeyou days. All of the articles related to Earth? Weeks? Months? Who knows.! The entries on Wikipedia grew to be huge, intricate, and complex because amassively diverse collective of people were contributing to a massive diversity ofknowledge. The sum of all this knowledge is more than the sum of its individual parts.The editors at Wikipedia do it because they are learning from the collective andcontributing to the collective. This is an essential point. In this model, there is nodistinction between the individual and the collective. Both are learning, and both arebenefiting. The positive feedback loops apply to both circles, and amplify both to work.

!Youtube is home to an amazing variety of videos andinformation, some of it strange and quirky, others informative and

engaging. Every minute, over forty-eight hours of video is uploadedto Youtube (Allocca, 2012). Many of these videos are usergenerated, low cost and shot with personal hand-held recordingdevices. The majority of videos on Youtube have very few views.Less than 1% ever eclipse the one million view mark. Very fewvideos go viral.! When they do, their are several factors that drive them into the

cultural consciousness. According to Allocca, it starts with tastemakers or famous people.This is largely done through other sharing sites like facebook, twitter, or reddit to name buta few in an endless sea of possibilities. A famous icon (which are broad across spectrums

of interest, for example Guy Kawasaki who is a former Apple employee and now serves asan author and organizational speaker for corporations and government has close to onemillion followers) will post a link to his or her followers who will then share it with theirfollowers, where it will soon explode into something far beyond the scope of theindividual(s) who started it. It is decentralized and it spreads across cultures and groups.Someone may argue that a man sharing his love of double rainbows (please click) onYoutube is not a benefit to the cultural store of knowledge (I disagree, but that is the topicof a different paper), but it goes beyond day-to-day life happenings or strange videosabout esoteric or unique topics.! The occupy movements across the world, the pro-democracy demonstrations inEgypt, and vital news headlines and stories also travel in this manner. TED talks are now

on university syllabuses. Diverse groups of unicyclists are sharing videos from all over theworld and pushing their craft to a previously unimagined level. Language is no longer a


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barrier to entry, the visual and visceral is winning. In short, Gutenberg and the printingpress created a revolution of the written word, and Youtube (and all of the similar agentslike it, Vimeo, and DailyMotion to name a few) are creating a new knowledge sharingrevolution based on audio and video.! These videos invade our culture, and as Donald said in the previous section, cultureis where our knowledge and learning lives. Communities are born and participation isrampant. These videos stop being inside jokes or local issues, and they become ideasand phenomenon that all of us can participate in, contribute to, and enjoy. They are, whatAllocca calls creative participating communities. It is much more than 68,985,467 peoplewatching Nyan cats (as of March 28th at 10:17 Tokyo Time), it is a group of people sharingtheir ideas, remixing other ideas, and creating new ideas. It is emergence in action. It isour new Lascaux.! Marc Prensky (2001) called the people who inhabit this world the Digital Natives.Technology is their first language. They are a connected group of people who share andcollaborate, who exist in a participatory culture, and who think and process information in afundamentally different way from the generation before them. They are individuals who

inhabit a larger collective, and who, as Maturana and Varela would say, actively create theshape and existence of the their own collective.!The Threshold

! At this point, I am hopeful that you areon my side that the collective is a powerfulagent in learning and knowing. As wecontinue, I would ask you to cross a threshold(to steal a term from a colleague) with me,and continue with the assumption that the

dichotomy our culture places on collective/individual is based on a false premise. Theyare not separate agents, but rathercomplementary and nested within each other. One cannot exist without the other. Anindividual cannot be without a larger collective to reflect back on themselves, and acollective cannot be without the individuals that make it up. Both are essential for thesurvival of the other, and both are implicit in the process of learning, knowing, andintelligence. Finally, what benefits one, benefits the other.! Now, we are faced with an obvious question;

What does this mean for

teaching?

Working Definitiona learning collective is theorganization of diverse agents(consciousness in the case ofhumans) that produce meaningcreating new and emergent forms


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Teaching as Orienting Occasions for

EmergenceLearning Systems in Action

! Now that we have looked at a collective and defined our basic terms, I would like toget into the rising action of the narrative and discuss what this looks like in the classroom.The title of this section is a definition of teaching. Their are many definitions of teaching,and each teacher will probably have their own definition. Also, that definition will changeon a day-to-day, hour-to-hour, minute-to-minute basis. This particular metaphor is more ofa meta-view of what teaching is to me.! The first two words are incredibly problematic. Teaching is a term with a longhistory that is rooted in conceptions of knowing and learning (Davis, 2004). A simplesearch on a popular online thesaurus gives a stunning array of synonyms for teaching,each with its own implicit sets of values and assumptions. The web of associations is

overwhelming. Equally problematic is the word as. I could have used the is, but instead Ichose this because is suggests change and an openness to the fractal process of learningand knowing.! Rather than jump in to such entanglements, I would ask the reader to follow me intomy own web. It is important to note however, that my own personal definition is one that Ihave come to through my own experience, readings, and studies. I am not attempting tosuggest that this is THE definition of teaching, rather it is MY definition of teaching (fornow, who knows where it will evolve to next).! My view of teaching is grounded in complexity science. Before that, I came from aperspective of ecology and sustainability, but I have found the body of knowledge behindcomplexity science to have even more powerful metaphors and facets of awareness. The

seminal book in my travels down this fractal path has been Engaging Minds (Davis, 2006).For the most part, the ideas presented here are from that work, and others by the sameauthors.! In the first line of this paper I presented a quote by Ken Robinson from the LWFconference. During that same speech, he made a different quote that stuck with me. Hereferred to education as a complex adaptive system. What does this mean?! As Renert (2012) has summarized, complexity science, whose early roots can betraced to Poincar and the invention of chaos theory (Waldrop, 1992) shows that complexsystems are holistic, indivisible, and do not lend themselves to piecemeal analysis. Theyare open, evolving systems that maintain their identity in the face of constantenvironmental flux through the iterative processes of self-organization (autopoiesis) andemergence.

! Many of these terms have been introduced in the previous section. Yet, there ismuch more to complex systems that just a handful of terms, and the terms are completelydifferent depending on which discipline you find yourself in. Biologists, ecologists, networkprogrammers, economists, and physicists (to name a few) are all using the language ofcomplex adaptive systems, and using different language to define the terms (see Waldorp,1992 for an excellent trans-disciplinary overview). In education, there is a growing body ofliterature that is using terms from complexity, chaos, and fractal geometry. The rest of thissection will focus on investigating one such set of terms presented by Davis, Sumara, andLuce-Kapler (2006).!! Id like to start with a completely overwhelming diagram and dive in.


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Enabling Constraint! !! Enabling constraints may appear to be an oxymoron, however it is quite simple. Bylimiting choices, you increase possibilities. It is asking for harmony when creatingactivities in the classroom between possibilities that are a) too confining and prescriptive,thus shutting down the potential for new thinking to emerge, and b) too open-ended andcan lead to frustration and lack of productivity. Davis (2006) offers a helpful example in thefollowing learning objectives:

a) By the end of this lesson, students will demonstrate their understanding of someof the core elements of a poem by identifying the rhyme structure, the principalfigurative devices, and the core themes of Rime of the Ancient Mariner.

b) Students will write original poemsc) Students will explore poetry-writing process through inventing characters and

plots based on unfamiliar items and unexpected juxtapositions.

! The first is too confining, and the learning will result in little that is new or novel.The second is too wide open and will lead to such varied responses that their will be noredundancy among the agents. The third has sufficient constraints, and sufficientopenness. It ensures that everybody in the collective is working on the same set of shared

commonalities, yet it is open enough that it will lead to great diversity in the variety ofinterpretations that it will occasion.


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Redundancy and Diversity

! Intelligent unities are simultaneously stable and innovative(Davis, 2007). If wereject some of our closely help dichotomies that we spoke about in the previous section,we may accept the phrase that a complex system can be both steady and unchanging andwildly creative at the same time. In fact, these two seemingly polar opposites are actuallycomplementary, and completely necessary for the other to exist. Like our distinctionbetween individual and collective, there is no difference between the two.! Redundancy is the part of a system that is shared among its agents and allowsthem to work together. In the case of a collective of people, this is enabled by sharedlanguage, culture, and interests. In fact, most groups have much more in common thanthey do differences. This sameness allows for errors within a group to be corrected by theother members of the group. The error is fed into the collective, and the redundancy of thecollective will correctthe error. In education, this is implicit on many levels, as the kids inour classes often tend to be from similar age brackets, live in the same geographical

locations, speak the same languages, and share common interests (even within a classlike mine where the students are from a variety of different cultures and backgrounds, theycontinue to have much more in common than they do differences).! However, if a system is too redundant, it loses an element of its intelligence. Itbecomes unable to respond to new perturbations and is unable to respond to a newstimulus. This is where diversity comes into play. The strength of a learning collective liesin its ability to produce different ways of knowing, where the feedback loops amplify andcreate new interpretations. These diverse ways of seeing the subject allow for newunderstandings to emerge as the different ideas bump into each other (Davis, 2007).! In the classroom, this happens when students are working together and they bringtheir diverse understanding together to create a new idea. If a student who possesses a

high spatial sense is working with somebody who possesses a heightened number sense,their diverse ways of seeing the mathematical problem will amplify and each one will beable to see the problem on a much deeper level. Their combined ways of knowing willproduce a new way that is only possible through their interaction with each other.! We have another potential dichotomy arising here, in that the collective benefit isseparate from the individual benefit. Yet, I see them as amplifying feedback loops, wherethe collective intelligence is increased in harmony with the individual intelligence. Theysupport and enable each other to grow.

From the Classroom! I asked my class one day what they saw as my role in the classroom. After we gotover the initial hump of the teacher as the center of knowledge, they began to see that I

play many roles in the collective. We made a poster andcalled these Teaching Roles, and they included suchrepresentations as guide, leader, narrator, assistant, editor,reflector, observer, consciousness, etc. (the list has beenupdated since the photo was taken). Most of our meta-cognitive practice in class is focused on the what thestudents role is, and rightly so. Yet, at the same time, I ama part of the learning collective, and maybe that explicitunderstanding of what I was doing could be used to makenew insights.! On several occasions during the following months, my students have oriented

attention to the role I was playing. They have asked me to stop being an observer and


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start being a leader, or to stop being a critic and start being a listener. In each of thesecases, they are enacting the principles of redundancy and diversity. They are asking meto stop giving new ideas and overwhelming the system with too much diversity, or to stopcontributing to the redundancy and start contributing to the diversity.! We also made a list of learning roles that the students may move between,organizer, synthesizing, creator, editor, visualizer, criticizer, etc. It was never my attentionto have students choose a role and then enact this role in a given activity. Rather, I washoping that they would be mindful and reflective on what roles they were playing duringwhat times and during what type of activities, and how they bounce between roles frommoment to moment. After activities, I occasionally ask them to reflect in their journal onwhat role they thought they played.! A couple of entries have caught my eye. One student reflected that we had toomany creators and not enough organizers. This student is saying that the group was toodiverse, and they could not move forward because they lacked a strong redundancy.Another said, we worked well together because J was being an creator, K was being asynthesizer, and E was being a organizer. This student is recognizing that the harmony in

the group is correlated to the diversity and redundancy that led them to work togethersuccessfully, and each member of the collective benefited in a way that made themindividually satisfied. Reflections of this sort help students to notice the harmonies ofcomplex adaptive systems, and to make better choices in orienting their own attentions tothe aspects of those systems that will lead to reciprocal benefit of both the individual andthe collective.

Nested Systems

! A learning collective, as we have seen in the previous section, does not follow alinear path. Learning occurs in an iterative way, folding back on itself and expanding what

is possible. Iteration can be roughly understood as the process of repeating a processand then using the new results to frame the next process. In fractal geometry, this wouldrelate to the simple rule that grows into incredibly complex wholes. In the case of alearning collective, it means that learning isnt accumulated, but rather it is revisited andthen expanded.! Ill give an example from my practice as a primary school teacher. At the beginningof a students journey into the concept of addition, it is a process of putting two groupstogether to get a whole. I have three bananas, and she has four; together we have sevenbananas. As the student develops this concept, they are faced with challenges to how thisprocess works. We introduce the addition of fractions, which forces the student to rethinkhow they combine two parts, since they are no longer combining wholes. Again, we seethe addition of integers to the mix, where now we are adding two numbers together thatare not necessarily accumulating into a larger whole.! Throughout this journey, the student is asked to elaborate their understanding ofaddition (for an excellent look into a similar journey with multiplication, see Is 1 a primenumber?by Davis, 2008). They are asked to revisit their previous understanding andexpand on it. The original understanding of addition is not thrown out or discarded. It isstill important to see addition as combining two wholes to get a larger sum. Rather, thestudent is asked to add a new layer to their nested circles of understanding, and to keepboth understandings simultaneously. The circles are getting larger, but the original circle isstill implicit in the outer layers.! On a collective level, we are knee-deep in nested systems. As we saw in the lastsection with the ideas of Maturana and Varela, our biology is implicit within our physiology,

which is implicit in our personality, which is implicit in our interactions with fellow member


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of the various collectives we inhabit. Also, we move between collectives. We have ourfamily lives, our professional lives, our cultural lives, our national lives, and our humanlives. Each is an elaboration and an expansion of the others. I am at the same time, afather, a teacher, a Canadian, and a human. The distinction between these levels isartificial. They all exist and make up the grander whole that is me.

! This is also true in the classroom. As Davis (2007) says, An individual, a dyad, asmall group, a cluster of groups, and the whole class are all knowledge producing systems(ie learners). None is privileged over the others; rather, these nested systems are mutuallysupportive and intelligent, unfolding and enfolding in one another.! One way to approach this type of collective learning in the classroom would be toset up activities that use these principles in order to elicit a deeper understanding. Whenintroducing a new topic, a teacher could start with an individual reflection on the questionor idea, have each person explain and share with a partner, have each set of partners findanother set of partners, and so on and so forth until the whole class is working togetherand sharing their ideas. On each level along this simple lesson progression, theindividuals perceptions and ideas are being both reinforced by the ideas of others, and

challenged by different ways of knowing. Eventually, what emerges is a collectiveunderstanding that is far richer that where it started with the individual.

From the Classroom! I am in the midst of a unit with the central idea of every culture is unique. In order tostructure the shape of this unit and provide a more in depth and complex understanding ofculture, I used a nested symbols metaphor. We started our journey into culture by definingwhat are uniquely human attributes to culture. What makes us human? What, if any, isthe shared human culture? We did several activities to help us answer these questions,and when the group agreed on a shared set of attributes and ideas, we shrunk the circleand moved to the topic of national culture. We repeated this process several times (local,

family, classroom) until we were left with the smallest circle in the middle, our individualculture.! Through this structure and format, the studentswere able to understand some of the variouscomplexities that arise from clashes of culture and howtheir personalities and identities are shaped by thecollectives around them. We also saw that our ownclassroom had a culture of its own, and while thatculture helped us to understand the whole diagram, itwas not the only agent implicit in our learning. Eachlayer of the diagram was effecting the others, andpositioning yourself in a given circle at a given time

brought up a plethora of complications and problematicquestions.! Another simple activity I have had success with issomething that I co-opted from a diagram in Engaging Minds. When looking at a conceptor big idea in class (in my case it was a unit on recycling) we try to brainstorm and look atthe idea from many different levels. Using the diagram on the left, we start with the basicbiological implications and move our way upwards until we reach a planetary, orenvironmental impact or understanding.


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Negative and Positive Feedback

! This is a tricky one and it is important to make a distinction right from the beginning.Our society has an understanding of negative feedback as a bad thing, something thatdelimits potential and stops growth; and positive feedback as something beneficial toourselves. Bad vs. Good. Complexity science suggests a different view of these terms.! Rather than think about it as negative and positive feedback, I will steal a term froma teacher of mine and use the term regulating feedback (negative) and amplifyingfeedback (positive).! Amplifying feedback is a loop in the learning collective that pushes the collectiveoutput in a certain direction. One child gets excited about a project, her excitementspreads to another, and soon you have the whole class engaged and involved. Also, anamplifying feedback loop could work in another manner, where a task to too difficult andleads to decreased resilience which spreads through the collective until everybody isfeeling disengaged and frustrated. The important point to remember here is that theoutput continues along this amplifying path, whether for the good or the detriment of the

group.! Regulating feedback loops work in a different manner. They stabilize or dampenthe system by feeding their output towards a limit. If the goal of the class is to get to acertain grade or score or certificate, then the scope of possible paths of emergence andlearning are limited to that goal. Cheating and other counterproductive measures maybreak out (Meadows, 2001). However, a collective may also have a shared set ofbehavioral values and rules that limit the scope of what is acceptable and allow thecollective to remain at a level of shared dynamics. If speaking out of turn is frown upon bythe group as rude and disruptive, then the feedback loop will stabilize that behavior andcreate more opportunity for all voices to be heard, which will lead lead to a greaterdiversity of opinions being expressed and more possibilities.

! Teachers can occasion these principles to motivate and challenge their students byexpressing greater confidence in all learners or groups of learners and selecting tasks thatare challenging but do-able (Davis, 2006). This would be an example of occasioningamplifying feedback loops. Similarly, a teacher can create a shared environment built onrespect and responsibility through class rules like a talking piece (similar to the conch inLord of the Flies), which creates a regulating feedback loop that opens up discussion andleads to new ideas.!

From the Classroom! In my grade 5 math class I had several students who were routinely finished beforetheir peers. As a way to keep them busy (interpret this as keep them out of hair), I allowedthem to go onto one of the class iPads and use an interactive math app to help theirconceptual understanding of fractions. What emerged however, was rather thanexpanding their learning, it was giving them cause to rush through the work in order to playthe game. An amplifying feedback loop (positive feedback loop) of rushed work anddiminished effort was created which quickly spread through the class. Before I knew it,everybody was rushing through their work and not taking the proper time to try andunderstand.! In order to right this wrong, I admitted my mistake to the class and asked them toinstead help their peers to finish their work with more focus and conscientious effort. Inessence, I asked them to correct my mistake and work towards the goal of the whole classunderstanding so that everybody could use the technology together. In a sense, I used aregulating feedback loop (the common goal of finishing our work together to a specificstandard), to correct an amplifying feedback loop which had spiraled out of control.

! It is a mistake I will never make again.


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Neighbor Interactions and Decentralized Control

! In Walter Isaacsons biography of Steve Jobs (2012), he tells a very interestingstory. In the early days of the founding of Pixar animation studios, the plans for the HQwere brought to Jobs for approval. Originally, there were three buildings in the complex;animation, marketing and technical. Jobs stated empathically that this was a gravemistake, and pushed the decision makers at Pixar to make one large center, rather thanthree separate structures. He wanted theoffices and desks mixed up so that all threedifferent groups would see and interact withone another. Also, he pushed for anotherstrange request, rather than having manybathrooms spread throughout the complex,he wanted one very large bathroom at thecentre of the complex to drive foot traffic in

and out of a central place. Obviously, abuilding the size of that has more than onebathroom, but according to Isaacson if youspend any amount of time in the building,you will notice that the central restrooms area hub of conversation and activity.! Jobs vision was a decentralized network, where agents could come together andinteract with each other. Google has used this principle to their advantage in the design oftheir offices and common rooms (see photo). These places are designed as fun placeswhere employees can rest, play and socialize with fellow workers. Most importantly, thecommon rooms are not individual to each department, but are shared among many

departments. The employes have a voice into the design, purpose and functionality of therooms.! The purpose for this is obvious. It is the sharing and exchanging of ideas across adiverse range of disciplines that leads to innovations in other areas. The structure is inplace for ideas to stumble across each other and bump into each other (Davis, 2007). It isthrough these interactions of agents that new interpretations arise. In both of theseexamples, there is no central body in charge, telling the agents to go and share ideas (it isdecentralized). Similar to the wikipedia model from the first section, this is a participatoryway of being, where agents are given autonomous choice, and the environment ispurposefully set up for them to interact in a way that is meaningful, social, and beneficialfor the individual members of the collective, as well as the collective as a whole.

From the Classroom! I recently tried to reduce the amount of coffee I drink in a day. To help, I decided toattempt to drink more tea. I brought an electric kettle from home, a plastic tray, and anassortment of different teas that I bought from the local supermarket. I set up a little teastation in the corner of the class.! A couple of days after this change was made a student asked me why I wasdrinking tea. I honestly replied that too much coffee is not good for you and I am trying tocut back. He agreed with me and said that he also loves to drink tea, as it reminds him ofhis time with his grandfather. I suggested that he bring in his own cup and bags of tea andwe could have a cup together during morning break.! Within a week, the entire class had brought in their own cups and bags. They didnot ask, I did not have to give permission, they just did it on their own. My morning cup of


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tea had transformed into a social activity. More than that though, this time was more thatjust drinking a cup of tea. The students would talk about their interests, be it video gamesor drawing, and give each other advice and pointers. They would also use this opportunityto create new games that they could play at recess, talk about projects that we wereworking on in class, share projects that they were undertaking at home, and set up play-

dates after school and activities for the weekend. New ideas emerged because there wasa structure in place for them to do so.! Not every child participated everyday, but they would come in and out of the teacollective as they wished or when they wanted to have a chat about something. The breaktime was theirs to do as they pleased, and some students continued to prefer to jump intotheir iPhones or books. Yet, they had this place to come to if they wanted to talk, and

when they wanted to use it, it was there for them.! I had inadvertently set up a decentralized systemaround the tea station, one which has proved to be avaluable source of ideas and inspiration, not just fortheir school work, but also for their play.

! It has also led to my favorite line that a studenthas ever uttered in my classroom, Ahhhh, graphing isso much more enjoyable when you have a cup of tea.! (On a side note, I have switched back to coffee)! Another example of neighbor interactions anddecentralized control would be an activity that I have

done on several occasions involving GoogleDocs. The basic premise is this; you set agroup of students to a task on a joint document and have then share and create an artifactthat is greater than the sum of its parts. While in the document, students are focused ontheir individual task, yet at the same time they are aware that there are many other

students working on the same task in the same document. Since the goal is collaboration,each student expands and amplifies their classmates ideas. This is a constant process,and although it is a challenge on their attentional systems, the end result is usuallysurprising and invigorating. Ideas create new ideas, which spawn new thoughts, whichlead to new insights. Through a hive like production of thoughts, the collective is elevatedand the individual understanding is strengthened through the diversity of thought andopinion. The agents are interacting with each other, not is a physical sense with theirbodies, but mentally with their ideas. This invariably leads to a decentralized system, aseach student is free to connect with the thoughts they choose to connect with, and free toexpand on the areas that interest them. Since the activity is largely anonymous, socialcliques and groups that exist in every collective are discarded, and the collective functionsmore as a whole than it would while in the physical world of face to face contact.

! A very interesting activity that I am eager to try again and analyze further.!Consciousness of the Collective

! Individuals brains have co-evolved with their environment to learn and remember.Yes, there are ways that we can improve the remembering process and weaken theforgetting process, but for the most part, our brains know what they are doing. Culturealso plays a major role, as we have seen in the previous section with the work of MerlinDonald and the evolution of human consciousness.! Collectives memories on the other hand, need more specific orienting strategies.One of the roles of the teacher in this view of teaching is, as stated with the title of this


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section, teaching as orienting occasions for emergence. In this view of teaching, two ofthe most important roles of the teacher are orienting and preserving.! Preserving what is known by the collective so it can be recalled later is part of aclassroom and a learning system. The teacher plays an important role in this task, and isable to create a narrative that keeps the

students grounded in the presentsense with a firm grip on their sharedhistory. There are many ways thatthis is done in a typical classroom;wikis, photos, work on the walls,posters, etc.! Within this context ofpreserving is an element of selecting.The teacher may select whichinterpretations are going to beremember by the class, and what

aspects of the collective will beallowed to flourish and grow. Thiscan be problematic and powerful,when attention is directed to oneplace, shadows are cast on another. The main point however is that during this processwe have the idea of directing the groups attention.! Orienting has to do with the communal cognition of the group and the direction ofattention to what is salient, new, emerging, etc. As Davis says, teacher as theconsciousness of the collective is a suggestion that the teacher is responsible forprompting differential attention, selecting among and emphasizing the options for actionand interpretation that arise in the collective. He continues with teaching cannot be

about zeroing in on predetermined conclusions. It must be something beyond thereplication and perpetuation of the existing possible. Rather, teaching seems to be moreabout expanding the space of the possible and creating conditions for the emergence ofthe as-yet un-imagined. The emphasis is not on what-is, but what might be broughtforward.! This is a powerful metaphor for teaching and schooling. I have it printed off andglued above my desk. But, philosophy aside, how practical is this in a classroom andlarger educational settings? I realize that this is an incredibly problematic question toanswer and that it has no prescriptive formula to follow. The larger system must beunderstood and taken into account. Yet, I have some observations to make and a coupleof examples that I have noticed from my own practice.

From the ClassroomUnicorns! On the first day of school I was joking around with my new class and telling them astory of a friend of mine. This friend is a unicorn. He loves to learn and is very curious.The kids immediately tried to prove to me that this unicorn was fake and that I was lying.Yet, no matter what they said, I had an answer to the question that proved the existence ofunicorns. They loved the activity and towards the end they had a better understanding ofmy style of teaching. I was telling through my story that I was interested in the way theythink. Creativity, curiosity, story telling, asking good questions, and having fun was whatthey were being asked to bring to my classroom. However, something else emerged that I

do not anticipate.

Whose class is it?In Japanese HS and JHS, teachers do not havetheir own classroom. They rotate through differentclassrooms. The room belongs to the group ofstudents that inhabit it. They spend their wholeyear in the same room, learning each subject in anenvironment that belongs to them. Over thecourse of a year, the classroom transforms from anempty room with bare walls, to a living fossil recordof the tear behind them. At the end of the year, it

all comes down, they move to a new room, and thecycle repeats itself.


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! The kids began to refer to themselves as unicorns, and the ideaof a unicorn had soon become our class symbol. Kids brought inunicorn pictures and dolls, and started writing stories about their ownunicorns. The unicorn became a powerful metaphor for being creativeand thinking about new ideas, and the children and I routinely evoked

that metaphor during class. When we created a wiki for our class, wenamed it after unicorns. It has become a tool in our communal toolboxthat is used to orient attention to or from what we are trying toaccomplish. The unicorn is a consciousness of our collective. Thisemerged as a metaphor in a decentralized manner without any direct

plan or action on my part (aside from telling a goofy story). Yet, there are ways that wecan occasion the possibility for this type of emergence.

The Class Brain, or The Narrative of Us! My classroom, as a colleague has so eloquently put it, is an absolute mess. I puteverything up on the walls. Every last poster, piece of paper, or pamphlet from a field trip

we went on is stuck to the wall. At the moment of writing this, I am sitting in my class. As Iscan the room I see the following items; about 20 apple juice cans lining the inside of abookshelf, towels hanging from the ceiling, a cardboard box cut into the shape of eaglewings with a plastic tiger taped to the underneath,a Fujica 8mm video camera, paint brushes dryingon the window sill, a tire, a tangle of wire coathangers, three 2-gallon tubs of playdoh, and apicture of Harry Potter glued to a ruler and stuckto the whiteboard. To an outsider, it appears tobe a chaotic and messy. To the unicorns ofgrade 5 and 6, it all makes complete sense.!

Our history is embodied and engraved inthe room. When we speak about a concept inour unit on culture, we can jump and look at anartifact that reminds us of that from our unit anancient civilizations. When a child is havingtrouble with a math problem, I can suggest thatthey look at a similar math problem that was done previously in the year for inspiration orideas. I do not know what they will use the environment for, but by making it rich with pastexperiences that were meaningful, I am occasioning the possibility to interact with it. Inthis case, the classroom environment is the consciousness of the collective.! Going back to my list of items that I spotted around the class, I would like orientyour attention to the tangle of wire coat hangers. We used them for a creative thinking

activity earlier in the yearand then my kids tangled them up andhung them from the window of the classroom. They have beenthere ever since. Since December, on threeseparateoccasions Ihave heard the question, can I use a coat hanger? If we rememberthe layers of evolutionary consciousness from Merlin Donald andsection one, the first layer was episodic consciousness, in whichthe eyes scan the environment for a tool to solve the problem.! First, it was a math problem. A student was trying to figure outhow find the area of a circle and needed a circle template to movefrom place to place. She made a circle out of the coat hanger (notan easy task in and of itself!). Second, making a model airplane out

of cardboard. The coat hanger was substituted as a


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bone,similarto a bat wing. Third, a student was trying to think of a way to make a modelof a planet with a moon. She used the coat hanger to hold up the planet, and a paper clipto hold up the moon. A colleague asked me, why do you keep that big tangle of coathangers around? I responded with; you never know when you are going to need a coathanger. Steven Johnson (2008) said it best in an RSA animation; environments that are

unusually innovative create a space where ideas can mingle, swap, and create newforms.

Cave Paintings! In the previous section I talked about Lascaux in France. In my class, we made ourown version of the famous cave paintings. At critical points during our investigation intoancient civilizations, I asked the students to stop and reflect on an idea we had justencountered (for reference we were creating our own civilization at the time). I askedthem to create a story that would representthis concept to a future generation, and then Iasked them to write that story using only

pictures, such as the pictures done atLascaux. Through-out our unit and thebuilding of our civilization, these picturesserved as a reminder of the hurdles we hadovercome and the lessons we learned.! It is important to note, that in thissituation, the teacher was the one driving thereflection asking the collective to rememberand make meaning. In other words, I wasorienting their attention to the point oflearning that I wished them to focus on. This

would be an example of teacher as consciousness of the collective.

Webs of Complexity! At the end of every unit of study, we gather as a group and examine all the artifactsfrom our learning and create a narrative of the unit that just passed. We swap stories,laugh, talk about our success and our failures, and what we could do differently next time.One of the biggest aspects of this process is Big Ideas. As a group, we focus on the large

concepts that we studied, or the big concepts weunderstood.! This has been an emergent process. At thebeginning of the year, it was me who would

produce most of the ideas, and I would orienttheir minds to aspects of the grander narrativethat I thought were important. Yet, as the yeargoes on, the students have learned from mymodeling and are beginning to notice the ideasthemselves.! After we make a list of these Big Ideas, westick them on the wall outside our classroomand use string to connect them together. Everytime the students see a link between concepts

or ideas, they are encouraged to explain their reasoning to the group, and if everybodyagrees, we connect the ideas. This visual artifact has served as a source of many writingactivities, and is like a narrative of the year gone by.


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Mindful AwarenessGetting lost in the branches of the fractal tree

! If knowing and learning are dynamic processes, then teaching should be too.Complexity science, Chaos theory and Emergence all have very powerful metaphors andimplications for education. However, it is NOT a prescriptive method of teaching, and it isNOT a way to teach. Rather, it is about a mindful awareness of the environments that we

inhabit, whether they be biological, cultural, or environmental. An understanding of howthe characteristics of a complex collectives learning system operates would help teachersto create occasions to allow the emergent nature of these activities to come to life. And inthe end, that is what learning and teaching is all about to me, life.! Scanning the literature of complexity science across a broad spectrum of domainsand disciplines, it is apparent that their is no simple definition of what a collective is, orwhat a complex adaptive system is. There is no clear guide to complexity or emergence.It is an elusive thing to define, partly because it is not a thing, and partly because we areso embedded in it that is makes seeing it troublesome. Like Maturana and Varela (1988)said, a fish does not understand water because it spends it whole life in it. If a bookarrives on your doorstep that claims to show you how to teach a collective, or how to

control a complex system, I would be wary and skeptical of such a claim. It is aboutseeing, understanding, and being aware. It is NOT a standardized formula.! Even within the discipline of education and complexity, there is no clear consensuson what it means. If a joint definition of complexity in education emerged, I feel it woulddampen the diversity of the system and take away from the robustness of education. Myown ideas about this topic are formed by my own research and understanding. A differentperson who considers themselves to be a complexivist(I use this word not because I likeit, but rather because I cannot think of a more appropriate noun) will have a differentapproach and definition. And, those approaches and definitions will change. They willevolve, and they will grow. I have attempted to share how I interpret and embody thesecharacteristics in the classroom, but I am NOT suggesting that they be copied. Some ofthe ideas presented in this paper may be transferable to other collectives, while others are

completely unique to my classroom collective and my life.! So, what would be the common thread that exists between these activities, andwhat would be the similarities between other complexivistteachers? I believe this has todo with a mindful awareness of complex learnings environments. An acceptance of theadage, life is complex. It is a tuning in to the life of the classroom, and a desire to continueto hone and practice the ability to skillfully regulate and amplify that environment. Also,there is a shared understanding in the role of education as more than learning facts andskills, by helping kids to be aware on a conscious level of how the nested circles of co-implicated learning systems affect and influence their lives. This, to me, is one of thecentral aims of education; to be aware of the stories and narratives of life.! Complexity science is a lens for living in the world. All collectives are complex, andall classrooms are adaptive systems. Having a sense of where you are in the system, andwhat is happening around you is a skill that I will continue to practice mindfully throughout

Ineverteachmypupils;Ionlyattemptto

providetheconditionsinwhichtheycanlearn

(AlbertEinstein)


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my teaching career. My definition of teaching; Teaching as orienting occasions foremergence, is one that will continue to evolve and change. I hope to continue to travelalong the branches of the fractal tree and see what new possibilities arise and emerge.Most importantly, I hope that this self-reflection and attention to my environmentstranslates into greater learning possibilities for my students, and expands the space of

what is possible.! At this point, I do not wish to summarize and round off my thoughts into a straightforward one-line sound-bite. The point of this whole journey has not been to arrive at apredetermined place, but rather to arrive at different interpretive possibilities. Educationhas too long been focused on the predetermined place, and not on the multitude ofpossibilities.

! A final thought from Briggs and Peat (2000):The sad fact is that our organizations isolate and and keepeach of apart as much as they hold us together. We have

assumed that because individuals are essentially separateparticles, collective action must be coordinated through theseimposed external structures. But what if we dropped thatassumption and allowed for self-organization to create ourcommunities? What is we intentionally forged our socialsolutions in the fires of creative chaos?


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References

Davis, B. and Simmt, E. (2003). Understanding learning systems: Mathematicseducation and complexity science.Journal for Research in Mathematics Education,

34(2):137-167.

Maturana, H.R. and Varela, F.J. (1992).Tree of Knowledge. Shambhala.Johnson, S. (2001).Emergence: The Connected Lives of Ants, Brains, Cities, and Software.Scribner.

Capra, F. (1997). The Web of Life: A New Scientific Understanding of Living Systems.

Davis, B., Sumara, D., and Luce-Kapler, R. (2007). Engaging Minds. Lawrence ErlbaumAssociates, Mahwah, NJ, USA.

Davis, Brent. Inventions of Teaching: A Genealogy. Mahwah, NJ: L. Erlbaum Associates,2004.

Capra, Fritjof. The Hidden Connections. London: HarperCollins, 2002

Donald, Merlin.A Mind so Rare: The Evolution of Human Consciousness. New York:Norton, 2001. Print.

Jenkins, Henry. Confronting the Challenges of Participatory Culture: Media Education forthe 21st Century. Cambridge, MA: MIT, 2009

Dick, Philip K. The Man in the High Castle. New York: Vintage, 1992.

Bradbury, Ray. The Stories of Ray Bradbury. New York: Knopf, 1980.

Waldrop, M. Mitchell. Complexity: The Emerging Science at the Edge of Order and Chaos.New York: Simon & Schuster, 1992

Meadows, Donella H., and Diana Wright. Thinking in Systems: A Primer. White RiverJunction, VT: Chelsea Green Pub., 2008

Isaacson, Walter. Steve Jobs. New York: Simon & Schuster, 2011

Briggs, John, and F. David Peat. Seven Life Lessons of Chaos: Timeless Wisdom from theScience of Change. New York: HarperCollinsPublishers, 1999.

Renert, Moshe. "Mathematics for Life: Sustainable Mathematics Education." For theLearning of Mathematics 31.1 (2011).


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Websites

Robinson, Ken. "Sir Ken Robinson - Leading a Learning Revolution." YouTube.

YouTube, 22 Feb. 2012. Web. 11 Apr. 2012.

Talks, TED. "Kevin Allocca: Why Videos Go Viral." YouTube. TED, 27 Feb. 2012. Web. 11Apr. 2012.

Talks, TED. "Daniel Pink on the Surprising Science of Motivation." YouTube. TED, 25Aug. 2009. Web. 11 Apr. 2012.

Animate, RSA. "WHERE GOOD IDEAS COME FROM by Steven Johnson."YouTube.RSA Aniimate, 17 Sept. 2010. Web. 11 Apr. 2012.

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