Fractals, Self-Organizing Principles, and Self-Segregation

Fractals are all around us

Came across this study on planting patterns, “Fractal planting patterns yield optimal harvests, without central control” that bears some closer review.

What’s fascinating about this is that it seems to present a real-world solution to a problem commonly referred to as the “tragedy of the commons,” in which the self-interest of individuals leads to the destruction and overuse of shared natural resources.

Spatial patterning often occurs in ecosystems as a self-organizing process caused by feedback between organisms and the physical environment. “The centuries-old Balinese rice terraces are also created by feedback between farmer’s decisions and the ecology, which triggers a transition from local to global scale control,” explains Lansing. “Our model shows for the first time that adaptation in a coupled human-natural system can trigger self-organized criticality.”

This is absolutely fascinating, and it’s interesting to consider this in relation to other ideas on a “self-organizing criticality” that we’ve explored here before, such as in brains and sand piles.

For proponents of ed reform who argue against centralized control, this seems like it could be worth digging into further.

The aspect of fractals here is also tantalizing. After chatting with a colleague about the article, he referred me to Ron Eglash, a mathematician who has studied fractals in African history and culture. Do yourself a favor and watch his TED talk, it will blow your mind.

Eglash raising an interesting point about self-organizing principles: they can be wonderful, as in Google search, or our brains. But there is also a dark side, such as in the spread of HIV or the damaging effects of capitalism. He suggests that the fractal algorithms employed in Africa could present us with “robust” “ways of doing self-organization — of doing entrepreneurship — that are gentle, that are egalitarian.”

I’d love to explore more about how the fractal design of school structures and systems could be utilized for a productive purpose. Please share if you’ve got more on this.

Another interesting angle on the Balinese rice farmers is suggested in an earlier study reported also on, “Phase transitions of rice farmers may offer insight into managing natural resources.

Their study and modeling seems to suggest that smaller self-segregated communities within a society are desirable in the long-run.

They found that the downside of the segregation is that it increases the social disharmony throughout the society as a whole. The upside, however, is that the social disharmony within each community becomes very low. In some communities, individuals are more likely to keep cooperating with each other—using the shared resource fairly—compared to the situation without segregation. These results were very similar to what the researchers observed in the segregated society of the Balinese subak.

This seems to be a dark side unmentioned in the more recent study on how the Balinese farmers exemplify a self-organizing society in harmony with nature. Or perhaps this isn’t a dark side — it’s a suggestion that some self-segregation can be positive.

But I don’t know anything about the Balinese subak, either, so not sure how much to read into this. Certainly worth going deeper into this. If any readers have knowledge of African fractal algorithms or Balinese subaks, please share!


Sunday Smorgasbord: Race, Pedagogy, Business, and Science



Andrew Rotherham, aka Eduwonk, advises us to “buckle up” and expect more of the sort of suburban bred “local control” fearmongering against diversity and federal intrusion seen in this op-ed.

For more context and history on the racism that underlies that brand of fear, as well as to understand how it relates to crusades for local control of public land, read this excellent longform piece.

Federal protections can backfire, however, such as in this sad irony of fair housing laws used to prevent “community preference” in lotteries for affordable housing in San Francisco.

Even in diverse schools, students of color can still be denied a quality education. The question seems to be: how do you “create a more equitable environment and also keep the most powerful parents happy”? It’s a sad question to have to ask, but finding a solution to it will determine the success of future efforts in increasing school diversity.

Diversity is worth it, though, at least when it comes to working on a team. The work feels harder, but the outcomes are better. (This parallels the idea of fostering “desirable difficulty” in classroom learning.)

Because we all want money.


The inimitable E.D. Hirsch, Jr., makes the case that “good teaching can often depend more reliably on the coherence of the wider system, and on the cooperation it brings, than on virtuoso performances.” Stop blaming the teachers, and start developing better systems and curriculum.

Doug Lemov interviews Tim Shanahan, who articulates the nuance of teaching reading strategies, provides a sound definition of close reading, and dispels the myth that leveled reading is worth any teacher’s time.

At the Windward School in Manhattan, they are using gesture and movement to teach reading to students with disabilities, and having powerful results. There’s something to this connection between corporeal movement and conceptual understanding; in the math realm, research suggests the same area of our brain that counts on our fingers continues to be activated when we move to higher level problem-solving.


Speaking of bodies, traders who are more effective listen to their bodies when making decisions under stress, rather than their minds.

We always hear from business leaders about how we’re not equipping our kids enough in K-12 with the high-level skills they are trying to hire for. But the FiveThirtyEight argues that there’s less of a skills gap, and more of a lack of job-specific training provided by those businesses.

In the most positive and exciting news in this presidential campaign thus far, both Donald Trump and Hillary Clinton are strongly committed to investing in infrastructure.


Our brain’s connectivity and wiring may be determined by its physical structure, not simply by its chemistry.

It may be possible to predict life success from a test at birth. This has much to do with “education-linked genes.” Which is scary.

And an important reminder that context and nuance is much needed when discussing research.



EdBuild Report: Can the US overcome the ‘fault lines’ of segregation?

EdBuild has released a damning indictment of economic segregation in the United States. The report and interactive sheds much-needed light upon an illogical system that ensures poor kids are kept segregated by arbitrary district lines and confined to poorly resourced schools.

I urge you to read EdBuild’s full report. There’s a scathing resonance to the sentences that helps to convey how cruelly unjust and unnecessary school district lines are. Here’s one example:

“The fact, too seldom acknowledged, is that district boundaries themselves compound the inequalities that our public schools were intended to conquer. In present day America, we allow invisible lines to determine the fate of our youngest and most vulnerable citizens.”


“Our wealthy are consigning lower-income students to a lesser caste by cordoning off their wealth and hiding behind the notion of ‘local control’.”

Reading this report, I couldn’t help but think of parallels to the current political battle on NYC’s Upper West Side over potential rezoning of a school district. The rezoning would place a well-off segregated school in the same zone as a segregated school that serves the projects just down the street.

Some well-off Upper West Side parents have made statements such as:

“It’ll take thousands, maybe a hundred thousand dollars off the value of my apartment.”


“We moved here basically for that school, and that school is kind of like our right.”

Is this what a public school has become? A status symbol of the property value of a neighborhood?

Even “progressive” NYC Mayor De Blasio has defended the rights of private property owners to their own segregated public schools:

“. . . families who have made a decision to live in a certain area . . . made massive life decisions and investments because of which school their kid would go to.”

Our public schools have become de facto private schools for those with money and means. Such parents can “invest” in the property that allows them to live within the district boundaries of their chosen school. They then can rely upon hale and hardy school district boundaries to keep less fortunate kids out. In this dismal reality of the US education system, instead of a Game of Thrones, it’s the Game of School Zones. This cut throat game determines the fate of our nation, and we play it with our children.

What does a public school really stand for in this country?

Must providing a quality education for some students mean denying a quality education to others?

Does ownership of property entitle you to be relieved of any commitment to the common good?

The US Education System: Hard-wired for Inefficiency

“This tradition of hyperlocal control, hard-wired for inefficiency, hinted at one reason that the United States spent so much more than other countries on education.

. . . America’s tradition of local control was a nightmare for teachers. They were left to pick and choose between clashing standards as best they could, repeating subjects again and again under the direction of repetitive, sprawling textbooks. . . .

In Minnesota, a coherent, clear set of standards, which focused on a few important topics each year, rather than dozens, had helped repair this damage. . . His state had intentionally modeled its math education after the best practices used in the world’s education superpowers, and succeeded.”

—Amanda Ripley, The Smartest Kids in the World

The Roots of Educational Warfare

By Kate Mereand (originally posted to Flickr as Lifeforce) [CC BY 2.0 (, via Wikimedia Commons
I just finished reading Dana Goldstein’s The Teacher Wars. It has been interesting to learn how cyclical educational mores and politics have been. The romantic ideal of the missionary teacher, for example, has its roots in Catherine Beecher and Horace Mann’s advocacy for troops of underpaid female teachers spurred to teach morality and character. Goldstein also traces the tension in educational philosophy of serving African American students to debates between W. E. B. Du Bois and Booker Washington. Washington was a strong proponent of vocational education, while Du Bois advocated for a classical education for the “talented tenth.” “Over the next half century,” Goldstein writes, “vocationalism remained the ascendant education reform ideology among philanthropists and politicians. . . ”

Goldstein’s presentation of the rise of teacher’s unions is balanced–she demonstrates how unions provided much needed advocacy for the rights of women and of labor, while at the same time noting the tension between maintaining worker’s interests and the educational interests of children. Goldstein writes, for example, that “amid increasing political and business pressure on schools during the interwar years, teachers unions in Chicago and beyond often found themselves making unsavory alliances, and engaging in rough-and-tumble politics far afield from education itself.”

I especially appreciated Goldstein’s presentation of efforts at desegregation, as this has been a topic of study here at Schools & Ecosystems. She notes the promising results of districts which did make substantive efforts to integrate, while also noting the challenges and complications, such as “Where integration led to staff redundancies and school closings, black schools were disproportionately closed and black teachers disproportionately dismissed or demoted, regardless of their seniority, qualifications, or success in the classroom.” She also spends time digging into the Black Power and community control movement in NYC and the warfare that erupted against a Shanker-led UFT. “This seemingly local event triggered not only the most infamous and largest teachers’ strike in American history, but also a political and racial crisis of national proportions, which continues to reverberate in almost every debate about contemporary school reform.”

One insight that really struck me here was how teacher’s unions are in reality more closely allied to a strong, central administration, rather than community control. Goldstein attributes this insight to historian Marjorie Murphy’s Blackboard Unions, and she states, “Under collective bargaining, it was easier for unions to negotiate with one strong administrative body, such as a city superintendent, board of education, or mayor, than with a plethora of neighborhood school boards or principals, each with their own set of demands.”

I was also interested by Goldstein’s tracing of the the lineage of the community control movement to present-day “no excuses” schools, a correlation which I’ve sensed when exploring the issue of segregation with my students. Goldstein writes that “Though the rhetoric of black separatist politics has all but disappeared, in many ways today’s “no-excuses” school reform movement has inherited the mantle of community control by aligning low-income parents with elite school reformers and philanthropists from outside their neighborhoods.” She points out that such schools, however, tend to be “deeply segregated,” and not necessarily high performing. What she also brings to the fore is how the critique of teacher’s unions which arose from the Black Power movement has been co-opted by reformers since the “Reagan Revolution”: “These new centrist critics rejected Black Power, but, more powerfully than ever before, they promoted a view of career public school teachers as professionally incompetent and insufficiently committed to closing racial and socioeconomic achievement gaps.”

Goldstein presents support for the success of school integration efforts, and suggests that perceptions that “desegregation did not work” are unfair “because the United States did not, in fact, commit to integration.”

The Teacher Wars explores various reform efforts, such as merit pay and value added. On the latter, she points to the detrimental effect of tying individual scores to evaluation systems, and notes that the repercussions of this can be to increase competition, and reduce collaboration. Her presentation of the fall-out from past evaluation schemes is especially salient right now, given NY Governor Cuomo’s push for heavier weight on value-added measures in an individual teacher’s evaluation. “If the key to systemwide improvement is not through mass firings or union busting, than what remains is to turn the existing average teacher into an expert practitioner . . . [which] will require a shared vision of what excellent teaching looks like, and the mentorship and training to get teachers there.”

Goldstein advocates for a bottom-up efforts that seek to “replicate the practices of the best.” “These practices conceive of veteran teachers as assets, not liabilities. As history has taught us,” Goldstein writes, “that is a pragmatic stance crucial to sustaining any reform program, which teachers must carry out on the ground.” She points to programs that provide in-classroom professional development and coaching, such as The Children’s Literacy Initiative, as actions that hold much greater promise than typical reform efforts like merit pay, charter schools, and evaluation. She also points to the promise of urban teacher residency programs beyond TFA, which can boost longer term teacher retention, such as the Memphis Teacher Residency and Boston Teacher Residency.

Unlike many out there who try to tell us that teachers shouldn’t be developing curriculum, Goldstein advocates for increased professionalization of teachers: “reform programs that combine high-stakes standardized tests with scripted lesson plans and a limited arsenal of pedagogical strategies may make teaching a less attractive job for exactly the sort of ambitious, creative, high-achieving people we most want to attract.” She provides an example of a former TFA teacher, Alex Caputo-Pearl, and his efforts with teachers at Crenshaw High School to create an “Extended Learning Cultural Model,” in which “teachers worked together to create interdisciplinary units built around neighborhood problem solving.” This model reminded me of an Australian model of a Global Learning Village we once discussed on this blog.

In the Epilogue of her book, Goldstein presents some conclusions from her research which are all tenets that I can get behind:

  • Teacher pay matters
  • Create communities of practice (she gives NYC’s Relay School and San Diego’s High Tech High shout outs here)
  • Keep teaching interesting (please!)
  • Focus on the principal as much as the teacher (yes, yes, yes!)
  • Return tests to their rightful role as diagnostic tools
  • Recruit more men and people of color

And many other lessons worth considering. Her final suggestion is to “be real about the limitations of our system.” She points out that the US system of education is decentralized in nature, and that as a result, we put unrealistic expectations upon the federal government and upon individual teachers, leading to the volatile political battles at the heart of “the teacher wars.” She hopes that “sustainable and transformative education reforms” can be “seeded from the group up. . . built upon the expertise of the best teachers.”

This is certainly a recommendation that a recognition of schools and school systems as ecosystems also supports.

I recommend reading The Teacher Wars: A History of America’s Most Embattled ProfessionHistory has much to teach those of us who work in the educational minefield. It’s remarkable how many of the debates that are ongoing in our field can be traced consistently over the course of these last two hundred years, like motifs in a novel.

Tragedy Does Not Have to Define Our Management

Anderies JM, Janssen MA (2012) Elinor Ostrom (1933–2012):
Pioneer in the Interdisciplinary Science of Coupled Social-Ecological Systems.
PLoS Biol 10(10): e1001405. 
Image credit: Courtesy of Indiana University.

Following a link from Aditya Anupkumar on Twitter, I read this excellent article from Tim Harford in the Financial Times contrasting approaches to “the tragedy of the commons” between Garrett Hardin, the coiner of the term, and Elinor Ostrom.

To review, the tragedy of the commons refers to the conundrum of managing natural resources that require collective sacrifice, but individual incentives are to over harvest.

Hardin saw this tragedy as inevitable, and advocated for strict policies to reduce overpopulation. He made the assumption that all situations in which a commons was at stake would play out in the tragic manner that he described.

On the other hand, Ostrom observed successful collective management of natural resources, and derived principles from those observations.

“These principles included effective monitoring; graduated sanctions for those who break rules; and cheap access to conflict-resolution mechanisms. . . Lin’s only golden rule about common pool resources was that there are no panaceas.”

Note that I can’t provide any more quotations from the original Financial Times article, as they have a rather strict copyright policy.

Something that stood out to me was Ostrom’s observation that the complexity of problems of the commons rendered top-down policy largely ineffective. What was effective was a community driven “polycentric” approach, following such principles as Ostrom outlined above. Polycentrism is a term which means “a political or cultural system which contains many different centres, especially centres of authority or control.” School systems could rightfully be said to embody that concept.

Reading this, I was struck by how this approach to managing complexity mirrors a vision for collaboration between political divides I cherish for the model of schools as ecosystems, which I’ve written more about on “Beyond Ideology“:

  • The idea of minimizing top down control with a goal towards community self-governance, and a restoration of human dignity
  • A focus on a methodology demonstrated to be effective
Our management of complex public systems and resources does not have to be tragic. With the proper recognition for the necessity of community driven collaboration, rather than the infantile broad dismissal polarized “sides” have for one another, public education can be effectively managed.

A System of School Intensification

This recent article in The Guardian about a method of rice farming termed “System of Rice Intensification“(SRI) that can potentially increase yields dramatically without the use of chemicals immediately piqued my interest, firstly because I am strong believer in farming without pesticides and herbicides, and secondly because it holds implications for our ecological metaphor as it applies to schools.

A theme which I have been pursuing over some of my last few posts has been the idea that complex systems, given their proclivity for chaos and entropy, must be “intensively managed.” This idea can be witnessed in full in SRI, as the method requires the controlled transplanting of seedlings from a nursery into the area where the rice is to be grown, one by one.

“Rather than any magical theory, it is good husbandry, skill and attention which results in the super yields. Clearly in certain circumstances, it is an efficient resource for farmers. But it is labour intensive and nobody has come up with the technology to transplant single seedlings yet.”

No magic indeed. It is rather a set of good local management practices that requires an initial upfront investment in order to lay the painstaking foundation for a strong and resilient crop. As a farmer who practices SRI put it:

“When a farmer does SRI the first time, yes it is more labour intensive,” says Santosh Kumar, who grows 15 hectares of rice and vegetables in Nalanda. “Then it gets easier and new innovations are taking place now.”

What is fascinating is that this method has been around since the 1980s, and yet scientists continue to direct their attention to silver bullets, such as technology and genetic modification. Why is this?

SRI offers millions of disadvantaged households far better opportunities. Nobody is benefiting from this except the farmers; there are no patents, royalties or licensing fees.” 

For 40 years now, says Uphoff, science has been obsessed with improving seeds and using artificial fertilisers: “It’s been genes, genes, genes. There has never been talk of managing crops. Corporations say ‘we will breed you a better plant’ and breeders work hard to get 5-10% increase in yields. We have tried to make agriculture an industrial enterprise and have forgotten its biological roots.” (Bold added)

Better local management, unfortunately, is not as sexy, nor profitable, as technological fixes. Plus, it’s just so messy.

Bihar, from being India’s poorest state, is now at the centre of what is being called a “new green grassroots revolution” with farming villages, research groups and NGOs all beginning to experiment with different crops using SRI. The state will invest $50m in SRI next year but western governments and foundations are holding back, preferring to invest in hi-tech research. The agronomist Anil Verma does not understand why: “The farmers know SRI works, but help is needed to train them. We know it works differently in different soils but the principles are solid,” he says. “The biggest problem we have is that people want to do it but we do not have enough trainers. 

“If any scientist or a company came up with a technology that almost guaranteed a 50% increase in yields at no extra cost they would get a Nobel prize. But when young Biharian farmers do that they get nothing. I only want to see the poor farmers have enough to eat.” (Bold added)

I am aware that this is only one article and that I should hesitate to draw larger inferences from it. But given that the research that has been done on SRI seems promising, I think I may be excused in drawing some connections between SRI and its implications for public education.

If we imagine a school district, a community, as a plot of arable land, we might perceive that our approach to its cultivation is all too often to become reliant on external supports and inputs, rather than to train community leaders and professionals to utilize practices and methods that are ultimately self-sustaining.

We can also perhaps draw some inferences from the idea of carefully transplanting seedlings from nurseries into the soil, as opposed to the traditional method of haphazardly dispersing clumps of seeds. It is no secret that there are toxic environments that all too many of our nation’s children are being raised in. Without a strong foundation in early childhood, academic education for many children is an increasingly uphill battle.

From these thoughts on SRI I draw two main implications for education policy:

1) Universal access to pre-K services is essential. All children must be given the opportunity to have access to as many “nutrients” as early as possible

2) Transplant students raised in toxic environments into schools offering positive, diverse learning environments

What do you think? Am I grasping at straws, or does SRI represent the next “green revolution”?

The Paradox of Regulation

I found Mark’s recent post on ideology quite interesting, particularly the question it raises about community control of schools. As I wrote in my comments, it seems to me that education reform is currently geared towards increased centralization of power, with local communities given little say in the direction their neighborhood schools may take. Mayoral control, the Common Core standards, No Child Left Behind: the dominant trends in education policy all seem designed to freeze parents and communities out of their children’s schools.

In principle, there’s a lot wrong with this approach. Most of us think parents should have some say in how their children are raised, and as Americans we all probably have some knee-jerk, “don’t tread on me” distrust of centralized authority. This distrust of government raises an interesting paradox, which I’ll call the paradox of regulation.

On one hand, if we believe in real democracy, we must believe that communities should have significant power over community institutions like public schools. On the other hand, we’ve often seen that without some regulatory authority, local communities often pursue policies that are fundamentally anti-democratic (such as the radical privatization-of-public-schools experiment taking place in Louisiana). Similarly, without federal intervention, discriminatory policies like Jim Crow might still be the norm in much of the U.S.

So, things to start to get circular: without regulation, communities may pursue policies that disenfranchise large segments of the population. With regulation, communities may be frozen out of the political process; regulation thus becomes another form of disenfranchisement.

Certainly, No Child Left Behind and mayoral control (as practiced in New York City, for example) have been practiced with such contempt for democracy that many educators would be rightly skeptical of the role of any centralized authority in public education. That said, regulation is necessary; it protects public resources like schools (and ecosystems) from those who seek to do them harm. How then can we create a system of regulation that protects public schools without marginalizing local communities? I don’t know the answer, but the current approach, wherein central governments impose policies upon communities, regardless of those communities’ concerns, has created a poisonous political climate. This is bad for teachers, students, and schools.

The Culture of Public Schools

In my last job in retail management, our company would talk about “intangibles” in leadership training sessions. What they were referring to were things such as how a customer feels when they leave a store, the interactions that were had through conversations between customers and staff, and the overall sense of happiness or adventure that a customer might feel in the store. Another way of stating the idea of intangibles when we are discussing business is “anything that you can’t gauge by a dollar sign.” But the fact is, that particular company is extremely savvy, because they explicitly recognized that their bottom line would be enhanced by paying attention to things that might not be immediately quantifiable. They pay attention to something that many businesses (and as I will now begin to examine – schools) do not take into consideration: the culture of their everyday business.

Similarly, in public schools across the nation, children and adults every day enter buildings where they succumb to a sense of drudgery, fear, paranoia, or even just plain chaos. The reasons for this reality are myriad, but one of the things you will hear frequently referred to when you talk about problems in education is the standardized test-taking and accountability movement. You’ll hear the horror stories from teachers about being pressured to “teach to the test.” In public education, the tests are to schools what the bottom line is to a business. All decisions are made based on the tests, more or less.
As many are so angrily pointing out, there is much more to teaching and to students than what shows up on a standardized test. And I would argue that what does show up on a standardized test has a lot to do with factors that are contextual, not simply a matter of an individual teacher and an individual student. Just as the company I was speaking about enhanced their bottom line and profited from addressing “intangibles” directly, so too could a school raise the test scores of their students if they spent more attention to factors within the school that have nothing to do directly with the test.
Now let’s be careful here. We all know that there are things going on in students’ lives that delimit their capabilities academically. A school can’t do much except perform consistent outreach efforts to the community to address such matters. But what we’re talking about here are the intangibles that are under a school’s control.
We’re talking about the feeling that you get before you even walk in the front door. And we’re not just talking about the signs, the display cases, the bulletin boards, the colors–although all of those things factor into it. We’re not just talking about whether the school follows some program of anti-bullying or anti-drugs or a social skills or life skills program.
We’re talking about how the students talk to each other. How the adults talk to each other. How the adults talk to the students. The everyday interactions, relationships, and rituals that foster and nurture a community. These are things that are perhaps largely intangible and not easily quantified (unless one is trained to quantify such things), but certainly worth investing attention in.
I would be willing to place a bet that if research were conducted that attempted to quantify the presence of a school culture (please notify me if such research has already been done!), they would discover that a nurturing, inclusive, and positive school culture correlates highly with student performance on tests. In other words, they would find that something so fuzzy as how happy or accepted students and adults feel overall would result in stronger performance on state tests. It would also most likely correlate with greater retention of effective teachers.

Improving the culture of a school is thus more important than a simpleminded focus on achievement. So in addition to enriching and challenging content, if we wish to improve the quality of our public schools, then we must also focus on designing and creating strong and positive school environments.

This modified post was originally written on my personal blog last year when I first began considering the metaphor of schools as ecosystems.

More on Schools and Gardens

I saw this article today and was struck by the similarities between the fight for public education and public space. In particular, this story of Chicago parents occupying their neighborhood school reminded me of similar stories about the fight for community gardens in the Bronx.

Mark already identified many of the parallels between education and gardening. The fight for community control, particularly in urban contexts, is another. In both cases, communities used occupation or encampment tactics to defend spaces vital to their communities.

Beyond that, they used these tactics to assert that schools and gardens belong to their communities– not to the city government or whatever company the government wants to subcontract the space out to. This seems like an appropriate response to city governments that seem determined to shut people out of the public conversation about what happens to their schools, their gardens, and the future of their cities.