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 Phys.org, “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!

A complex system is defined by system-level goals, not only by the movement of its parts

Hoel and his collaborators claim to show that new causes—things that produce effects—can emerge at macroscopic scales. They say coarse-grained macroscopic states of a physical system (such as the psychological state of a brain) can have more causal power over the system’s future than a more detailed, fine-grained description of the system possibly could. Macroscopic states, such as desires or beliefs, “are not just shorthand for the real causes,” explained Simon DeDeo, an information theorist and cognitive scientist at Carnegie Mellon University and the Santa Fe Institute who is not involved in the work, “but it’s actually a description of the real causes, and a more fine-grained description would actually miss those causes.”

https://www.wired.com/story/new-math-untangles-the-mysterious-nature-of-causality-consciousness/

Special Education: Inclusion or Specialized Intervention

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“Street Crowd” by Théophile-Alexandre Steinlen (French (born Switzerland), Lausanne 1859–1923 Paris) via The Metropolitan Museum of Art is licensed under CC0 1.0

A fair amount of academic literature calls for clinical, evidence-based models of intensive intervention for students with disabilities in K-12. Yet in the field, there is limited effective implementations of such interventions.

Models such as Response to Intervention (RTI), multi-tiered support systems (MTSS), and standard, evidence-based protocols and programs all make complete sense when you learn about them. But there’s also a problem with these interventions: they are based on clinical frames of implementation, as in a trained clinician in the given model or protocol delivers the intervention in a prescribed manner.

The daily reality of a K-12 school, however, is far from clinical. Opportunities to deliver prescribed interventions, whether in a small group or in the ideal of a 1:1 setting, are few and far between. Moreover, opportunities to be trained in such interventions are few and far between. One is certainly not trained in any given intervention in any traditional education program.

The very model of a self-contained classroom, a class in which students with more severe disabilities are separated from their peers, relies upon this clinical ideal. And again, in isolation, as an ideal, it makes perfect sense. Let’s separate out the kids with greatest of needs so we can provide them with individualized, supportive instruction.

Similarly, within an inclusive classroom, district leaders continually speak about and prescribe the need to move away from a one-teach, one assist model to a parallel, station, or team teaching model. Or they speak of the need to “differentiate” and “individualize” instruction.

Idealized models that make perfect sense and sound great, but that rarely play out that way on the ground.

A Division Between Inclusion and Specialized Intervention

There is some scholarly debate about this. Fuchs et al, in a 2010 paper, “The ‘Blurring’ of Special Education in a New Continuum of General Education Placements and Services,” provides a useful delineation into two camps they term IDEA and NCLB. The IDEA group advocates for a top-down (i.e., replicable), linear, and time-sensitive process with fewer tiers of instruction, which serves both prevention and a more valid method of disability identification. They believe in evidence-based programs at Tier 1, the strength of standard protocols in Tier 2 and Experimental Teaching for Tier 3 intervention. They believe in the importance of a distinct special education program.

On the other hand, the NCLB group focuses on a problem-solving approach based on standards. “Whereas special education remained a distinct entity in reform making in the 1980s and 1990s, many in the NCLB camp today are advocating for obscuring, smearing, dimming, and confusing special education by blurring it into general education. In their plans—however implicit—special education vanishes in all but name (and maybe in name as well).”

Research suggests that the standard-protocol approach is superior to problem solving in accelerating the progress of children with serious learning problems. However, the authors acknowledge that “because there are insufficient numbers of such protocols in many academic areas and in the higher grades, and because ‘the school bus arrives every morning,’ many practitioners may have little choice but to rely on some variant of problem solving.”

In a more recent paper in 2015, “Inclusion Versus Specialized Intervention for Very-Low-Performing Students: What Does Access Mean in an Era of Academic Challenge?“, Fuchs and other authors again examine the split between those who push for a problem-solving, inclusionary approach vs. that of “specialized intervention” approach and advocate for a focus on explicit, specialized intervention delivered in a separate setting.

Here’s a couple of provocative quotes from this paper that struck me:

“. . . access cannot be assumed even when inclusive instruction reflects state of-the-art accommodations and support. Instead, only evidence of adequate student outcomes demonstrates that access to the curriculum has been accomplished. In fact, the present analysis indicates that such access is sometimes more satisfactorily achieved under a service delivery arrangement that occurs outside the physical space of the inclusive program and using instructional methods that differ from the inclusive program. All this argues for a definition of access to the general educational curriculum that is based on empirical evidence of adequate learning— regardless of the setting in which or the instructional methods by which that learning is achieved.”

“…it is not possible to ignore students’ foundational skill deficits if progress toward CCSS is to be realized. For example, to demonstrate meaningful improvement with informational text, specialized intervention must address very low performers’ decoding, word recognition, and vocabulary deficits, and this often requires out-of-level foundational skills instruction. Therefore, although reconceptualizing access as empirical demonstration of learning, schools must also recognize that the access mandate often requires schools to provide out-of-level instruction to meet students’ needs for accessing the grade-level curriculum.”

Yet I don’t agree with the authors that putting in place explicit instructional intervention programs will solve all the problems they’ve identified with inclusionary practices. You can place my own professional stance as firmly within the “NCLB” camp outlined above. Schools are not clinics, and unfortunately, special education teachers and other personnel in school buildings are rarely, if ever, trained in the delivery of specific interventions.

In fact, I think the issue of either strong inclusionary instruction or specialized intervention comes down to the same fundamental issue: there is a general lack of instructional capacity and expertise in most schools, in addition to a general lack of curricular coherence and vision.

Either way, we certainly need to rethink how we are putting in place supports for students who struggle the most and assessing whether those supports are actually effective.

My argument, however, is to place our primary and immediate focus on establishing coherent and rigorous curriculum and expectations for all students. I thus argue for inclusion and a problem-solving approach.

A recent article in Education Next,”Reforming Remediation” neatly encapsulates the rationale for this inclusionary argument. Students placed directly in college-level statistics did far better than their counterparts in remedial classes.

While that example is focused on a higher education setting, we can find parallels in K-12 by looking at access to Advanced Placement (AP) or International Baccalaureate (IB) programs, or to difficult academic subjects such as Latin. Disadvantaged students rarely have the opportunity to experience such rigorous curriculum. Yet when they do, as Bronx Latin teacher Peter Dodington put it, “The combination of a difficult topic and a well-ordered, step-by-step curriculum allows even otherwise weak students to succeed, and gives them a new understanding of their own strengths and talents.”

If we raise our expectations and the rigor and coherency of our curriculum, then we will see more educational benefit for all students. The dire reality of poor teacher training and knowledge of the content they teach is a significant problem, but a stronger school-wide curricular program can help to assuage this.

I strongly believe in the need for specialized interventions for students who require the most support. But how can we put in place effective interventions when a strong and well-implemented core curriculum is not present?

Let’s address the foundations first before moving to the clouds.

Principles for Robustness

“Snow Crystal” — Wilson Alwyn Bentley

In an article in Harvard Business Review, “The Biology of Corporate Survival*” the authors lay out some principles for managing complex adaptive systems. While framed for a business audience, these principles could be applicable to the complex adaptive system (or, perhaps more aptly, the “complexicated” system) of a school.

The authors delineate a set of principles for robustness into structural features, and managerial levers:

Structural Features

  • Heterogeneity (Diversity)
  • Modularity
  • Redundancy

Managerial Levers

  • Expect surprise, but reduce uncertainty
  • Create feedback loops and adaptive mechanisms
  • Foster trust and reciprocity

How might these principles apply in a school?

I’ll leave that to you to contemplate, but for the record, I’ll note that most public school managers typically do quite poorly in reducing uncertainty and in fostering trust.

 

* “The Biology of Corporate Survival – Harvard Business Review.” 2015. 15 Apr. 2016 <https://hbr.org/2016/01/the-biology-of-corporate-survival>

Schools are Complexicated

A 6th century Coptic frieze

When I first started this blog, I hoped–as my younger, more idealistic and grandiose self–that we would uncover ecological principles of complex adaptive systems that could be applied in everyday practice.

While I have certainly uncovered many interesting themes and patterns along the way (such as obliquity, or the influence of unconscious bias on behavior), my slightly more hoary-eyed self can say, in an honest moment, that I have not discovered an alchemical praxis that will transmute principles of self-organizing systems into pedagogy or school organizations. Sorry!

A blog post, “Life Is Complexicated,” by Benjamin Goertzel helped me to clarify a reason why it might be so difficult to distill principles of complex adaptive principles into readily applicable practices.

Goertzel critiques the “Santa Fe Institute” concept of complexity, which has examined complex adaptive systems that have qualities of self-organizing emergence to identify universal principles. For Goertzel, the problem is not that there aren’t such systems, but rather that the real world systems that we wish to most understand aren’t simply complex—they are an admixture of both complex and complicated:

They are complex (in the Santa Fe Institute sense) AND complicated (in the sense of just having lots of different parts that are architected or evolved to have specific structures and properties, which play specific roles in the whole system). . . .

They are messy in a lot of different ways.  They have lots of specialized parts all working together, AND they have complex holistic dynamics that are hard to predict from looking at the parts, but that are critical to the practical operation of the parts.

When considering a school or a school system, this messy confluence of self-organizing emergence and highly specialized roles and frameworks sounds like a more apt description. Our analogy of a school to an ecosystem is meant to push back against the linear thinking that many apply to schools—but I will readily acknowledge that a school is far from an actual ecosystem (really, it’s perhaps more akin to a garden). Schools are institutions embedded within a wider complexication of bureaucracy, policy, culture, economics, and politics.

So perhaps I shouldn’t feel bad about having difficulty in simplifying the realm of education based on an analysis of schools as complex adaptive systems. Schools are complexicated.

 

 

Accountability for the Long-Term

time_distance

I receive a monthly newsletter from bcg.perspectives that I scan for any relevant connections to school systems. Their work often centers on business policy, but sometimes their work has either a direct or indirect connection to the education sector.

A recent post,”Gauging Long-Term Impact in the Social Sector” on developing a system of long-term evaluation for a large international nongovernmental organization (INGO), there are lessons well worth considering in developing systems of long-term accountability for schools.

The INGO discussed, named SOS Children’s Villages, works towards “improving the situation of children who are at risk of losing, or who have already lost, parental care” across 134 countries.

The assessment methodology that SOS Children’s Villages developed jointly with BCG evaluates two elements of the programs’ long-term impact: the nonfinancial (or all-around) impact on the individual program participants and the community and the financial impact on society. The determination of the long-term impact on individual participants is based largely on information gleaned from interviews of former program participants by external researchers. This is supplemented by qualitative research conducted through focus group discussions with former child participants and their caregivers. . . 

The programs’ long-term financial impact on society is gauged by the programs’social return on investment (SROI), a comparison of the programs’ total costs and benefits to society. . .  The calculation of societal benefits is based on easily quantifiable elements.

This combination of intensive qualitative and correlated quantitative data gathering seems to make great sense when considering systems for school accountability. Many school systems have been relying primarily on isolated testing data — but why not go straight to the source, and interview the ones we most seek to impact? The students and families and community. And then correlate that with longer-term impacts via “social return on investment”? What are the long term outcomes of students after they graduate?

Raising test scores is wonderful. But enriching one’s community and society over the long-haul is the true goal of education. Developing better combinations of quantitative and qualitative evaluation of our school systems that can help us determine long-term impact is key to not losing sight of that higher purpose.

These Little Avalanches

Visitor running down a dune in Great Sand Dunes National Park.
“If you frequently trigger small cascades, you never get really massive events, but you [sacrifice] all that short-term profit,” D’Souza explained. “If you prevent cascades at all costs, you might make a lot of profit, but eventually a cascade is going to happen, and it will be so massive it [could] wipe out your entire profit.”

—Jennifer Ouellette, “The New Laws of Explosive Networks” on Quanta Magazine

This quote, referring to a concept termed “explosive percolation,” runs parallel to best practice in fire prevention.

After decades of overzealous fire prevention (think: Smokey the Bear), we’ve ended up with a situation wherein apocalyptic wildfires have become a norm. Fire prevention, experts have come to recognize, now requires smaller burns—or, in the absence of controlled burns due to the risk involved, actively thinning underbrush and trees through human labor.

The concept of “explosive percolation” also relates to a concept we’ve explored here before, termed a “self-organized criticality,” in which complex systems maintain stability via “small avalanches” that spontaneously transition between states of chaos and order.

In schools, this confirms the notion that to maintain stability and order within a school community (or classroom) requires “frequently triggering small cascades” of new learning and activities interspersed within stable norms, rituals, and traditions that any school or teacher maintains.

In schools where order is so strictly maintained as to suffer from a “blind application of rules,”  greater disorder may await further down the line. As always, a healthy balance necessitates diversity.

Initiatives I’m Excited About at My School This Year

There’s an unfortunate narrative that sometimes gets pushed in the ed reform community that charter schools are places of innovation and effective practice, while traditional district schools are maintainers of the status quo.

At my school, Jonas Bronck Academy, there’s a few initiatives that I’m excited to help support in this new school year that I think any school, whether charter, district, or private, might learn something from. Check out a short overview of those initiatives in this presentation:

If you’re interested in learning any more about any of these initiatives or would like to share resources, feel free to reach out to me!

We Need Charter AND District Systems: On Private-Public Partnerships

Building on my last post, in which I challenged Neerav Kingsland’s presumption that charter systems and schools are inherently superior to that of district systems and schools, here’s an important TED talk by economist Mariana Mazzucato worth watching that presents a refreshing new angle on this topic:

The narrative that charter supporters often promote is one in which traditional district schools are failures because they are:

  • Mired by bureaucracy and politics
  • Constrained by teacher’s unions
  • Unable to innovate and adapt to the needs of the 21st century
  • Beholden to the state
  • Unresponsive to the needs of parents and communities

All reasons, they suggest, that require us to turn to the private sector and its proven ability to disrupt, innovate, and provide competitive choice. The market, they claim, has been demonstrated to promote quality and efficiency, whereas the state has proven only to be cumbersome, to stand in the way of change, and to maintain the status quo.

Parallel to that conversation is our national shift away from representative democracy’s mechanisms for political decision-making and deliberation via a balance of power to that of the vagaries of capitalist markets.

NYC stands central to that shift, tracing back to the fiscal crisis of the 70s.

A Short Diversion into History

Prior to the 70s, NYC was the paragon of a social democratic state. City colleges were free to attend*. Public transit, daycare, hospitals . . . The government worked with labor unions to deliver strong public services.

But that beatific vision came crashing to an end when NYC found itself on the verge of bankruptcy in 1975. It had been borrowing to pay down debt for far too long.

Though the unions ended up bailing the city out—most notably via Al Shanker-led UFT’s investment of teacher’s pensions into municipal bonds—that moment is when, as Richard D. Kahlenberg suggests in his book on Shanker¹, “the relationship between democracy and capitalism had shifted.” Quoting journalists Jack Newfield and Paul DuBrul, Kahlenberg notes that at this moment, there was “a revolution in the governance of New York City,’ where bankers effectively took over the running of the city.”

Writing in The Nation, Kim Phillips-Fein² provides further perspective on the legacy of the crisis:

Today, the rituals of fiscal crisis—the blaming of public sector workers, the vilification of the poor who use government services suddenly deemed excessive luxuries—may seem familiar. . . . 

The crisis brought about a transformation of the very language and conception of politics, as the rhetoric of fiscal necessity and business acumen replaced a vision of politics as a domain of struggle and negotiation.  

. . . the diminished expectations we have for the public sector and the increasing difficulty of living a middle-class life in the city suggest the legacy of the fiscal crisis even now. City governments today—including New York’s—seem primarily to be vehicles to attract and maintain private investment. 

Back to Our Narratives on State vs. Private Sectors Today

Thus, the narrative about the efficacy of charterization for delivering what was once solely a government service is placed within a wider context, and it helps to explain why so many pro-charter folks not only denigrate unions, but furthermore the public sector et al.

And this is why Mariana Mazzucato’s challenge is so important to pay heed to.

Mazzucato argues that contrary to the anti-government narrative, innovation occurs as a result of government intervention. At minute 7:00 in her talk, she states:

Now, what’s interesting in all of this is the state, in all these examples, was doing so much more than just fixing market failures. It was actually shaping and creating markets. It was funding not only the basic research, which again is a typical public good, but even the applied research. It was even, God forbid, being a venture capitalist.
. . . In all these sectors, from funding the Internet to doing the spending, but also the envisioning, the strategic vision, for these investments, it was actually coming within the state.

Rather than wasting wind denigrating the state, she suggests, we should instead seek “public-private partnerships.”

This is what I was suggesting in my last post when I stated “Perhaps the answer lies somewhere in between [district or charter systems].”

As a side note, I recently read Peter Thiel’s Zero to One, and I found his ideas about how to innovate as an entrepreneur compelling. Yet I had a moment of cognitive dissonance when he suggested, in his contrarian way, that enterprises are most successful when they can gain a monopoly, rather than endure heavy competition. When I read that, I thought:

But the state IS the biggest monopoly!

The government is not necessarily the enemy of innovation. Unions aren’t either.

And on the other side, the private sector is not necessarily the enemy of democracy and strong social enterprises.

The question becomes: how can we leverage partnerships across government, unions, and private organizations to most effectively serve our nation’s future?

* Can you even imagine that happening today in the US? You’d have to be some kind of a socialist!

1 Kahlenberg, Richard D. Tough Liberal: Albert Shanker and the Battles over Schools, Unions, Race, and Democracy. New York: Columbia UP, 2007. Print.

2  Phillips-Fein, Kim. “The Legacy of the 1970s Fiscal Crisis.” The Nation. The Nation, 16 Apr. 2013. Web. 23 Aug. 2015. <http://www.thenation.com/article/legacy-1970s-fiscal-crisis/&gt;.

Charter vs. District Systems

By NASA’s Aqua/MODIS satellite (http://visibleearth.nasa.gov/view_rec.php?id=6204) [Public domain], via Wikimedia Commons
Neerav Kingsland looks at the recent findings on professional development via the TNTP Mirage report and the Rand Corporation study, and comes to the conclusion that “Professional development only seems to lead to student achievement increases in charter schools!”

I noted in a recent post that in the TNTP study, teacher effectiveness and growth was notably more observable in a CMO, and I hypothesized that this could be attributable to some charter networks having more tightly managed systems of assessment, curriculum, teacher practice, and observation.

But to suggest that this is an innate quality of charter schools is questionable. There is absolutely no reason for a district school not to be in possession of such qualities, and indeed, many do.

Kingsland argues for NOLA-style systems, in which the government merely regulates, rather than operates, schools, with the idea being that the private sector can conduct operations more efficiently and effectively. But there’s a potential, and possibly critical, issue with such a system: a lack of coherency.

Within a well-managed district, on the other hand, there is potential for greater coherency. A state or central office can provide specific direction on operational shifts via policy that all district schools would be expected to adhere to.

Kingsland asks, “is it more likely that we can achieve major gains in districts or scale highly effective charters?,” I think he’s created a false dichotomy. I think the more interesting question is, “How can we achieve major gains by leveraging federal, state, and district policy to implement effective and coherent systems, content, and practices across all schools?”

A NOLA-style system might be able to make swift initial gains, due to well-managed networks putting into place strong systems of assessment, feedback, and practice. But it’s certainly feasible that a well-managed district system can make even bigger gains over the longer haul.

I disagree, therefore, with Kingsland’s position that charter schools are inherently superior in enhancing teacher effectiveness and promoting student achievement. In fact, I charge that a NOLA-style system may ultimately run up against its innate incoherency, at which point, large-scale gains would stagnate.

I could be totally wrong on this, of course, and admit that this is conjecture and based on my own values. It may be that a NOLA-style system may end up leading to greater coherency in operations due to competition, and thus, best practices evolve through demonstrated gains in one organization and subsequent adoption by those who are attempting to compete.

I may also be overstating the ability of district schools to establish coherency, given constraints in operating within often volatile political contexts.

The problem is, of course, that while NOLA has demonstrated significant academic gains on tests since moving into a private sector operated system, it’s still purely conjecture as to whether the same benefit would transfer to any other district simply due to a  structural change. It’s also still conjecture that those gains can be solely attributed to a structural shift to private sector operation, rather than the simple mechanism of distributing students across geographical boundaries.

But let’s assume for the moment that Kingsland is correct that a private sector operated school system is the optimal system. I would still argue, even in such a case, that this doesn’t mean that such a system will necessarily scale effectively into different social and political contexts.

In the face of great complexity and uncertainty, we can hedge our bets by planning for robustness, rather than optimality.

The question therefore becomes: what is the most robust? A school system operated by the public, or a school system operated by the private sector?

Perhaps the answer lies somewhere in between.