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

dp808378
“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.