Author: Lensyl Urbano

Montessori, cooperation and the Tragedy of the Commons

The essence of dramatic tragedy is not unhappiness. It resides in the solemnity of the remorseless working of things.
— Whitehead (1948) via Hardin (1968)

One of the greatest challenges in designing a cooperative environment is dealing with the potential for free-riding and abuse of shared resources. When dinner needs to be made but one member of the group will not participate everyone suffers, even those who contribute fully. Often, someone else or the rest of the group will step up and do the job of the free-rider, who has then achieved their objective. But what is the appropriate consequence? The social opprobrium of their peers is enough for some, others though seem unfazed.

Overuse of resources is a similar problem, which economists refer to as the tragedy of the commons (Hardin, 1968). When the extra-large bag of M&M’s is full, everyone can grab as many as they desire and everyone is happy. When resources are scarce, however, everyone grabbing is a recipe for disaster. Scarce resources need to be rationed in a way that everyone views as fair. Yet the rational behavior of the individual is to try to maximize their utility by taking as many as they need, regardless of the desires of everyone else, and especially if they’re first in line and no-one else is counting.

Ruin is the destination toward which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons. Freedom in a commons brings ruin to all. … The individual benefits as an individual from his ability to deny the truth even though society as a whole, of which he is a part, suffers.
— Hardin (1968)

The market solution to the commons problems is to make them not commons. This is usually done by assigning property rights to the previously common resource and allowing the owners to trade. This puts a price on what was once a “free” resource. Of course the price was always there; someone or someones had to go without when the M&M’s ran out (resource depletion). Unfortunately this is particularly difficult when you dealing with a non-currency economy, though I’m sure it could be done.

Reading through Hardin’s original Tragedy of the Commons article it seem that if the embarrassment of violating social norms is insufficient incentive for temperance then some sort of mutually agreed form of coercion is necessary. Interestingly, Hardin was arguing for population control, but the point still stands.

We’re due to have the small groups discuss how the worked together over the last cycle so we’ll see how that goes, but I think we’ll have to discuss the issue of the commons as a whole group when we next have our discussion of classroom issues. I’d like to raise the point that what happens in the classroom is a microcosm of larger society and get in a little environmental economics at the same time.

Education can counteract the natural tendency to do the wrong thing, but the inexorable succession of generations requires that the basis for this knowledge be constantly refreshed.
— Hardin (1968)

LaTeX

The easy way to stick mathematical equations into documents would probably be to use Microsoft’s Equation Editor in Word. But that makes it difficult to transfer things from one computer to another, especially if someone does not have MS Word. I prefer to use LaTeX. It’s free, open-source and usually pretty easy to set up on a server. It enables me to put equations inline on the class wiki and now, thanks to the Easy LaTeX plugin I can have them on the blog too.

I’ve been wanting to do this especially since doing the jam algebra post. Then I was lucky that I could, just barely, do everything with text. Now, however, instead of:

(7) 0.4 s / 0.4 = 0.6 j / 0.4

I can do this:
(7) ! \frac{0.4 s}{0.4} = \frac{0.6 j}{0.4}

Which has it’s pluses and minuses. However, before I would not have been able to do this (at least not very easily):
! \sqrt{x} = \sqrt[2]{x^1} = x^{\frac{1}{2}}

Using the LaTeX math markup is not exactly trivial (if you put your cursor over the equation you can see it), but Kocbach (date unknown) and Downes (2002) are great resources.

What if everything we know about how students learn is wrong?

“The contrast between the enormous popularity of the learning-styles approach within education and the lack of credible evidence for its utility is, in our opinion, striking and disturbing,” — Pasher et al., 2008.

What if there was no such thing as learning styles? What if tests were a great way to help students learn? Benedict Carey has a fascinating article in the New York Times that reviews some of the cognitive and educational research on how students learn.

Among the more interesting findings are that there is practically no evidence that different learning styles make a difference in learning (though this is largely because there aren’t any good studies the met the stringent criteria of the authors’ of this review). The pattern of work in our Montessori Middle School program is designed around the idea that different students have predilections for certain types of learning. And my own anecdotal observations, of myself and of my students, indicate that this is the case. However, even if learning styles were not important at all, Carey’s article points out another observation that highlight the power of our approach.

The cycle of work. Within each subject area there are different types of assignments designed to provoke learning in many different styles.

First off, though we believe different students have different learning styles, the cycle of work is designed to expose all students to multiple learning styles. So the belief in learning styles is not stifling. If students do learn better from reading, they get the chance, but for any given topic and on any given week, they’ll see the same information in diagrams and get to talk it over with their small group. This ties into Carney’s observation that varying the study environment, and the information studied, aids learning. For example, in the case of identifying different painters by looking at their work:

“What seems to be happening … is that the brain is picking up deeper patterns when seeing assortments …; it’s picking up what’s similar and what’s different about them,” — Nate Kornell (in Carney, 2010)

Overspecification is something I wonder about when I hear about the School of One program in New York City, which I discovered via the Freakonomics podcast. (I’ll post more on this intriguing program later).

Carney also points out the research that shows that testing helps students learn. But here the important point to highlight is that it testing is most effective when it’s used as a formative assessment, when it helps guide learning, and when it is used to reinforce ideas students are learning. This is how I use our cycle tests. Summative tests, like standardized tests, which try in one big lump to assess a student’s learning, are susceptible to so many small variabilities and are so prone to overinterpretation and overemphasis that it’s hard to say that their benefits overweight their problems.

It is important that, as teachers, we remain cognizant of the educational research. But it’s just as important the we not just jump on the latest fads or get overexcited about the latest research results. The Montessori Middle School program is constantly evolving, but it has a long and successful history, so it behooves us to approach the research with caution and to dig beneath the surface to see if the results are really fundamental at odds with what we know (at least in our experience) works.

Little Red Riding-hood

And, saying these words, this wicked Wolf fell upon poor Little Red Riding-Hood, and ate her all up. — Perrault, 1922, p. 25..

Little Red Riding Hood.
Little Red Riding-hood as illustrated by Harry Clarke.

One of my students chose to do their first writing assignment in the mold of a classic fairy tale. So, as part of the revision process, I suggested they read the original Little Red Riding-hood to get away from the conventional, Disneyfied storylines. The Guttenberg Project, which aims to make available all the books that are now in the public domain as free ebooks, has Charles Perrault’s original book of fairy tales.

The student was somewhat surprised that Little Red Riding-Hood was eaten by the wolf in the end. They shared this with the rest of the class quite loudly.

Mural

Artist Mary Cour throwing herself into the mural.

We’ve been really lucky to have the artist Mary Cour help us out with our classroom mural. She came up with the idea about two cohorts of students ago to paint students’ outlines on the wall and let the students fill them in with words and images that were meaningful to them. Early adolescence is a time of self-discovery and exploration, so this type of project is a wonderful way to encourage self reflection. I let students work on their silhouettes during personal reflection time, and they’re always eager; it’s easy to see why Facebook is so popular with this group.

The mural became quite the marker for the students and for the school, so now, every two years, we add the new group of students to the wall. The new outlines are superimposed over the older ones so you can still see previous generations of students, a tangible reminder of their legacy in the classroom.

Classroom culture

One of the most powerful aspects of a multi-aged classroom is the institutional memory that develops and makes learning a whole lot easier than starting off, every year, from scratch. All the aches and toil of last year did not just disappear when the new crop of students started. The new kids look to the older students for cues about how to behave and it has been saving me a whole lot of time and energy.

That’s not to say that bad habits don’t persist too. But having a slew of new students mixes things up enough so that even the returning students are receptive to some change.

So now I have a bit more time and energy that I can now put into new projects and tailoring the curriculum to make life a little more interesting for one and all.

Well we’re on our first immersion now and I’m getting a little reflective. Probably because it’s close to 2 am and they’re still not asleep.

Jurassic Park: Web of Issues

Web of issues for the movie Jurassic Park.

Well we watched Jurassic Park last night and concluded it with a discussion about the issues underlying the movie, the same way we’ve been studying analyzing the issues underlying texts. Discrimination based on race and obesity came up first (the fat guy and the black people “always” die), but I was able to coax a bit of discussion about the role and responsibility of science and scientists. Our discussion is summarized in the graphic organizer above, but there are many more subtexts to the story that we did not have time to explore.

Jurassic Park by Michael Crichton (the book).

I like both the movie and the book because, like most good science fiction, they explore some interesting issues that relate quite nicely to the curriculum. Jurassic Park has a nice little introduction to DNA and gene sequencing that is tied to some the history of life on Earth. As works of art in their respective fields, however, I prefer the movie. The novel has a lot of wonderful detail, and the scientist in me loves the detail, but the characters are not as well drawn and the story seldom strays from its main thesis, scientific hubris. What it has to say about that issue is well expressed and well researched so it does capture the interest of the reader. (The follow-up book, “The Lost World”, sails adrift of the science, is logically incoherent and has a proportionate deterioration in the quality of the writing.) I do however recommend the original Jurassic Park book to my students as a personal novel.

Steven Spielberg makes a great movie, extracting empathetic performances from the actors. Since the book’s author, Michael Crichton, also wrote the screenplay, the movie stays true to the core issues in the text. I think its a great example of a successful, dare I say synergistic, collaboration.

Tomorrow, instead of retelling around the issues in writing, my students are going to try to do so in a skit. This could get interesting.