Author: Lensyl Urbano

Creating a market in the classroom

The Tragedy of the Commons has been on my mind of late, and something serendipitously popped up in class today that’s started me thinking of new ways to introduce some important economic concepts and make classroom jobs work better at the same time.

You see, one way of preventing abuse of shared resources is to assign the rights to the resource to someone, anyone really, and allow them to trade and regulate the use. Who gets control of the resource does not ultimately matter for conservation. As long as the owner and their rights are clearly defined they will try, in a rational world, to get the most for them, and make them last as long as possible, thus preventing overexploitation.

But what’s necessary for this to work is some form of goods or services that’s worth trading. The miracle of capitalism is that it allows people to do what they’re best at and trade with others for the other things they need (or don’t want to do). I’m not about to start letting students pay cash to each other, but I’m trying to think if there’s any reason to not let them trade their classroom jobs on a daily basis.

Say a student if done with their daily work and is feeling bored with a little time to kill at the end of the day. They take out the compost and clean up the microwave, their classroom job is done. Well, they could offer to do someone else’s job, someone who is, say, trying to finish up their math and don’t want to break away from it, and, in exchange, the student with the math work would do the microwave and compost job tomorrow while the first student takes a break. Everyone is happier!

Image by Katrina. Tuliao.

In theory, as long as the rights and responsibilities for each job are clearly defined, then students will be able to come up with the most efficient trading schemes for themselves. Once trading starts I’m sure students will come up with some interesting agreements and contracts will need to be enforced (fortunately we already have judges built into the classroom constitution). But we might just need a special white-board that would make it easier to trade jobs. Tadah, we now have a market in the classroom that makes doing jobs a little easier for everyone and brings some important economic concepts directly into the classroom. Why have I not thought of this before?

I am quite enthused by the idea, but I’m really curious to see if anyone can come up with any downsides.

School of One

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. There they collect a lot of data, multiple times a day to carefully observe the individual student and tailor their environment based on what works and what does not. This sounds like a great way to customize the environment for the student if used carefully. My own biases lead me to the suspicion too close of observation, and too much tailoring is likely to be detrimental in the longer term. It’s a bit quantum in that the more detail you have about a student at one snapshot in time, the less you know about that individual’s trajectory of learning. If something worked well today, maybe it will tomorrow, or maybe not. If the people customizing a student’s learning environment tailor it to what works today, then they’ll forever be trying to catch up to where the student needs to be. But they’ll certainly know there is a problem even if they don’t know why.

The constant testing should provide a wonderful dataset on how well different approaches to learning work with different students and to answer the questions I note above. I’d also be curious to see if there is some sort of half life where the effectiveness of certain learning methods deteriorate over time (in the same way perhaps, that test scores tend to converge on the mean).

I need to find out more about this program because it sounds so full of potential.

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.