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.
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)
“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.
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 (inCarney, 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.
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.
Daily life, for all its basic routine, is always popping up surprises. The human brain is attracted to mystery; it is after all just a fancy problem solving machine. David Mitchell gets up on his soap box to give a wonderful screed about how having sophisticated references tucked into childrens’ programming is a good thing and there should be more of it. Kids are naturally curious. If they’re interested enough they’ll look it up, and, in the age of the internet search engine and smartphones, the barriers to looking anything up are negligible. So include more Greek references in your discussions because although inciting curiosity in the internet age is a bit like opening Pandora’s box, you’re much more likely to get better results.
Binomial cube.
It also ties a bit into Montessori Philosophy. Students start “playing” with artifacts like the binomial cube in kindergarden, where the goal is to convey mathematical concepts is a solid, sensorial way. They don’t get into binomial formula until years later in algebra, but their familiarity with the cube allows them to take the step into the abstraction of algebra on familiar, safer ground.
This discussion also highlights one of the major advantages of using websites and hypertext for educational materials. References can be embedded in the text with links to credible sources even further reducing the transaction costs of the student having to search around the web trying to look something up. There is an argument to be had, however, on if hyperlinking is too distracting and reduces our ability to focus, but perhaps we need to work on study habits and using invisible hyperlinks rather than not using technology altogether.
(I discovered David Michell’s Soap Box via Somewhat in the Air, who notes that, “Few of David Mitchell’s posts are child friendly but the “Passionate about Sofas” is terribly funny, too.”)
Two years ago, the middle school’s flagship project was to put up a fully functional greenhouse (using this design). It took all year but we did it. On the way, we got to practice geometry, mapping and construction, while learning and growing plants and studying soil profiles. It was so successful that, with our spring plant sale we broke even on the entire project.
Last year, however, the greenhouse was somewhat neglected. My plans to add an automatic window opener, which would have been a wonderful tie-in to our electronics and Newtonian physics studies, did not work out; we just did not have the time. We’d taken the plastic covering off, so only the bare, forlorn PVC frame was left standing around a plot of waist-high weeds.
Though I could not have predicted it, this year we have a strong core group of students who are highly enthusiastic about resurrecting the greenhouse and making it work. My suggestion was that we try to grow produce this fall that we could cook in December when we do our Dinner and a Show. Well, two weeks in, they’ve already put together a menu plan, weeding is well on its way and I’m being harassed to hurry up and arrange a trip to Home Depot. The excitement is so infectious that another student has volunteered to bring in his electric weed-whacker during the immersion. It’s amazing!
I’m having the hardest time not butting in. There is a beauty in seeing a well oiled machine executing a project or solving a difficult problem. But there is another even more wonderful aesthetic visible in a the birthing struggles of a nascent team. The forward motion of infectious enthusiasm is pulling puzzle pieces into its wake, and the pieces just seem to click into place when the time is right. I have to keep reminding myself that my job is to prepare the environment and let the kids do the rest.
The cycle of work. Within each subject area there are different types of assignments designed to provoke learning in many different styles.
The lessons, the individual works, the different group works, the reading; they’re all set up in this elaborate combination so that different students with different learning styles can get the information they need in the way that’s most meaningful to them. But the students also get to experience a wide range of learning styles so that they can become acclimatized to the different styles while actually figuring out which ones work best for them.
The logic behind this approach comes from Howard Gardner’s ideas on multiple intelligences. He argues that we have aptitudes for different ways of learning, and learning is easier and faster if students take advantage of their preferred learning styles. Whether we acquire these preferences through nature or nurture is an intriguing question, but by middle school I’ve found that it does not take long to recognize that some students have rather strong preferences.
[T]here exists a multitude of intelligences, quite independent of each other; that each intelligence has its own strengths and constraints; that the mind is far from unencumbered at birth; and that it is unexpectedly difficult to teach things that go against early ‘naive’ theories of that challenge the natural lines of force within an intelligence and its matching domains. – Gardner (1993)p. xix.
The learning intelligences have been defined in a number of different ways (see Smith, 2008 and BGfL for examples). We parse them like this:
Linguistic intelligence – learning from the written word or hearing words (auditory).
Logical/Math – using numbers and logical reasoning.
Bodily-kinesthetic – learning from doing.
Visual/Spatial – emphasizes images and relationships in space.
Interpersonal – learning from/with others.
Intrapersonal – introspective learning.
Musical – rhythm is important
Naturalistic – comprehending of the environment.
I prefer students to discover their preferred intelligences via the variations convolved into the curriculum, however, the BGfL has an online, multiple intelligences test that I’ve used in the past. However, as with standardized tests, you don’t want to stereotype students or have them stereotype themselves. All the intelligences interact. Different challenges force us to take different approaches, using different combinations of our intelligences to best effect. As always, a growthmindset is best. With their mental plasticity, adolescence is the best time to explore different learning approaches.
Matt Might, a computer science professor, has a wonderful article posted called The illustrated guide to a Ph.D.. I like how it illustrates the broad base of knowledge you should acquire through high school.
