All animals are equal, but some are more equal than others.

This winter I ventured over to a part of campus that I hadn’t explored in the ten years I’ve been hanging around Harvard. In January, I took a two-week boot-camp style overview course on the ‘Foundations of Urban Education’ at HGSE. As many of you may know, I’ve always had a sweet tooth for teaching and learning. As an undergraduate I helped teach in the Mathematics for Teaching graduate program at the Extension School. After graduation I ended up at a publishing company where I wrote the chapter exams for middle school math books. (If you’re a sixth grader in California, I’m sorry.) At the same time I started in a spunky, free-thinking masters program in education at UMass Boston before getting whisked away to teach introductory computer science elsewhere in the university. Along the way, I hung around an urban charter school in Dorchester as part of my coursework. To be sure, education is really important to me.

So at first I wasn’t sure what to make of my HGSE course. These days I spend most of my time in the lab with delicate scientific instruments, goofy and less delicate scientists, and large, slippery, and quick-moving frogs. The pressures of real-time classroom conservation in a field that I’d been away from for so long with people who live and breathe this stuff everyday was, to be perfectly frank, intimidating. We had received our course pack and reading list in early December. Because time was at a premium, all of the lectures were prerecorded and posted ahead of time. And the teaching staff encouraged us to hit the books nearly a month before the first day of class. Yowsers. I had a lot of catching up to do.

But then the course started. I assumed course discussion would reflect the same sort of openness and thoughtfulness I had enjoyed at UMass. But if I learned anything in those classes, it was that I need to dispense with assumptions, suspend judgment, and, as we say sometimes in biology, let the data speak for itself. And, oh, did my classmates speak.

Never before had I encountered such persistent intellectual bullying. Not just at Harvard, but anywhere. It was shocking to me that some ideas could be heretical; certain topics entirely taboo. The main theme of the course was exactly what I expected: there are large groups of people (mostly blacks and Hispanics) who have been systematically disadvantaged throughout their history in this country. On the other side, another group (of wealthy, white men specifically) has manipulated mainstream social and political structures so that their children are systematically advantaged. To level the playing field we need a swift injection of money and multiculturalism. All of this seems completely reasonable if done reasonably. I want to give a voice and power back to the dispossessed; don’t you?

The sermon was predictable. Course material provided us with sound bites that we could wield quickly in a pinch. But the way I was supposed to think was fundamentally unchanged. In fact, it felt like that was by design. Opinions that weren’t recognizably aligned with the gospel truth were denied flatly. Those ideas that actively disagreed with mantra of the noble but disadvantaged youth—savage is no longer politically correct, but the sentiment is—were silenced. My classmates rode around on the white horse of moral supremacy to quash discussion and avoid making concrete suggestions for fear of criticism. Whenever someone took a definite stance, someone else inevitably asserted their fears that the dominant power structure was secretly creeping in to rob the poor of their humanity. Now don’t get me wrong, many times that was exactly the case.

The extent to which people who extolled the enlightened practice of listening burrowed their heads in the sand to hide from new ideas would have been laughable were these people not actual educators who interact with actual children. In group break-outs, my classmates railed against me (and other heretics) with passion but without evidence. During an exercise on curricular planning, for example, I suggested that mathematics isn’t itself hierarchical and that our classes need not be. Algebra doesn’t need to precede geometry. We just insist it does because of an accident of history that has been frozen into the curriculum. I didn’t mention my experience in math education. I wanted my ideas to stand for themselves. A classmate of mine insisted that math follows a linear order. Basics first. Advanced topics later. And that’s that.

Another time, I pointed to models of inequality that abolished race but were unable to dismantle financial segregation. Consequently I suggested that we should investigate how people acquire and maintain wealth and incorporate what we learn into our classrooms. This time another student, at a loss for words, told me that segregation was about race. It just is. Full stop. My TF consistently commented that my response papers could be stronger if concluded something that I believed contradicted my main arguments. Naturally, her arguments recapitulated the party line: in this case, that honors tracks are categorically bad. Like Lisa Loeb, I was only hearing negative, “No, no, no. Bad.”

My meeting during office hours with the professor was the most surprising example of this multiple-ways-of-knowing, except-in-this-class philosophy. Initially I had scheduled time with her to talk about careers in education, but by the time our appointment rolled around it was clear that our conversation would focus on my final paper and its subsequent rewrite. I should admit two things about my final exam. First off, I was confused about what a semi-reflective, semi-analytical paper ought to look like and my first guess was bad. My paper was disjointed and poorly written. Second, I put a lot of original thought into it. The version I submitted contained what I believe to be a thoughtful proposal for urban educators that integrated, if indirectly, most things we had read, discussed, or otherwise touched on in class. In lecture, our professor asked, “how can we best respect the diversity in our classrooms?” To come up with an answer, I defined respect and diversity, drew meaningful connections between them and proposed a framework for thinking about diversity which differed usefully from those found in our readings. But my response wasn’t “recognizable” to my TF or professor. And more, importantly, it seems, my paper didn’t explicitly retell the history of inequality in American schools. They needed a book report narration to prove that I had done the assigned readings. These were important, after all. At one point during our meeting I asked directly if I should just parrot back the readings one at a time for my redraft. At this point the professor responded that she would not usually want to sound so “anti-intellectual”, but that yes, that would indeed suffice.

The point of my favorite reading, one by Hirsch, argued that in order for a marginalized voice to be heard, it needs to speak the same language that those in power speak. The class had universally dismissed Hirsch, because they claimed (incorrectly) that he privileges rich, white viewpoints. In doing so, they proved his point: if you don’t sound intelligible, no one will treat you intelligently. So figure out how intelligent people sound and talk like them, but say what you think. The conversation I had with my professor, who specializes in civic education, marginalized voices, and social justice, did just the same. My point wasn’t recognizable, so it didn’t exist. (Like my TF, she also decided that my paper was about the necessary evils of tracking.) I’ll tell you how I rewrote my final paper in case you ever take a class at HGSE. There’s a recipe you can follow. It doesn’t require much thinking but guarantees success.

Animal imagination

This time I have a question for you, the kind reader: can anyone tell me (or point me to a study that suggests) whether non-human animals practice their skills outside of a group?

On many a PBS nature documentary, you can find a gathering of young, fury things play-fighting one another to hone their hunting and social skills. However, human athletes will substitute physical competitors with imagined or abstracted ones. It’s common for athletes to compete against recorded times, high scores, or a mental reincarnations of a previous or idealized self during practice in the absence of a physically present opponent. And this sort of activity isn’t confined to sports like running or cycling. Full teams can visualize a routine or match performance for positive effect. Marines are instructed to imagine their hitting a target—and this sort of practice increases accuracy. These pretend opponents have real, demonstrable, and causal power. In short, human imagination is pretty powerful aid to skill acquisition, at least.

So let’s get back to my opening question: to what extent can non-human animals imagine? Please help me out if you can.

Technorati Tags: , , , , , ,

Games: a Ludic Structure for Problem-Solving

Today I’ve decided to post a journal together with a longer paper about games. You hear all the time that we need to inject more play into education, that we need to return to childhood, etc. But why? You don’t as frequently hear why play is useful in education. People claim things like “If learning is fun, children will learn better.” I’m not sure of the connection. I suppose that if kids are engaged in learning, then they have a better chance of actually picking something new up than if they’re not trying to learn at all. That’s like saying if you look for something you have a better chance of finding it then if you don’t look at all. Sure, I buy that. But why play? By the same argument, we could just as easily pay kids to go to school and do their homework.

Of course some people do give reasons why play is useful. In these two papers, I’m building on some insights found in a 1933 paper by Lev Vygotsky entitled Play and its role in the Mental Development of the Child. (Vygotsky, you may well know, is one of my current heroes.) I remind the reader that in play, you can find all sorts of higher-order thinking skills taking place. Imaginary play is a very natural, distilled, abstractly difficult thing to do. Yet kids seem to do it on their own anyway, and before they even step foot in a classroom. If taught effectively, I think play is a useful vehicle for transfer of skills and tons of that ever-so-hot interdisciplinary work that goes on nowadays. (Wait until I get my genetic algorithmic music up and running.)

Journal 4 Journal 4: Methodological Doubt, Belief, and the Structure of Play

Paper 2 Reflection Paper 2: Decision-making as Game: A Mode of Prediction and Solution

Peter Elbow introduced concepts of methodological doubt and belief in his book Embracing Contraries: Explorations in Learning and Teaching. They’re central to his believing game and doubting game. Traditionally, doubt has been used as the primary tool in critical thinking. This unbalanced attention really makes a lot of analysis blind to new insights that can be gleaned from a moment of pure, suspended disbelief. (My ego won’t let me pass up an opportunity to say that both games show up automatically in my coffee mug model of classroom education.)

In my first paper I remark that all games require its participants to engage in the believing game—they have to believe that the rules imposed by the game are real and that the game itself is real. There are no consequences in any game if you don’t except them. You can always pick up the ball with your hands in soccer, unless you firmly believe that you can’t. For this reason, we might frame any situation as a game.

In the second paper, I extend my ideas to show that framing a situation as a game can greatly improve your power to predict behavior and arrive at winning strategies by simply considering the acceptable moves in your game. To illustrate my point, I work through a problem of the type sometimes given in consulting or computer science job interviews. The example shows, additionally, how mathematical reasoning (which I believe is no different than plain, old, vanilla reasoning) can be used to solve a problem without once using “math.”

As always, please comment freely. I’d love to get some feedback on this stuff.

Technorati Tags: , , , , , , , , , , , , , , , , , , , , , ,

Critical Thinking Journal/Weak-sene, Strong-sense, and Probabilities

That’s right. It’s time for another installment of “What has Josh been writing for class?” This week I responded mostly to an old article by Richard Paul—who, I think, bears a striking resemblance to Walker Texas Ranger: hold on to that.

He differentiates mainly between two types of styles of problem evaluation: weak-sense and strong-sense critical thinking. To paraphrase, perhaps unfairly, weak-sense is marred by an overly narrow subproblem formulation. It’s atomistic. First you take a big problem, chop it up into smaller problems, and then solve each of the bite-sized pieces one at a time. Paul rightly notes that oftentimes this method misses the larger problem that arrise from the interplay of the otherwise well-behaved subproblems. The mathematician in me has to note that the local-behavior-does-not-imply-global-behavior phenomenon has been a central theme in differential geometry from about its beginning. The same problem creeps up just about everywhere else you look for it. I’ve tried to talk about this before in vague terms relating to urban planning and chaos theory. Maybe I should try again sometime. But for now:

Journal 3 Journal 3: Weak-sense, Strong-sense, and Probabilities

I agree with Paul. Strong-sense thinking is more appropriate for lots modern problems. International conflict, curricular design, and global warming all require strong-sense critical thinking, for example. (Ordering dinner at a restaurant typically does not.) While I like Paul’s network approach to problem solving, I think the primary weakness of weak-sense thinking lies in its absolutist view of truth, not necessarily its divide-and-conquer methodology. Truth, when viewed as a certainty, is rigid and fragile. Today’s demanding social and business landscape calls for something more adaptive, fluid, and functional. (Yes, you were supposed to read that last line with an announcer’s voice.) So how do I amend his framework? With probabilities of course. Really dedicated readers will see that I’ve mostly recycled my blog entry about assumptions. But to keep things fresh, I had to add something. And you knew it would happen eventually. I couldn’t resist.

I center my discussion around a theorem from linear algebra. Gleason’s Theorem tells you exactly what the probabilistic measures on the closed subspaces of a Hilbert space are (basically they’re projection operators). And according to some, it’s central to future research in information retrieval. I use it to show the usefulness of multiple points-of-view with some scientific flare. Of course, my treatment is clumsy—but technically I’m only allowed one page per entry. How thorough could I have been? Maybe later I’ll clean this up and expand it a little. For now, it’s probably okay.


Paul, Richard. “Teaching critical thinking in the ‘strong’ sense: A focus on self-deception, world views, and a dialectical mode of analysis.” Informal Logic Newsletter, 1982.

Technorati Tags:, , , , , , , , , , , , , , , , , , , ,

Critical Thinking Journals/The Coffee Mug Model

Every few weeks, we take time to reflect on our reflections on class—a sort of mega-metacognition, you might say. This is the first reflection paper for the semester. The material builds on my journal entries and my final paper from that course on dialogue processes. The Coffee Mug Model shows up once more, but this time it’s got a little more power behind it. Take a look.

Reflection Paper 1 Reflection Paper 1: The Coffee Mug Model of Classroom Education

In this paper, I flesh out the idea behind a behavior space, and note that classrooms, like most other institutions are not grounded to physical space. Instead, classrooms, companies, and society itself are examples of behavior spaces—i.e., groups of actions. The language of action provides a way to communicate information, and, indeed, is more often used to transmit knowledge than verbal communication. Using these observations, I decide to center classroom instruction around a particularly useful behavior, which I call respect. Here, respect takes on a special meaning—the willingness to learn from others. Once that identification is made, I am able to show how this single behavior is especially well suited to encourage the conventional dimensions as well as progressive others around which classrooms [should] normally be designed.

Technorati Tags:, , , , , , , , , , , , , , , , , , , ,

Critical Thinking Journals/Skills and Dispositions

One of the texts we use in CCT 601: Critical Thinking is a book that came out of the Harvard Graduate School of Education group called Project Zero—yes, it’s the same one that Howard Gardner runs. The Thinking Classroom gives the educator some very concrete tools to approach some rather abstract concepts in the classroom. The format of the book is more helpful than most: two chapters cover each chunk of material. The first of the pair always introduces the concept and gives a little justification for its relevance. The second chapter illustrates the concept in practice through a handful of annotated examples. I don’t fully agree with everything they say, but I like format. That’s saying a lot.

Anyway, it’s useful to know many of my journal entries respond (in part) to this book. We also read a lot of articles, if I get the chance I’ll put references at the bottom of each of these posts.

Journal 2 Journal 2: Skills and Dispositions

Here I continue to investigate building learning environments from the community up. In particular, I briefly examine the differences between raw skill and dispositions actually to use those skills. I decide that there really is no difference from the standpoint of culture. Instead, I propose that the schedule (or sensitivity) of practice of a skill is built into the culture through a mechanism which I call tradition. Equipped with traditions of practice, educators can instill really abstract things like intrinsic motivation and measured risk-taking in their students simply by provided the proper community, proper culture, and proper traditions.

Let me know what you think.

P.S.—This entry is missing a graph in the right margin of the first page where it says “Performance over time.” [I drew it in by hand on the copy I submitted in class.] The graph starts out relatively flat, dips down, and then rises up above the starting level and flattens out again.

Technorati Tags:, , , , , , , , , , , ,

Critical Thinking Journals/Culture of Thinking

Well, last semester I kept a journal for my class CCT 602: Creative Thought. This semester I’m doing the same for CCT 601: Critical Thought. I think that what I’m writing now is more interesting. I’ve been able to build on my work from previous classes, but somehow things seem to be coming together now. To indulge my narcissism, I’ve decided to post my papers right here on my blog—that way at least my grandmother can read them.

Journal 1 The Culture of Thinking

In this entry, I try to tease out some of the more obvious components of society. In doing so, I look for applications in a learning environment context. Values pop out as a the centerpiece of attention—and whether a classroom is structure to enable the learning and use of higher-order thinking skills is really a commentary on the values of the classroom. The implication is somewhat surprising: there is no such thing as a morally neutral education. Every action in a classroom is a statement of value judgment.

In particular, I introduce a concept of central importance to my later journal: a behavior space. After all, how can you “take me to Funkytown?”

Technorati Tags:, , , , , , , , , , , , , ,