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: , , , , , ,

Crab Canon

This week we had to create a sound collage for my computational media class. I didn’t set aside a lot of time to work on it, so it became something of a last-minute project. Today I spent most of my day meeting with bioinformatics folk to discuss herberia and taxa and distributed architectures. I may end up working in a CS research group playing with this (or other) stuff. Anyway, by the time I got home, I only had a few hours to start and finish my project. Luckily, I’ve been toying around with MIDI on my own. So I took a line from J.S. Bach and tried to reconstruct part of his crab canon. (This amounts to reversing, compositing, and normalizing a small bit of data.)

Here’s what I started with.

Two hours later, here’s what I ended up with. True it’s not precisely a crab canon—I prefixed a short introduction before the canon starts proper. But if you played from then on backwards, it would sound exactly the same. That’s right: I one-upped Bach. He thought he was writing a musical palindrome. Unfortunately, he couldn’t reverse the attack and decay of each note. He needed me to come along and help him out with the minor, technical details. There’s no shame in that.

You can even download my project in spiffy MP3 format if you like. I’m just that sort of guy. Giving, courteous, clean.

Crab Canon.mp3

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:, , , , , , , , , , , , , , , , , , , ,

Grassy Field

Since all I do these days is post my school projects to my blog, here’s another one for you. This week we had to create a collage. The requirements were pretty bare: at least five instances of the picture, one rotation, one rescaling, and at least one color modification. Try to spot each of the requirements in the final product below. (Maybe you’ve seen the original image before.) I had planned on using longer strips than the squares I ended up implementing, but I got lazy. The checkered effect is a little busy for my tastes; hopefully it’ll make the grade.

I tried for freakin’ ever to get the sky to soft clip to the hill top. I was able to adapt the intermediate image technique described in this article to create a tacky sun (not shown for art’s sake), but not for much more. Instead, I used the built-in, jagged setClip() method native to the java.awt.Graphics2D class. In case you were wondering, the clip was made with about six straight lines. I hate spline fitting, and try never to use curves—especially if line segments will do just fine. File that little tidbit away, it could be useful someday.

But convolutions rock. I’ve always thought so. Ever since I started using them to do signal processing in astronomy class. Our professor made us do a lot of convolutions using a visual calculus that really changed the way I thought about calculation in general. Drawing it out refined my sense of geometric interaction and avoided a lot of messy integrals. Here’s to qualitative methods: hurrah!

A field in collage

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:, , , , , , , , , , , , , ,

Geometry Lesson Plans

For one of my final projects, I wrote the first of three lesson plans for a high school course on plane geometry. When designing learning environments, it’s important to work around four dimensions that affect learning. They are to what extent your classroom is knowledge-centered, learner-centered, community-centered, and, of course, assessment-centered. Sadly there is no absolute consensus about what those words actually mean. And even worse, there has been considerable emphasis on learner-centered and assessment-centered environments to the near exclusion of the other two. And even worse still, many politics have tricked the general population into thinking that there is a zero-sum binary between learner- and assessment-centered classrooms. The fact of the matter is, a good instructor will make sure to provide classroom that is well balanced among all four components.

Knowledge-centered is perhaps the easiest of the four concepts to pin down. Make sure there is substance to what you’re doing. Teach something. Knowledge-centered environments require just that: knowledge. My lesson guides to geometry are filled with—you guessed it—geometry. Passing mention of concepts from real analysis and abstract algebra show up. Were I to write a fourth installment, you’d read about symmetry groups, group representations, and addition. A proper discussion about measurement would dive deep into the definition of number itself, equivalence relations, and probably prove Euclid’s so-called Common Notions. (That A=A; if A=B, then B=A; and if A=B and B=C, then A=C. Yes, students should be able to explain why self-evident facts are true, too.)

Student-centeredness takes into account what the learner already knows—or doesn’t know, or misunderstands for that matter. For this reason, my lessons are written for the instructor but led by the students. I use a list of questions that the teacher can use as a model. Taken together they form a cohesive mathematical narrative. But since the point of student-centered environments is that each classroom ought to be tailored to the individual needs of the particular students in the seats, the idea of a student-centered lesson plan that has been blindly written and mass-distributed is somewhat antithetical to its own aim. The Socratic question-and-answer method gets around that. Instructors have both the license and responsibility to dovetail the lessons in a way that best suits the students in the class.

Because of the individual nature of the plans, assessment becomes a problem. How do you figure out if the students have figured out the material if there is not one but several possible right answers? There are over 350 published proofs of the Pythagorean theorem, for example. And all of them are equally correct.

Student-directed learning has assessment built right into it. The teacher can constantly monitor student responses to gage their depth of understanding. The count of prompting questions (given by the teacher) to achieve a particular response can be used an index of mastery over the material. This sort of examination is not obvious to the students and therefore relaxes the pressure associated to more conventional means of testing. Moreover, sustained dialogue between students and the teacher promotes a collaborative, community atmosphere within classroom. Students and instructor exchange roles dynamically, which fosters all sorts of other leadership qualities and instills intrinsic motivation and proactiveness within the students. Having students talk and draw on the board takes care of three of the target components all at the same time.

So, all that you really need my plans for are the knowledge. And the notes are pretty insightful, if I do say so myself. At least have a gander at the very pretty marginal glosses. I employed some artful information mapping techniques. You’ll find that the diagrams are rather palatable. I’d be interested to know what other teachers have to say about them, how I should change them, and if I should write more.

Geometry Lesson Plans 1–3 Geometry Lesson Plans 1–3

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

Creativity Journals

Since I write these things for class, I’ve decided to post my disorganized ramblings on creativity and the creative problem solving. I’ll update with a new installment weekly (or thereabouts). You can always find the link to the right under Pages > Creativity Journals.

Since everyone has something to say about creativity, maybe some of you will comment. I’d love to know what the anonymous masses think.

Technorati Tags: , , , ,