Attaining Intangible States A Personal Narrative and a Lesson in Applied Philosophy

A Teacher Pursuing Intangible States
original artwork by Tavet Rubel, created for Dewey to Delpit

Last post, I wrote about a powerful, impersonal kind of certainty that, under the best circumstances, a teacher feels about the instructions she gives. The incident of the classroom interloper, which I chose to illustrate that certainty, is an especially clear example, but in the course of my two months teaching precalc, there have been countless subtler instances in which this sense of the inevitability of my injunctions has come to my aid. It is the first time in my teaching career (now in its fifth year) that I have felt this kind of sureness, and of course, it’s thrilling.

When I taught at an inner-city No-Excuses charter school two years ago, I had the opposite experience. I was deeply insecure and hesitating. I expected my instructions to meet resistance, and they almost always did; and when that resistance was forceful, as it often was, my very dignity and pride were threatened.

The Brief Tale of the Classroom InterloperRuminations on Authority, Confidence, and Intangibility

The Fates: the ultimate authority figures

(This is the second in a series of posts based on my experiences teaching a pre-calc class at a private school. See my last post for a more complete introduction.)

The other day, a girl who’s not in my class accompanied one of my students into the room at the start of the period. The two were sharing a fit of Thursday afternoon giggles and entered full of unexplained hilarity. Now, the culture of the school where I teach permits a certain amount of deviation from proscribed routines, and it’s not so unusual for a student to follow her friend into a classroom simply for the fun of it—and, I suspect, to see what it’s like in there. The purpose of such excursions is surely benign, but I find the loosening of structures to be a slippery slope, and I try to make sure classes start on time and start focused. In short, I wanted the interloper gone, and I knew she soon would be.

Autonomy, Respect, and ObedienceObservations from my own Teaching Practice

So, I was having a hell of a time finding an image for this post, when I ran into this weird little drawing in the google image results for "teacher." As my friend Erica points out, and as I don't know how I missed, it's clearly a drawing—or a schematic almost—of Jesus and the apostles. What interested me about it initially were the yellow lines over the "teacher" which seemed to indicate an authority that went beyond discipline and obedience towards something moral. The authority indicated, I now see, is a divine one, but, for a secular Jew & pantheist like myself, the distinction is minor. The vision is of teacher as purveyor not merely of knowledge but of wisdom and moral direction. Moral authority comes less from what one knows of morals than of how one's students view one.

Evidently, I am not efficient enough to simultaneously keep up with my new teaching schedule and post regularly to this blog, so instead of my usual essays, I’m going to start posting brief thoughts and observations arising out of my own teaching practice. These will come primarily from the pre-calculus class that I began teaching two months ago.

The class is held at a high-end private day-school, whose philosophy is Romantic—that is, permissive, individualist, and committed to teacher autonomy, student choice, and learning as the pursuit of truth and beauty. Sixteen students are enrolled in my class, which I think may be the perfect number for the instructional methods I’m using. The course content is loosely defined and oversight is minimal, so that within the (unfortunately brief) confines of my 45-minute block, I have a lot of freedom to teach what and how I like. Because my other weekly commitments are small, I have more time and energy than any full-time teacher could ever hope for to devote to planning and preparing my curriculum and to assessing student work. In short, I have the ideal conditions for rigorous, thoughtful pedagogical innovation, and the result is that I am teaching by far the best class I’ve ever taught.

If my reflections on the class appear at times big-headed, let me explain that I have been, in my estimation, the worst teacher in an entire school—incompetent, weak, and ineffectual—and if I am doing even a halfway decent job now, it is only because I have learned a little from my mistakes. I am still painfully aware of my shortcomings as a teacher, but the conditions of my pre-calc class—not only those factors listed above, but the cultural similarity between myself and my students, the maturity and intelligence of the students, etc.—show my teaching in the best possible light.

How to Make it Stick: The Psychology of Learning and Memory

Apologies to my readers for the long delay. I recently started teaching a pre-calculus class at a private school in Brooklyn, through which I’m putting into practice many of the pedagogical theories and methods that I’ve observed and studied over the last few years; the process is exciting, but the extra planning required to implement so many new ideas takes up most of the time that I previously devoted to this blog. Further retarding my posting schedule, the post that I’ve been working on intermittently for the past few weeks defies my best efforts to tie it down to finitude and linearity. In the interim, I wanted to post a couple links & a “brief” discussion.*

The Research

My friend Sam Gershman, who studies the neuroscience of memory was thoughtful enough to pass on to me a bunch of cognitive-psych research (see links below) on the conditions that facilitate long-term learning retention. The broad principle around which this research coheres is a theory, strongly supported by experimental data, about the relationship between long- and short-term memory: learning conditions that facilitate short-term recall hamper long-term storage, and vice versa.

On Vividness of Language and Experience

The Carding of Wool

The Trying of Fat

A reader—alright, let’s be honest here: my dad—left a comment on this blog regarding Dewey’s language in the passage that I excerpted last week. His point seems to me so interesting and so consonant with Dewey’s own beliefs, that I want to address a brief post to the subject. The comment itself is excellently written, and I reproduce it here in full:

What strikes me first in the Dewey passage is the vividness and specificity of his language. The "carding" of wool, the "trying" of fat, a whole world of natural processes and self-sufficiency for which we no longer have even the words. The passage helps explain, among many other things, the richness of Shakespeare's imagery. He lived the life Dewey is describing in which human beings actually made the things they used and understood, therefore, in a way we cannot, the material world around them and the properties of the objects in it, the weight of the cloth, sharpness of the tool, the density of this wood and the flexibility of that one. They saw and knew (knew and saw) the world they lived in, and their language for describing it was abundant, particular and precise.

Dewey Speaks

On closer inspection, my thoughts about math concepts proved too inchoate to form the basis of the taxonomy promised repeatedly in my last few posts. It is, I suppose, the nature of a serial journal of this kind that one cannot always deliver on one’s promises without sacrificing intellectual integrity. Thus, the “cliff-hanger” at the end of my last post proves nothing more than a tease, and the hungry reader, after a long delay, is served an entirely unexpected dish: a bit of Dewey, fresh from the freezer. What follows is an excerpt from The School and Society, 1900.

Those of us who are here today need go back only one, two, or at most three generations, to find a time when the household was practically the center in which were carried on or about which were clustered, all the typical forms of the industrial occupation. The clothing worn was for the most part not only made in the house, but the members of the household were usually familiar with the sheering of the sheep, the carding and spinning of the wool, and the plying of the loom. Instead of pressing a button and flooding the house with electric light, the whole process of getting illumination was followed in its toilsome length, from the killing

The Sweet Spot: Balancing Conceptual and Procedural Instruction in Grade-School Mathematics

The purely procedural approach to long division.
I stole these colorful illustrations from this website.

A few years ago, I was working in a charter school where the sixth-grade math teacher was having a hard time teaching long division. (I myself, let it be noted, was having a hard time teaching anything at all.) I sat in on some classes, and it was easy to spot the problem. The teacher had reduced the process of long division to a series of five steps: divide, multiply, subtract, bring down, repeat, with a mnemonic, which I forget, to help remember them. This must have seemed like an easy-to-follow script when they were planning the lesson, but it’s deceptively complicated: you have to know which numbers to divide, multiply, subtract, and bring down and what to do with all those quotients, products, and differences once you get them. (See Appendix A, for an idea of just how complex this gets.) The students didn’t understand why they were doing any of these steps, so they found all that information extremely difficult to keep track of. Long division, taught this way, became a dull and intricate labyrinth, riddled with small procedural booby-traps to derail the unsuspecting scholar. Yet, pure procedural methods like this one seem to be prevalent in contemporary instruction—try Googling “long division” and see what comes up.

More recently, my girlfriend asked me to teach her long division, a skill she’d never gotten her brain around back in elementary school. Eager to show her that mathematics is logical and comprehensible, not arbitrary and byzantine, I dove into a thorough explanation of the inner-workings of the long-division algorithm, complete with diagrams and concrete examples. After ten minutes, she was frustrated