Thursday, February 24, 2011

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.

Thursday, February 17, 2011

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

Friday, February 4, 2011

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