On Dec 15, 2012, at 2:27 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> For example, it is easy to illustrate the distributive law with such a picture. Most often, the distributive law is pictured as an N x M grid divided into two smaller rectangular grids.
You used an interesting word, illustrate. Don't these illustrations in math serve essentially the same purpose as do the illustrations in a story book? And what is the crux of a story book? The story, or the illustrations? If you had to choose to keep only one, which would it be? The story or the illustrations?
I love illustrations in story books but I recognized a couple years ago, in one of my textbook reviews, that illustrations are no substitute at all for the story. Yet, at the same time, I recognized that I would never write a textbook without them.
From the beginning of one of my favorite stories in my youth...
"ONE summer afternoon rather more than eleven hundred years ago, the boy Roland was sitting in the cleft of a broken rock that forms the crest of one of the hills in the neighborhood of Sutri. Above him was the deep blue sky of Italy, unflecked by any cloud: on either side of him stretched a dull, uneven plain broken here and there by wet marshes, and long lines of low hills. A mile or more to the south, and partly hidden behind the brow of the hill, could be seen the old town, with its strong castle, and its half-ruined amphitheatre and its white-walled monastery. Directly beneath him was the dusty highroad which, after winding among the straggling vineyards and little farms that dotted the plain, was lost to sight in a strip of dusky woodland a league and more to the northward. Along that road King Charlemagne, with the flower of his great army, was hourly expected to pass, marching on his way to the castle of Sutri, where he was to be entertained for a time as a guest; and it was for this reason that the lad sat so still, and watched so long, in his half-hidden perch on the hilltop." (The Story of Roland by James Baldwin)
An illustration would fit rather nicely right about here, but I wouldn't trade it for the story.
Most of the popular modern math textbooks have stopped telling the story. No plot development. No character development. No formal development.