From Art and Fear:

The ceramics teacher announced on opening day that he was dividing the class into two groups. All those on the left side of the studio, he said, would be graded solely on the quantity of work they produced, all those on the right solely on its quality. His procedure was simple: on the final day of class he would bring in his bathroom scales and weigh the work of the “quantity” group: fifty pound of pots rated an “A”, forty pounds a “B”, and so on. Those being graded on “quality”, however, needed to produce only one pot -albeit a perfect one - to get an “A”. Well, came grading time and a curious fact emerged: the works of highest quality were all produced by the group being graded for quantity. It seems that while the “quantity” group was busily churning out piles of work - and learning from their mistakes - the “quality” group had sat theorizing about perfection, and in the end had little more to show for their efforts than grandiose theories and a pile of dead clay.

As the RightWing Prof says, "There’s a lesson there."

Yes, there certainly is. In HighSchool World (different from REAL World), the idea of practice has gone out the window. Practice is labeled "Drill and Kill" and those who practice it are denigrated and denounced (though maybe denounced is too harsh a word). Our curriculum coordinator uses "Drill and Kill" to kill any reform that smells of mastery. She much prefers spiraling and discovery and "Guide on the Side" -- to the exclusion of everything else.

And then there's the textbook that I get to use:

"Factoring is the process of using the distributive process to represent a mathematical expression as a product. For example, the expression 2x+6 can be factored into the equivalent expression 2(x+3). Similarly, the expression 2xOn the face of it, that sounds okay. We've avoided any mention of FOIL. Succinct and clear. And then you realize that there's nothing more. Those three sentences are the extent of the factoring. That's it. No further explanations, no practice problems.^{2}+3x-5 can be expressed as (2x+5)(x-1)"

The whole "book" is like that.

Thankfully I have plenty of stuff of my own making and of the Dale Seymour series so I've got as much as the kids need, but it still amazes me that the authors of this course (and the people who chose it) don't feel it necessary to explain HOW or give some repetitive DOING.

Right, so there's another side. Once upon a time lots of kid wouldn't have attempted math past algebra.

ReplyDeleteGetting more kids to do more math - positive.

Doing it by destroying the content - pointless.

There's got to be some balance, something that gives all kids a chance to do more math, serious stuff, but doesn't get there by watering down the content, and certainly not by cheating the kids who really could/should be handling far more challenging content.