This is taken from an essay by Phil Daro, William McCallum, and Jason Zimba, February 16, 2012
“You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year. You object; he says “don’t worry, I’ll make sure that you
get every single piece, and the markings are clear, so you’ll be able to glue them all back together. I’ve got it covered.” Absurd, no? But this is the way many school systems require teachers to deliver mathematics to their students; one piece (i.e. one standard) at a time. They promise their customers (the taxpayers) that by the end of the year they will have “covered” the standards.”
The full essay can be found here. It’s a good read and does a nice job explaining where we are, and where we’re heading in math teaching.
Many (most?) teachers present material straight from the book, and may not realize how this method fragments the material that is already challenging for students. If there is an overarching theme and approach to the methodology of teaching mathematics, more students would probably understand and succeed at mathematics better. Here’s hoping . . .