email@example.com wrote: >What I think is useful is a >whole K-12 curriculum, what topics to be discussed in what grade levels >and how the entire curriculum fit together to form a coherent whole.
to which firstname.lastname@example.org replies: >That is what we have here in Canada.
That is true, Genevieve. It is a Canadian trait to see both sides of a story, to extract and internalize the best parts of each, and then to help produce a superior set of circumstances for all involved. The New Ontario Curriculum for Mathematics, 1997, a post-NCTM Standards-based curriculum based on rigor and accountability, is a testament to that trait.
It is an American trait to plod forward wearing blinders, as if ours is the only country in the world, until, like a bump on the head, a test like the TIMSS points out blatantly that, not only are we not the only country in the world, but other countries apparently have better ways of teaching mathematics and science. Then, the American way is to start pointing fingers, making blanket either/or statements that blame the other guy's way of teaching the subjects, and wax nostalgic about the good old days when the Mighty U.S.A. was the best at everythingÃÂnever mind that those days never existed, only days when the media was even more insulated and internally focused than it is now. Perhaps this is one reason I have never returned to the land of my birth.
Even more disturbing than the "verbal spanking" and associated insultsÃÂwell-precedented tactics of those lacking in more highly-developed communication skillsÃÂleveled at Michael Paul Goldenberg by another participant on this list, are the "my way or the highway" attitudes expressed at times by both sides of the Standards debate, though more often by counter-reformists. A testament to these attitudes can be found in the article at the end of the long URL posted a few days ago by Charles J. Masenas: http://www.pathfinder.com/@@QDIxBwcAwP1FpHGI/time/magazine/1997/dom/9708 25/education.this_is_math_.html (You will have to copy and paste that back into a single line in order to follow it.)
This article was of particular interest to me because it started off with a description of a rather chaotic undertaking of the famous handshake problem. I will begin my first full-time professional teaching job ever in less than two weeks, and I am considering using this very problem as the basis of one of my first lessons. I have used it with great success in my practice teaching, and my internal debate about whether to use it this early in the year revolves around what I feel is necessary to establish prior to tackling the problem. It would not occur to me to put the kids into groups for an hour and "roam" the room without some type of teacher-directed introduction. And yet I consider myself perhaps as much as 90% pro-Standards, and 100% pro-reform.
"It all started in 1989, when the National Council of Teachers of Mathematics,......." reads the article, a blanket, black-or-white statement if ever there was one. (I also taught my Language students to avoid absolutes like "all" and "always", but that comment should only be posted on NCTE-L.) Yet the article ends with,
"Says Thomas Romberg, a University of Wisconsin professor who helped write the revolutionary 1989 math standards: "We knew there needed to be a fair amount of research and teacher training. We knew it would take 20 or 25 years to pull this off." Parents whose 12-year-olds still can't count on their fingers may not want to wait that long."
In the article there is reference to "a straight-A algebra student" who reached for a calculator to find 10% of 470, but these inept 12-year-olds are saved for the final sentence, and it is my conclusion that they were invented by the journalists (Melissa August, Margot Hornblower, and Elizabeth Rudulph) for dramatic effect. They are implicitly blaming the Standards-based curriculum for the sad state of these hypothetical incompetentsÃÂwho were approximately 4 years old when "it all began" and could not possibly have been the recipients of "whole-math" instruction, even if they all grew up in California, a "leader" in implementing "cutting-edge curriculum" such as MathLand, which was first introduced in 1995. I haven't got a calculator handy, but something about this association does not compute.
"Decreased emphasis" does not mean, nor even imply, "dumping the most basic algorithms." The "cool stuff: calculators and geoboards, hands-on, open-ended problems, exercises that encourage kids to discover their own route to the right answer" is far easier to put to good use after, and along side of, some solid, teacher-directed instruction, including memorization of appropriate facts.
I read this list to help me find ways to improve my teaching of math. In general, it has helped me achieve that objective. I've heard both sides now, and my rhetoric filters are permanently in place. Let's see if we can construct some knowledge hereÃÂknowledge of a way to teach math into the 21st century without repeating the mistakes of the past, or wallowing in the mistakes of the present.