At 4:51 PM 10/7/95, DanH150093@aol.com wrote: >Mike- > >>As opposed to something meaningless like . . . what? Learning? Increased >>ability to appreciate and enjoy art and culture? > >I'd settle for enough learning to support oneself in a reasonable fashion >while producing enough competence to maintain our standard of living. > >Mike, I understand you've worked with students in the inner city, but I don't >really know how the world appears from the U of M. I know we have one thing >in common; we want to help kids. > >But from my perspective in LA, we've a hell of a problem. Kids without any >motivation. Yeah, an engaging lesson can captivate their interest for an >hour. Does it correspond to increased retention, fostering motivation, and >more learning? Not usually. > >We need help badly from the state. Arguing about this issue is sort of like >the man crawling across the desert dying of thirst, turning down a drink of >water because it's not Perrier. > >What is it about the new paradigm of teaching math which makes it so >impossible to detect it by any traditional form of assessment? > >Seriously. Is it possible that what you are proposing can be quantitatively >measured to any degree? I'm not bating you; I'd really like to know. > >Dan >"Los Angeles- where inference dominates"
I think the key to this issue is what you mean by "quantitatively measured" and how you would propose that such measurements be used. In my opinion, quantitative measurement is highly useful in the physical world: e.g., when I want to buy carpet for my house, I make out a lot more successfully if I know the dimensions of the rooms with a certain degree of accuracy; if I brew beer, doing statistical studies on various replicable conditions (combinations of ingredients, temperatures, brewing times, pressure, etc.) is useful if I want to be able to re-create an acceptably-similar product in the future.
Unfortunately, human behavior bears very little reliable resemblance to buying carpet or brewing beer. Education is not a product. Learning is very difficult, if not impossible, to quantify in a way that I find useful. Why? Because in the context of education, what would be useful would be to find the replicable conditions, measure them to a satisfactory degree of accuracy, and (this is the kicker) then REPLICATE them.
But any experienced and reflective teacher will tell you that very little is replicable in the classroom. Like the ancient Greek philosopher (Heraclitus?) said, "You can't step into the same river twice." Because neither you nor the river is the same, I would argue. And thus, it is impossible to teach the same lesson twice (assuming that so doing were desirable). But far too many teachers teach as if what worked this morning, yesterday, or last Thursday is guaranteed to work today. As Jake Barnes says at the end of THE SUN ALSO RISES, "Isn't it pretty to think so?" Unfortunately, it just isn't so.
This is neither to suggest that nothing should be tried twice, nor that teachers must be constantly making 100% revisions of previous teaching. But we certainly need teachers prepared to make and capable of making frequent reflections on their practice, with at least 20% of problems, activities, procedures, etc. being rotated out annually. The idea is to keep the class as close to fresh for the teacher as it can be without making things so intellectually dangerous that both instructor and students go to hell in a handbasket.
Teaching from such a perspective requires both courage and a great deal of administrative support. I would guess from many of your posts that you don't have a lot of the latter. I would further speculate that some of your pedagogic cynicism, pessimism, and conservativism (or at least what I perceive as being so) stems from a sense of the potential for you to wind up drowning in a situation that seems hopeless unless ruled with a fairly iron hand. Hence, the Saxon materials, which seem to offer a predictable, clear road, would appear attractive. Heavy emphasis on current conservative buzzwords like "accountability" would appear to provide some sort of prod with which to goad some of the wayward students back into the fold.
There are few, if any substitutes for hard-working, dedicated teachers who bring a sense of joy to their students to whatever extent possible. Bad teachers using wonderful curricula and pedagogy are not likely to produce desirable results, by whatever standard we choose. But I think that it is unlikely that well-meaning teachers using deathly-dull approaches to mathematics are likely to succeed with very many students either, again by whatever standards we measure by. Since I'm strongly convinced that the traditional approaches to mathematics teaching in this country are fundamentally flawed, that they over-emphasize the least-inspiring aspects of learning, put far too much emphasis on teacher, lecture, rote learning, algorithms, procedures, parroting, and other devices, useful enough in small doses, but mind-numbing when they dominate the classroom hour, day, week, month, and year.
I don't worry too much about "proving" that the reform approaches to mathematics education are "superior" in some quantifiable way. If tomorrow someone came up with statistics that said that school districts using Standards-based curricula were kicking butt on various standardized tests, I would not celebrate. Similarly, I would not mourn if the opposite statistics were produced.
Numbers will not settle this debate definitively because what we're dealing with, student learning, is quite nebulous. At some point, for me the educational debate comes down to the fact that every fiber of my being and experience as a learner and a teacher tells me that approaches like that of John Saxon to the difficulties of learning mathematics are a soul-less, quick fix; and that approaches to mathematics education similar to those of the NCTM Standards are, while not THE answer, an approach much more in tune with what makes intellectual pursuits worthwhile and humans as learners interesting.
I apologize for the length of this response, but it seemed necessary.
|--------------------------------------------------------------------------- |Michael Paul Goldenberg |University of Michigan 310 E. Cross St. |School of Education 4002 Ypsilanti, MI 48198 |Ann Arbor, MI 48109-1259 (313) 482-9585 |(313) 747-2244 | |"Truth is a mobile army of metaphors." |Friedrich Nietzsche |---------------------------------------------------------------------------