The list has been very active lately, with this discussion of lectures' and the Standards. Dan H, in a recent post, put a different twist on the discussion by challenging us to think about accountability as a motivator -- especially standardized tests for the students.
I am "just" a community college mathematics teacher, and don't have the credentials that many of you have, for commenting on K-12 mathematics education. (Interpretation: I don't work in the K-12 classroom everyday.) I do have a few comments though.
First, we are trying to teach mathematics in a culture that has a schizophrenic relationship with mathematics: "I've never been any good in math, but everybody needs lots of it." Such a love-hate relationship is unique; can you imagine the same paradox with writing?
This cultural background is well-imbedded, and resistant to change. In fact, our culture clings to some unique values that are not found in most others. Among these is the belief that judgement and accountability from above is a "bad" or "dangerous" thing. Our legal system, to some extent, codifies this belief. Generally, I don't think we are questioning this belief; however, we find ourselves uncomfortable with some of its implications. One specific implication is that we are very unlikely to have a uniform (standardized) test with substantial consequences for all students.
Others on the list have been talking about the assumptions about what "today's young people" are like. Most of these are myths. However, there is a culture-wide change for all of us. This change says: "Fast and soon is better than slow and later." Whatever our age, our cultural feedback says rewards must be now', and work (effort) should be entertaining. Education is, in some ways, trying to adapt to this nintendo culture'. (Don't get me wrong; I enjoy a good game ... a good thrill, as much as the next person.)
Next, look at the other motivations to learn. At your level, how many students come in saying "I am excited just to be here, and I can't wait to learn"? I suspect there is an inverse correlation between the number of such students and the grade level. Even in excellent schools, children have difficulty maintaining a positive attitude about learning in the face of the social environment.
Last, look at the factors we are trying to vary in the classroom. We weigh the advantages of "lecture" and "group" (cooperative or otherwise) work. We discuss the appropriate uses of technology. We insert more critical thinking or writing. Dan H. said "It's like ... debating the efficacy of a new carburetor on a Lola with flat tires." I am excited about the process of looking at these issues, but constantly feel a need to look at the other constraints that effect my work.
I seldom have complaints about my fellow mathematics educators. However, I do think we tend to avoid the cultural aspects of our work. For any meaningful change to take place, there must be a better match between the culture and what we are trying to accomplish. Some of the material in the "Standards" are steps in this direction. However, I would argue that the more powerful changes need a different focus. If we, as mathematics educators, have identified a body of knowledge that is important for people in today's world (and I think we have a sufficiently accurate picture of this), then the culture needs to be convinced that learning that knowledge is worthwhile and feasible. We can accept no excuses of "Mathematics has always been hard for me."
I hope my long-winded comments are of some help to someone. (It helped me clarify my thoughts.) <<<<<<<<<<<<<<<<<<<< from >>>>>>>>>>>>>>>>>>>> Jack Rotman phone (517)483-1079 Math Professor Lansing Community College Lansing, MI internet: ROTMAN@ALPHA.LANSING.CC.MI.US "Like all art & science, mathematics surrounds us." <<<<<<<<<<<<<<<< Math Success ! >>>>>>>>>>>>>>>>>