This message deals with several threads on the list: the math competence thread, the units and conversion thread, and the breadth versus depth thread.
Overall I am fairly pessimistic about chances of dramatic improvement in education in the United States today. I have faith there is a workable curriculum, but I don't think the chances of implementing are not good.
* * * * A Workable Curriculum * * * *
The words "spiral approach" were used by one person in the breadth/depth discussion. This is a time tested approach, and I believe it is a "no brainer." We start early (i.e. kindergarten) and keep it going through college. If this were maintained through middle school, then high-school teachers could keep things broad and apply the appropriate additional layer of depth, and college professors could do the same. It is my understanding from talking to good international students, particularly those from Europe, that this is the approach they have used all along.
As mentioned by several, this approach is currently failing in math and failing badly in science. The worst failure occurs in middle grades (starting roughly in the 5th grade) and that makes it difficult or impossible for high schools and colleges to recover. Often the upper elementary and middle school teachers are so ill prepared to teach science that any successful spiraling beneath them has already reached or surpassed their capabilities.
We are trying pretty hard right now to train science teachers at all levels, but especially the middle school level. Current Ohio standards require that middle school teachers specialize in two areas chosen from science, math, language arts, and social studies. We are having a fairly steady stream of competent students going through Bluffton College who are preparing for the science/math combination for middle school. In addition to biology we are giving them a good dose of physics, chemistry, earth/space science in the hopes they can teach more than simple biological science in grades 4 through 9. It will take a while, but I see these more stringent licensure standards beginning to change teacher competence in science in both the elementary and middle school levels, especially middle school.
* * * * The Real Problem * * * *
None of this will matter if we cannot combat another problem that has been plaguing education at all levels for as long as I can remember. Indeed, this problem is much worse now than it was 35 years ago, and it is even rampant at the college level. This problem is the attitude, belief, practice, that all education takes place within the class period. That is, students don't do homework. They view 8am to 3pm as the school's time (reluctantly) and everything outside of that is their own time. Their own time includes sports, music, jobs, fun... just about anything other than study. I realize some students have a terrible home situation and time outside of school can often be "survival time." That's a separate problem I am not addressing here.
When I was in high school (from 1964-68) my math and science teachers assigned daily problems. I believe I was one of about 15 students in a total class of 150 (i.e. about 10%) who worked these problems on a regular basis. I did homework faithfully every evening. Sometimes I enjoyed it and sometimes I didn't. I did homework because I somehow knew it was the right thing to do. I was well aware most students were not doing science/math problems and were not handing anything in. I was also aware some students were handing in problems they had copied from someone else, or were handing in the results of a group effort.
My children (a son with two years of college and a daughter with two years of high school) tell me hardly anyone does homework. At best, students divide the problems and share results, but even this is rare; most just don't bother. There seems to be a strong expectation that attending class ought to get you at least a B, and those who get A's either do a little bit of homework or were born at the genius level.
I attended my 15-year high-school reunion but was too depressed to attend any since then. When classmates realized I had completed college, grad school, a national lab experience, and was a college professor, they could scarcely believe it. This was not because they didn't view me as capable, but because they viewed their high school teachers as incompetent. During that evening I got tired and depressed over classmates telling me... "Well, I went to college and wanted to become a <doctor, engineer, pharmacist> but I couldn't handle the <math, chemistry, physics> in college. In high school our math and science teachers were so poor, how did you ever learn the math and science you needed to survive college?"
What I should have said was, "Well you know all those homework problems that Younkman, Patton, Gilbert, and Dotson assigned... I did them all." Instead I said, "I don't know... just lucky I guess." How do you tell these people that they have paid and are still paying the price for doing nothing in high school other than sit in class?
Contrary to most of my high school classmates, I view my high-school preparation as very good and my teachers as reasonably competent. Their primary fault was not the curriculum nor delivery of the curriculum, but that students were able to graduate without doing assigned work. From 1968 to 1972 I saw the same thing in college, but not so bad. A person who did not do significant work outside of class had a hard time getting through college, but many tried it. In my teaching from 1978 until now I have seen this slowly erode to the point that many students today do get through college in about the same manner as many of my classmates got through high school 35 years ago.
It is a good thing students view me as fair and basically on their side because it is not unusual for students to write on their course evaluations, "I did more work for this course than any course I have ever taken. Even so, I didn't do everything I could have and I am probably going to get a C. I realize this is my fault, but I need to have a life outside of class." Because I have a pretty good relationship with my students I believe they are being honest when they write this. Yet, I am not expecting them to spend more than two hours out of class for every hour in class. I suspect those getting A grades are probably spending 60 to 90 minutes out of class for every hour in class. Even so, I am perceived as one of the most demanding professors at the college.
If we cannot expect 30-60 minutes a night for homework in junior high, 60-90 minutes a night for high school, and 1-2 hours out of class for each hour in class for college... and if we cannot expect students to spend this time in a manner that enhances their personal understanding of the material... then I don't see how any curriculum is going to succeed. If "having a life outside of class" is the current standard for education, then we must change that standard or else accept the dumbing down of America. I don't see any way to have "less is more" if this is understood as less time spent can yield more learned. That "ain't gonna happen."
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817