Mathematics education in the US is a fascinating topic for those interested in educational policy.
First, we should take with a grain of salt the generalizations on comparative, international mathematics achievement. Almost all of these generalizations rest on the TIMSS study, which is open to some question as to its reliability and validity. It is very hard, if not simply impossible, to meaningfully measure comparative achievement across educational systems with so many different variables in terms of curriculum, instruction and assessment. Gerald Bracey, an independent educational researcher who does an annual 'Bracey Report" on the state of US education for the major education journal, the _Phi Delta Kappan_, has produced compelling critiques of a number of different features of the TIMSS study, although he -- like some of our LBO brethren -- has an excessive fondness/weakness for outrageous hyperbole. [www.america-tomorrow.com/bracey/gb.htm]
But there clearly are important international differences in Mathematics education. Stigler's and Hiebert's _The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom_ [Simon & Schuster, 1999] did a quite impressive ethnographic study of middle school/junior high school math classes in three countries -- Japan, Germany and the US. They videotaped hundreds of different classes, and developed an extensive coding system to compare the different teaching and learning cultures in each of the settings. Their findings? There was a spectrum of pedagogy and instruction, with the US on one side, Japan on the other side, and Germany in the middle. Japanese classes placed the greatest premium on education conceived in terms of learning through practical problem solving by students themselves, with most of the class time being students working "hands-on", in small groups to find solutions to a practical problem, while American classes were much more in the vein of whole group instruction, with the teacher explaining and illustrating some mathematical principle to the entire class, and the students then practicing it individually at their desks through various narrowly defined and abstract problems [i.e., solve for x]. They conclude that the Japanese math classroom engenders and produces a much higher level of mathematical thinking. I found their work, and their conclusion, largely compelling, although I think that they make too much of the TIMSS' results. It fits closely the anecdotal consensus within American education that Mathematics is the most pedagogically regressive field, the most resistant to change.
The obvious question is why there is this difference among the national Mathematics teaching and learning cultures.
One possibility, raised in Jan's posting below, is that the problem lies in the relative lack of preparation of American mathematics teachers. This is a complex issue, as I shall lay out, but I think the ultimate answer is that this is not the case. We are on the cusp of a looming teacher shortage in the US, largely as a function of the imminent retirement of large numbers of baby boomer generation teachers, secondarily, because of the extraordinary high drop rate of young teachers just entering the field [as many as 50% leave within the first five years, with a much greater drop out rate in urban areas]. Mathematics education will be particularly hard hit, because it and Science are fields -- unlike English and Social Studies -- where there are a wealth of better-paying jobs with much easier working conditions in related industries, and they are already experiencing much more difficulty in attracting academically qualified applicants. But this is still largely a _looming_ shortage, and it does not now and will not in the future hit evenly. If you look at New York State, for example, the first signs of the upward
curve of the teaching shortage can be found almost entirely in urban areas, especially NYC -- where one out of every 7 teachers is uncertified [i.e., has not met the minimal state requirements for licensing, but only has a BA in a field associated with their subject area of teaching]; none of this stops our brilliant mayor from declaring that there is no teacher shortage in the city, since there is a live body in front of every class. Thus, one will not yet find significant numbers of uncertified Mathematics teachers across the board in US schools, and certainly not at all in wealthy suburban school districts. As a consequence, it would be a mistake to generalize about the level of teacher preparedness and expertise in the US as a whole based on this emerging shortage. Although the coming shortage of prepared and experienced Mathematics teachers will make things much worse, it can not explain much of what is a preexisting gap in the quality of Mathematics teaching.
[On a slight aside, but linked to the recent thread of equity in schooling, there is a very instructive lesson here about the ways in which questions of equity permeate all matters of educational policy, and about how difficult it is to do educational reform successfully. One illustration: in the recent past, California undertook a major initiative to lower class size in the lower grades. Now all other things being equal, such a measure should be a very positive development, especially for students in inner city areas. Lower class sizes allow much more teacher-student interaction, and much greater teacher attention to the individual learning needs of the student. Research has shown again and again that lower class sizes at the elementary grades has a very salutary effect, especially for students who need more help in acquiring basic literacy and numeracy skills. [See a summary of this research in see Alex Molnar, _Smaller Classes, Not Vouchers, Increase Student Achievement_. (Published by the Keystone Research Center, 412 North Third Street, Harrisburg, PA 17101.; 717-255-1781).] Yet given the massive and immediate way in which California undertook this reform, it had unintended, undesirable effects for urban school districts and their students: suburban school districts with higher pay and better working conditions were able to attract many urban teachers to fill their additional slots, leaving the urban schools with smaller numbers of experienced, licensed teachers teaching a greater number of classes and forcing them to take on large numbers of novice, inexperienced and unlicensed teachers; and urban schools, already overcrowded, were much more likely to lack the space to set up additional classes.]
There is a school of thought, perhaps best represented by Diane Ravitch, which would take the question of teacher preparedness in a slightly different direction.
Continued: Part II
Leo Casey United Federation of Teachers 260 Park Avenue South New York, New York 10010 212-598-6869
===== Power concedes nothing without a demand. It never has and it never will. If there is no struggle, there is no progress. Those who profess to favor freedom and yet deprecate agitation are men who eant crops without plowing the ground. They want run without thunder and lightning. They want the ocean without the awful roar of its waters. -- Frederick Douglass
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