Faculty Forum

Vol 12 No 2
20 October 2000

In This Issue

Editorial: On Styles

Over the years I have found that style counts for a great deal in an academic administrator. As department chairman I dealt with five different Deans of Arts and Sciences, two Deans of the Graduate School, three Provosts and two Presidents. All of these had, I think, the right instincts to lead their parts of the University. But they were not equally effective in changing it for the better.

It is not a question of standards. It may be that in the past Duke's academic administrators let things happen as they might. But that time is long gone now. All of the deans and provosts I dealt with were anxious to see Duke move up in national esteem, quickly if possible.

The problem has always been that the faculty changes slowly and incrementally, while a typical administrator remains in his position for only a few years. No administrator is likely to see any dramatic impact of his work in selecting new faculty, even if he could make all the right choices. It is perhaps out of frustration that administrators sometimes make public lamentations about the situation they inherited.

Which makes style all the more important. I will describe two contrasting styles, although most administrators show elements of both.

The first style is imperial. The dean (or whatever) spends much of his time in isolation, considering who the new faculty should be, what the faculty ought to do, and how much support they will get from resources he influences. He is likely to pore over data he thinks measure the quality of faculty activities, separating winners from losers. He is obsessed by rankings. From time to time he will issue public pronouncements on his findings. But he will spend very little of his time actually getting to know the existing faculty, or thinking about how he might help them do better.

The other style is collegial. The leader gets to know a great number of faculty personally, becomes acquainted with their work and problems, and tries to find ways to help. He is less concerned with present prestige than with promoting improvement. He is aware that there are winners and losers, but does not think his main job is to pick them. He does not pass quick judgments on research about which he knows almost nothing, and seeks the opinions of peers in the same field.

The Duke administration has had both types. The imperial type rarely produces constructive results that wouldn't have happpened anyway, and is often destructive of morale. The collegial type often gets good results even from less distinguished faculty, and induces everyone to work to improve the institution. Our late and much lamented friend Charles Putman was of this type. Readers can pick their own examples of the other.

Ambitious Plans for the Pratt School

An Interview with Kristina Johnson

[Kristina M. Johnson, Professor and Dean of the Pratt School of Engineering, came to Duke in 1999 from the University of Colorado at Boulder, where she was Professor of Electrical and Computer Engineering. She received her B.S., M.S. and Ph.D. degrees in electrical engineering from Stanford University. She has been a Fulbright and NATO Fellow, has published over 130 papers in refereed journals, and is author on over thirty patents. She was awarded the Dennis Gabor Prize by the IOC in 1993 and received a Presidential Young Investigator Award from the National Science Foundation in 1985. She is a Fellow of the Optical Society of America. While a Professor at CU, she spun-off six start-up companies, and she sits on several corporate boards. Dr. Johnson was either P.I. or co-P.I. on over $40 million in research contracts and grants during her 14 years at the University of Colorado-Boulder. This interview took place on 2 October in Dean Johnson's office.]

FF There are many things to talk about, but let's start with the planning exercise currently underway. I assume the rules for you are roughly what they are for the others. You present a report to the Trustees this month, and they vote on a resolution in December.

KJ That's correct.

FF What happens in between?

KJ Discussion with the faculty to fine tune the report. They all have a draft of it. We have five working groups, on infrastructure, faculty affairs, education, research priorities and partnerships.

FF Partnerships with whom?

KJ Partnerships within Duke, partnerships in the Research Triangle Park, partnerships with groups we have not reached out to yet.

FF The formal report is presented by the Provost. Have you had feedback from him?

KJ Yes. He has been very helpful and responsive.

FF We'll get to some of the details later. The Chronicle today reports you as having said "Our objective as a school is to be a translation unit between corporations and the University." I take it that is a bit narrow?

KJ It's more to be a translation unit within Duke, taking scientific findings and relating them to possible applications wherever they might be.

FF You arrived at a time when the faculty had already been increased a good deal, and you anticipate a significant further increase. What is your goal, and how much of it is already underway?

KJ The tenure-track faculty increased from about 40 to 71 under the leadership of former Dean Earl Dowell. We plan to expand the faculty by another 30-40% in the next several years.

FF How much space does the proposed new building give you?

KJ About 240,000 sq. ft. That will bring us closer to the space per faculty member that our peers have, after we add the new faculty. We are significantly short of space now. Less than 40,000 sq. ft. of space was added during the previous faculty expansion.

FF Do you have any plans to add programs by creating new departments?

KJ No.

FF Any plans to reduce the number?

KJ No. But in filling our new faculty positions we will be looking for people whose interests will cross departmental boundaries. They will be formally located in a department, but their activities will be school-wide. A person whose interest is in bio-photonics might be located in biomedical engineering, for example.

FF On that subject, you have listed photonics as one area of high priority. Could you give us your definition of that term?

KJ Transportation of information by means of light.

FF And what is bio-photonics?

KJ Light interacting with biological materials for therapeutic, diagnostic, or for investigation of the fundamental properties of biological processes.

FF That is one of the missions of the free-electron laser lab.

KJ Right, and we work closely with several faculty in that lab.

FF So photonics is one of your major areas of initiative. I gather that another is what we in physics call nanoscience.

KJ Yes. Part of our focus there will be on wet/soft materials, with special emphasis on biomedical applications. We will also explore dry/hard materials for applications in photonics.

FF You expect a significant overlap with efforts in chemistry and physics in these areas, I gather.

KJ Indeed. At Colorado we had a group of four faculty from engineering, physics and chemistry who jointly developed a novel-display that launched an entire industry. Major companies such as Hewlett-Packard, Compaq, Samsung and 30 others are commercializing this technology. That's the kind of thing I would like to see happen here.

FF Where do you see the primary funding coming from for these initiatives?

KJ Government, industry, university and private sector funding.

FF This area doesn't have Hewlett-Packard or Compaq.

KJ Actually it does, along with other corporate partners.

FF How much of this awaits the building of new space?

KJ We can't wait for that. The new facility should start in late summer 2001 and be available in 2003. Meanwhile we have been negotiating for, and renting, space within Duke and around Durham.

FF You recently succeeded in recruiting two key people in electrical engineering.

KJ Yes. The first comes in January. I hope this is not premature, since the appointments have not yet been officially approved.

FF I also understand that you are concerned about maintaining biomedical engineering in its current highly ranked status.

KJ Yes. It's a great department with wonderful programs. We have applied for a leadership development grant from the Whitaker Foundation for $17M.

FF Is the undergraduate enrollment fixed, or will it increase with the new faculty?

KJ There may be some increase, but not rapidly. One thing I'd like to see over time is students transferring from Trinity to Pratt because it offers them a unique engineering undergraduate education.

FF Right now it's mostly the other way.

KJ Yes. As we grow in size and stature, students at all levels will recognize it.

FF With your planned increase in faculty, surely you expect to increase enrollment at the graduate level.

KJ Oh, yes. By at least a factor of two.

FF Is the applicant pool sufficient?

KJ I think so. Already several departments attract a large pool of excellent applicants, and some of the other departments are quite competitive.

FF Will the planned faculty be able to handle that many students?

KJ Yes. It's common for a research-intensive faculty member to be supervising six to eight students.

FF With your plan to recruit faculty whose interests cross departmental lines, do you plan to start new degree programs to reflect this?

KJ I think the Ph.D. programs will remain centered in the current departments. There might be some new interdisciplinary programs at the master's level.

FF You are currently looking for new department leaders, I understand.

KJ Yes. Searches are underway in Biomedical and Civil, and we expect a search in Mechanical next year. I'm a believer in term limits. Two is enough.

FF Looking internally or externally?

KJ There are a lot of great internal and external candidates who would really like to serve Duke in this capacity.

FF What are your major fund-raising priorities in the capital campaign? The new building comes first, I suppose.

KJ Yes, the building is our highest priority. And after that, enhancing our research and teaching laboratories and reducing the tuition pressure.

FF What's the projected cost of the building?

KJ About $80 million.

FF About the same as the LSRC.

KJ Yes, but with less space.

FF What ways do you have in mind to relieve the tuition pressure?

KJ We have to do something. States like California are beginning to give large subsidies ($10,000) to their students who attend even private institutions like Stanford. But we can do other things in addition to ordinary financial aid. We look to endowed scholarships to help. Also, we need to have more research based scholarships for undergraduates.

FF By that you mean students working in the research lab of a faculty member?

KJ Yes, in part-time positions. I'd also like to see us establish more co-op programs with industry.

FF You have good support within the school for fund raising, I understand.

KJ Excellent. Associate Dean and Director of Development Judge Carr and his team have been extremely good. In fact the whole staff of the school is first-rate. It was one of the many pleasant discoveries I made when I came here.

FF Are the faculty supportive of your ideas?

KJ Yes. They are ready to make a big move forward, and seem quite excited about it.

FF And the support from above you in the administration?

KJ The Provost and President couldn't be more supportive. Not having been in this kind of position before, I didn't realize how essential that is.

FF How would you summarize your hopes for the Pratt School?

KJ I want the school to become what Duke deserves it to be, a highly ranked, well-respected and distinguished place for the creation and transfer of knowledge.


When Fantasy Parades as Reality

Stuart Rojstaczer

[In an article published in the 22 September issue of Dialogue, Dean Lewis Siegel took on what he termed myths about the indirect cost recovery charge collected by the university on grants funding faculty research. As the title of his article stated, his intention was to provide a "reality check" on the misconceptions he saw in this matter, especially among the faculty. Prof. Rojstaczer found Dean Siegel's explanations less than persuasive.]

Recently, Lewis Siegel, Vice Provost and Dean of the Graduate School, tried to debunk some "myths" about university overhead (also known as indirect cost recovery) in the Duke Dialogue. Unfortunately, rather than debunk myths, he substituted for them alternative myths.

It's worthwhile to clear the air. Let's examine the difference between the reality of overhead and the myths that university administrators would have us accept. Here are quotes from Siegel's article, with my comments.

Duke's IDC [overhead] rate is computed by the federal government based on a careful analysis of the actual administrative and facilities costs of maintaining its research enterprise.

In fact, the amount of overhead Duke receives (54%) is arbitrary and simply reflects the political winds and the level of negotiating prowess of the Duke administration.

Indirect costs are not hard to understand. To assess overhead, a university estimates the cost of administering and facilitating research, from staffing libraries and administrative offices to paying maintenance on research labs. The university then divides that cost by the total amount of research money it expects to receive once items like major equipment purchases are removed. This ratio of estimated costs to research money received, multiplied by 100, represents a university's proposed overhead percentage.

The government typically audits and challenges this assessment of overhead rate because it is in a university's best interest to overestimate the costs of doing research. Hence for Duke there is a difference between its proposed overhead rate of 61% and what it actually receives, 54%. The difference more than likely reflects an overestimate on the part of Duke that was caught by federal auditors. (That does not mean that all of the overestimate was caught, as I note below.)

If all universities played the game fairly, or audits were rigorous, then overhead rates would strictly reflect costs. In fact they don't. For example, Stanford's costs, owing to many factors related to the extreme expense of the Bay Area, should be considerably greater than those of Duke, and at one time its overhead rate was 78%. In the 1990's its overhead rate plunged and, despite dramatic increases in the cost of running any business in the Bay Area over the last ten years, Stanford's overhead is now at 57%. The decline was due to Stanford getting in hot water over minor, but politically devastating, abuses in its assessment of overhead. Overhead rates reflect more about politics than about real costs.

Another curious observation is that lesser institutions have significantly lower overhead rates than elite institutions. Robert Ehrenberg and Jaroslava Mykula examined the national variability in overhead rate and research funding levels and hypothesized that an institution's indirect cost rate serves "as a 'price' of research" for lesser institutions, and as a "proxy for the quality of the institution's research infrastructure" for the major recipients of federal funds" (NBER Working Paper 6976, 1999). This is a nice way of saying that lesser institutions are honest in their assessment of overhead, and that elite private institutions inflate their costs and get away with it.

Elite universities charge what they can get, irrespective of the costs of doing research. The rate they charge may be reasonable; then again it may not. It all depends if you are paying or receiving the overhead. Our number of 54% has no real relation to the actual cost of doing research at Duke University.

Now the above paragraphs can certainly be viewed as elite university bashing, and I'd like to temper that a bit. Sure, universities cheat in their assessment of overhead. But there is some logic to it and it goes back to a change in government policy. Up until the 1970s, the government not only paid overhead (which was capped at 20% through much of the 60s), but also generously paid for building the infrastructure of the modern research enterprise, from the actual buildings to the equipment inside them. In the 1970s, the government significantly pulled out of university infrastructure programs (such as those authorized by Title VII of the Higher Education Act), and this created a paradox. Growth in research funding implies growth in infrastructure, yet the money to build the research buildings and fill them with equipment is no longer there like it was in the good old days (although universities are allowed to depreciate building and equipment costs). So universities cheat to partly make up for this loss.

Indirect cost recovery is profit.

Lew contests the notion that overhead is profit and technically I agree with him because universities are nonprofit institutions (with the exception of the emergence of some new profit making universities like the University of Phoenix). Defining what is "profit" in a university can be tricky, like Clinton trying to define the word "is" in his testimony concerning Monica Lewinsky. There are all kinds of accounting tricks used to make a profitable enterprise look like a pauper. Industries that pay royalties based on profits, like the movie industry, engage in this chicanery all the time. Elite universities, when they say that overhead is not profit, are engaging in the same kind of chicanery.

If overhead rates were not at least equal to university costs, then those in charge of finances would view every research grant awarded to a university with some dread. Instead, every year faculty members are exhorted to seek more grants. Grant success is a major component of tenure and promotion decisions for professors in the sciences and engineering. Employment offers to prospective new faculty members have been accompanied by explicit written statements of the expected grant performance (in dollars) required for tenure. Three years ago, the grant productivity of every faculty member in the School of Engineering was published, much as a real estate office lists the sales success of its employees. (To the best of my knowledge, the lead "salesman" in engineering was not rewarded with a vacation to Hawaii.) If research by existing faculty members is a money drain, why would our Arts and Sciences dean recently cite increased overhead return from grant support as one way to erase a $4.3 million debt?

By the way, it isn't research that is the money drain in Arts and Sciences. The real money drain is that it keeps adding more faculty members on a fool's errand to catch up to the four horsemen of American academia, the SHYP schools (Stanford, Harvard, Yale and Princeton). A discussion on that topic is, however, beyond the scope of this piece.

For a federal grant program paying full IDC, you will be awarded the same amount to cover your direct costs whether you're at Harvard (63 percent IDC rate) or Mississippi State (41.5 percent).

I don't know where Lew Siegel has been getting his grant money, but apparently his granting agencies have been far more forgiving about overhead than mine. Grant giving agencies are painfully aware of overhead rates and they make researchers (like me) sweat over them. I am by no means a major "rainmaker" for Duke University coffers, but over my years at Duke, I have received grant money from NSF, DOE, DOI, and NASA. The majority of grant awards that I've received have been preceded by painful negotiations with the granting agency over the amount of the award, including a discussion about overhead.

These granting agencies shouldn't do this. Overhead is a federally negotiated rate. They should just pay it like any tax. They shouldn't be nickel and diming me and challenging me to find ways to cut down on my overhead costs. But they do. And if I want to stay in their good graces pissing off a Duke administrator doesn't bother me in the least; pissing off a funding agency grant administrator is another matter entirely I have to go along with this game.

Granting agencies receive fixed amounts of money to hand out. They try to maximize the amount of research they can get out of that money. Overhead gets in the way of achieving that goal. I have never been refused grant money because Duke's overhead rate was too high, but I have been given a fixed amount of money (well below what I need) and been told to find a way to reduce the portion that is assigned to overhead if I want to do more research. If Duke had a lower rate of overhead or did not assess overhead on certain items that are only obtusely related to administrative costs (like conference fees, and overhead on top of enrollment fees for graduate students), I would have more money to do my research.

In short, overhead is a necessary, and burdensome tax on researchers. Its evolution as a source of university revenue has been significantly influenced by mistakes on the part of both university leadership and the federal government. The leaders of elite research universities have engaged in mindless spending in a pointless attempt to grow ever larger. The federal government has mindlessly added money to fund research without paying attention to infrastructure costs. The lack of rational behavior on the part of university leadership (for pursuing growth for growth's sake) and government funding agencies has created a god-awful mess that has no clean solution.

Lew Siegel used the 19th century creation Frankenstein as a metaphor in his piece on overhead. I'll be far less subtle and use a different creation, Dracula. What revenue universities can't get from their endowments, sucking the blood out of tuition paying parents (I realize that's not very subtle.), corporate partnerships (that frequently compromise the integrity of a university), and begging (otherwise known as fund-raising) to pay for their spiraling costs, they must get from overhead.

I'll conclude with one of the final points made by Lew Siegel in the Dialogue:

Since it's not [a] profit for the institution, Duke shouldn't pursue externally sponsored research just to earn it. Since it's not [a] loss for the investigator, Duke faculty shouldn't be afraid to include it in their project budgets.

This statement is like Bill Clinton's finger wagging disavowal of having "had sexual relations with that woman." Greed and avarice, like lust, are common character flaws that no one likes to admit to possessing. Whether lust is rampant within universities is debatable. But the American university is rapidly degrading into just another business sector obsessed with the twin gods of market share and revenue. Sadly, it is doing so with the full complicity of both the federal government and tuition-paying parents.

Home of the Brave: Press Rejects Book on Mascot

Jennifer K. Ruark

When Carol Spindel decided to write a book about a controversy at her university, the university's press seemed the obvious home for it. Dancing at Halftime, about the embattled University of Illinois team mascot, Chief Illiniwek, "was very much a regional book," says the writer, an adjunct faculty member in the English department at Urbana-Champaign.

Indeed, the University of Illinois Press was initially very interested. Peer evaluations of the manuscript were positive enough that the press asked her to revise it, and a local paper covering the Chief controversy reported that Illinois would publish the book.

But the revised manuscript never went back out to the reviewers. In April 1998, Ms. Spindel was surprised to receive a rejection letter from Ann Lowry, the press's assistant director, explaining the decision of the press's then-director, Richard L. Wentworth: The controversy between those who think the Chief is a racist caricature and those who think he is an honorable symbol of the region's past had grown more, rather than less, heated since Ms. Spindel had submitted the manuscript. Members of the university's board, which has long fought efforts to dump the Chief, had dug in their heels.

"Given that the Press's books are formally copyrighted in the name of the Board of Trustees, Dick is concerned that our publication of Dancing at Halftime would constitute an affront to certain members of that body," wrote Ms. Lowry. Moreover, Mr. Wentworth was scheduled to retire before the book could be published and didn't want "his successor to be plunged immediately into a protracted controversy." The director himself called Ms. Spindel two days later to apologize.

"They had been so enthusiastic," says Ms. Spindel. "It's not what I thought university presses did." Other observers on the campus cried "censorship!" and the rumor circulated that the board had threatened repercussions if the manuscript were published.

Not at all, replies Mr. Wentworth, who still works at the press part-time. "We've never consulted with the trustees on anything we've published," he says. He acknowledges that he was worried about putting his successor in a pickle, but emphasizes that the readers' reports on the manuscript were mixed: "There wasn't a good enough case for us to proceed. I'm sure it's a very different manuscript at this point."

Ms. Spindel thinks so, as does Eric Zinner, her editor at New York University Press, who urged her to broaden the book beyond Chief Illiniwek. In October, N.Y.U. will publish the result, Dancing at Halftime: Sports and the Controversy Over American Indian Mascots.

Chief Illiniwek is still Ms. Spindel's central case study. Although she has campaigned against him, her book is less a polemic than an exploration of the Chief's meaning for his supporters and detractors alike. Ms. Spindel, a transplant to Illinois who never expected to make her home there, initially supported the mascot. "I felt concerned that they were being criticized for creating a fictional character," she says. "As a writer, that bothered me."

But she finally decided that even "benign" Indian mascots obscure the truth of Indian life today. She thinks the tenacity of their fans reveals something about American life. "People have a real longing for connection to place. Well, if they think very seriously about how we acquired this land, they're caught in a tangle of ambivalence. Mythology is the human solution to that bind. But a myth that justifies the actions of the non-Indian majority does us real harm. Somehow we have to create a history that's encompassing and inclusive."

Copyright 2000, The Chronicle of Higher Education.

Reprinted with permission. This article may not be posted, published, or distributed without permission from The Chronicle.

Ethnomathematics: A Step Toward Peace?

Elizabeth Greene

[Editor's note: This article was published recently in the Chronicle of Higher Education, and became the subject of an online colloquy. It is reprinted here because I thought it would be of interest to many faculty, including those with children who have not yet finished school, as well as those who, for better or worse, teach subjects that depend to some degree on the mathematical skills and background our undergraduates bring with them to Duke.]

At California's Orange Coast College, students in mathematics classes learn about the geometric designs in Navajo rugs when their professor, Eduardo Jesus Arismendi-Pardi, teaches the concept of slope.

Students at Rensselaer Polytechnic Institute use African fractals patterns that repeat themselves at many different scales in their computer-graphics simulations for Ron Eglash, an assistant professor of mathematics.

At the Newark campus of Rutgers University, students in teacher-education courses led by Arthur B. Powell work out river-crossing problems based on different cultures in their study of algebra.

And using a cultural analogy that's close to home, Jim Barta teaches his elementary-education students at Utah State University a new way to think about the Cartesian coordinate system: street mapping in towns settled by Mormons is based on a system much like the one in which positive and negative numbers name intersections of lines.

In college classes in algebra, calculus, geometry, statistics, calculus, and the history of mathematics, among other subjects, and in degree programs for future elementary- and secondary-school teachers, professors are defining a new way of teaching math. They call it ethnomathematics math from a cultural perspective.

"Every day, more and more pieces of the puzzle are coming together," says Mr. Barta, an assistant professor who is treasurer of the North American chapter of the International Study Group on Ethnomathematics, a support group for people in the field. "We're looking at multiple perspectives to help us better understand human beings and relationships between being human and mathematics," he says.

Some professors strive to incorporate mathematical methods developed in non-European countries to calculate, measure, reason, and infer, among other things. Others take a broader view and include the practices of anyone be it African or African-American, Filipino or female, one's neighbor or oneself under the "ethno" banner.

Good-bye Pythagoras? So long Euclid? That's what the critics fear. "I'm all for uncovering mathematical contributions from China or India or Africa or anywhere else, and I do some of that in my teaching," says David Klein, a professor of mathematics at California State University at Northridge. "But when it comes to actually teaching how to do mathematics itself, if the professors are so politically correct that they are reluctant to use Arabic numbers and European theorems and the powerful ideas of mathematics that were developed in the last few centuries in Europe, then it handicaps the students."

Mr. Klein's view is typical of the skeptics: He objects more to professors who take up students' time working out math problems with non-European methods even when they do problems the Greek way as well than to instructors who incorporate the traditions of diverse cultures into their math-history lessons.

What worries critics the most is teacher education, where ethnomathematics is most prevalent. Some people feel that learning the mathematical methods of other cultures is not the best use of children's time, either. Kids must learn a lot in elementary and secondary school to do the higher-level math of college and beyond, they say, and math based on European thinking offers the most efficient, powerful tools. Courses that devote a lot of time to ethnomathematics, some critics believe, steer future teachers in the wrong direction, in essence dumbing down the school curriculum.

But even the most ardent professors of ethnomathematics say they are not trying to replace the great Greek and other European thinkers who have shaped modern mathematics. Instead, they say, they are blending European ideas with African, Asian, Native American, and other mathematical innovations, teaching both European and non-European practices.

And in most cases, they say, they are teaching the same concepts as other math professors, but also giving their students new reasoning skills and a cultural education to help capture their interest and put the math in context.

Call it mathematics with an anthropological bent.

Or, in some cases, math with a social agenda: By showing that math is not just the product of white-male thinking, a number of professors hope to make math more agreeable to nonwhite students and to women.

Or math meets politics: In the words of Ubiratan D'Ambrosio, a Brazilian mathematician who is a founder of ethnomathematics, the movement, which tries to increase respect for other cultures, is nothing less than "a step toward peace."

"Mathematics is absolutely integrated with Western civilization, which conquered and dominated the entire world," Mr. D'Ambrosio wrote in response to an e-mail interview. "The only possibility of building up a planetary civilization depends on restoring the dignity of the losers and, together, winners and losers, moving into the new."

Most people trace the beginnings of the ethnomathematics movement to a 1984 speech that Mr. D'Ambrosio, now an emeritus professor of mathematics at the State University of Campinas, gave at a conference of the International Congress on Mathematical Education in Australia. Soon after that meeting, a group of mostly American educators organized the international study group of which Mr. Barta is a member. The group's Web site, at http://www.rensselaer.edu/~eglash/isgem.htm, describes the field and has many links to related resources.

At most institutions, ethnomathematics offerings are still fairly limited. One or two courses taught by one or two professors might include math from this perspective; few faculty members show up when a colleague organizes a talk on the subject. But in California, especially at community colleges, there is a lot of interest in multiplying those numbers.

What started as a talk at a diversity conference last year has quickly made Mr. Arismendi-Pardi, an associate professor of mathematics at Orange Coast College, a big name in California community-college circles. Since April 1999, he has given 31 talks on ethnomathematics at conferences and colleges. Last spring, he won a diversity award from the California Community Colleges system for "his innovative approach to teaching mathematical concepts in a cultural and historical context." And the statewide group representing the faculty of California's 107 community colleges passed a resolution applauding the role of ethnomathematics in making the discipline more accessible to a broader group of students.

"At the community-college level, math is really a gatekeeper," says Mr. Arismendi-Pardi. "Students at the community college will take algebra or trigonometry, and they can't get out of it. They either don't pass it or are turned off by it," and then can't go on to more-advanced math and subjects that require it. "I'm trying to break down these barriers."

Empirical research still needs to be done to find out whether ethnomathematics draws students in, but professors like Mr. Arismendi-Pardi say they have anecdotal evidence that it works.

He moved to the United States from Venezuela in 1978, and has a missionary's zeal for helping other immigrants and people from minority groups succeed. By describing the contributions of an array of people, including women, to the history of mathematics, he hopes to make the subject more appealing to nonwhites and whites alike. "They feel good about the fact that they see themselves in the subject," he says. "Their eyes light up."

Proofs are not the only road to understanding mathematics, he tells his students. Six hundred years ago, the Incas used an accurate base-10 numeration system to collect important information on community needs. Greek geometry was derived from Egypt, he says; the Shoshone American Indians understood the concept of infinity; the Mayans calculated the orbit of Venus to be 584 days long, and modern astronomers peg it at 583.92 days. The list of achievements by non-Europeans goes on.

Robert N. Proctor, a professor of history at Pennsylvania State University at University Park, who teaches a history-of-science course, tells his students that until the Gregorian reform calendar was adopted in 1582, the Mayans had the most accurate calendar in the world, deviating only 17.3 seconds from the calendar we use now.

He believes it is the professor's job to open the world of possibilities to students. "The main thing is to overcome ethnocentrism and the view that the West is the be all and end all in mathematical traditions," he says. "With different world-views, you can come up with different kinds of sciences and different observations."

But some professors, while aligned with ethnomathematics, worry that too much focus on civilizations of the past does little to help today's students identify with the subject. Like their colleagues who talk about the innovations of ancient civilizations, these instructors employ cultural references in their teaching. But they stick to references that have useful applications now, and stay away from stories of long-ago, faraway civilizations their students can't relate to.

"The folks who call themselves Afrocentric have been focusing on ancient Egypt and saying, 'Well, we've got to realize that ancient Egypt was black and that the pyramids were this crowning achievement of African glory,'" says Mr. Eglash of Rensselaer's department of science-and-technology studies.

When Mr. Eglash discusses African geometric fractals with college students in his interdisciplinary courses, he shows how they were used long ago, and how they can be employed today.

"When I start presenting fractals in African-American culture, in particular in hairstyle patterns [based on old African designs], suddenly the whole classroom gets electrified," he says. "Here you have fractals, a very sophisticated mathematics that is used in computer-graphics simulations, suddenly being transformed into a bridge back across the middle passage." Rutgers University Press published Mr. Eglash's book, African Fractals: Modern Computing and Indigenous Design, last year.

Ethnomathematics may be creeping into the college curriculum for technology, engineering, mathematics, and science students, but it is already changing the way in which prospective schoolteachers are taught to teach math.

Lawrence H. Shirley, an associate professor of mathematics at Towson University, in Baltimore, says that teacher educators are searching for ways to help their students make math easier to understand and more interesting, especially in the difficult middle-school years.

"If kids don't take the advanced-mathematics courses in high school, then they are going to be underprepared to take the mathematics courses in college," Mr. Shirley says.

He shows his students slides of African textiles and plays mancala games, involving counting and strategy, in his math-history course, which is required of all teacher-education students.

One of his students, Erin K. Grossnickle, says she learned that while other cultures have different ways of computing problems, at the core, the math they use is similar. She plans to utilize some of Mr. Shirley's examples when she is a teacher. "It gives me more opportunities to teach to my students and explain to them how math is all over, not just here that everyone experiences it," says Ms. Grossnickle.

Some education professors are less interested in methods that expose children to other cultures than they are in helping kids identify mathematical practices from their own cultures.

"When teachers try to bring in multicultural mathematics, it's sort of like the black-history-month phenomenon: You pay attention to this for a certain time," says Joanna O. Masingila, an education professor at Syracuse University. She prefers to think of ethnomathematics as a way of making use of what people do regularly "the mathematics that are used by people as they go about their daily lives."

Ms. Masingila, a member of the International Study Group on Ethnomathematics, teaches her students to incorporate their students'"out-of-school mathematics" into their lessons. "We're trying to help the teachers make sense of the experiences students bring to school," she says.

So, when her juniors and seniors do their student teaching, they hand out questionnaires to find out about their pupils' interests. One student found a boy in her class who built bicycles, so she was able to introduce ideas about ratio and proportion to her class using an example from his work.

Some people worry that ethnomathematics can provide too much cover for schoolteachers who don't really understand math. "It could undermine the goal of actually providing students a rigorous education in the mathematics itself by giving teachers who are afraid of mathematics an excuse to teach something other than mathematics," says Alan D. Sokal, a professor of physics at New York University who does research on mathematical models that describe situations in physics.

Mr. Sokal says ethnomathematics may be useful in certain circumstances, but it is "not a panacea." He worries that the approaches "don't really address the most serious problem, which is the lack of teachers who have a deep understanding of the mathematics that they're supposed to be teaching, and how to convey that understanding to the students."

Mr. Klein of California State at Northridge says the number of calculus sections on his campus has been cut in half in the last 10 years, because of declining interest and ability. And the students who enroll are weaker, he says, because they did not receive an adequate education in high-school algebra.

Mr. Klein became involved in a parents' education-reform group called Mathematically Correct after being disappointed by his daughter's elementary-school curriculum. In addition, "I wondered what was going on between elementary school and when I see them in calculus," he says.

"The proponents of the programs that cause me to tear my hair out advertise them as being math for all students," he says. "The word 'all,' as far as I can tell, is a code word for minority students and sometimes a code word for women and girls, and the result of this push is really watered-down, weak programs that don't have much arithmetic in them."

Even some advocates of ethnomathematics feel it is time to do serious empirical research to see if the methods really do teach students at schools and colleges alike what they need to know.

"We are going to have to step forward and start running the tests and doing the research on it to see if what we're doing is making a difference," says Mr. Barta of Utah State.

Naturally, critics agree. "Strategies that get people drawn in and interested that work and are reasonably efficient in time are fine," says Michael McKeown, a professor of medical science at Brown University and a cofounder of Mathematically Correct. "We do need to ask to what extent those draw-in strategies allow us to cover the breadth of material we think students need to know."

Mr. Powell, an associate professor of education and academic foundations at Rutgers, and Marilyn Frankenstein, a professor of applied language and mathematics at the University of Massachusetts at Boston, argue that covering lots of material is not in and of itself a worthy goal.

"We're developing more than just mathematicians in the very strict sense of the word," says Mr. Powell, who edited a collection of essays called Ethnomathematics: Challenging Eurocentrism in Mathematics Education (State University of New York Press, 1997) with Ms. Frankenstein. "We are developing critical intellectuals who are scientists who are not only apt in their discipline, but also see the work that they are doing as connected to the society they're in, and see their society as connected to other societies on the planet."

Ms. Frankenstein adds that mathematics is about more than equations: "It's about what that equation is going to do to the world."

A Sample Problem

Arthur B. Powell, an associate professor of mathematics and mathematics education at the Newark campus of Rutgers University, uses the following "river-crossing problem" to teach a topic within algebra:

A man in North Africa must cross a river with a jackal (a predator), a goat (potential prey), and fig leaves (a potential snack for the goat). He has a boat that can hold him and two other items at one time. Neither the jackal and the goat nor the goat and the fig leaves can be left alone together on either shore. How can the man get the jackal, the goat, and the fig leaves across the river?
ONE SOLUTION: Take the jackal and the goat, leave the jackal while returning with the goat, and then carry across the goat and the fig leaves.

AN ALTERNATIVE: Some say the preceding solution is not efficient. What would be a more efficient solution? The man might carry over the jackal and fig leaves and return for the goat. This may be considered more efficient since in the first solution the goat is carried in all trips; an efficient solution should be concerned not only with the number of trips, but also with the lightest load on each trip. Moreover, the fact that the jackal cannot be alone with the goat and the goat cannot be alone with the fig leaves does not imply that the jackal cannot be alone with the fig leaves.

A Response

[Opinions posted in the colloquy were as varied as those quoted in the article. Here is one from an experienced teacher of mathematics at the university level.]

Mathematics is as ancient as human awareness. Every culture has made discoveries in and contributions to mathematical thought over the ages. Some of these have had long-range global impacts. It is good to recognize them, for all this is part of humanity's history.

When results and values (scientific, mathematical, of human concern) gain universal acceptance, they transcend geographical/ethnic importance and become humanity's heritage. The concept of the zero originated in India, but it belongs to the whole world now. The abacus originated in China, but it belongs to the whole world now. The seven-day week originated in Babylonia, but it has been adopted by most of the world now. The calculus originated in England and Germany, and Cartesian geometry germinated in France, but they belong to the whole world now. We should not regard these as ethnomathematics any more than that gender equality and human rights should be dubbed ethnovalues.

It is one thing to give examples of bedouins crossing the Sahara on Camel, or Californians driving on cars along a highway as problems in time and distance, and quite another to glorify these as ethnomathematics. A variety of examples from all cultures and countries would be interesting and educational to all students; it is good to teach Mayan geometrical patterns or fractals in African hair style to all students. But to think that this is the way to make minority students do well in mathematics is an insult to their intelligence, besides being a distortion of the enlightened view of respecting all cultures. It is not unlike the misguided call for "Black English" in another decade.

The good performance of students in (and from) India, Japan, and Korea (for example) in math has little to do with ethnomathematics, and a lot to do with the discipline and hard work to which they are subjected. "Ethnicizing" everything, however well-motivated, is trivializing the notion of ethnic dignity, and dangerous for cultivating the spirit of belonging to one human family. Only in the United States can one see this comedy, often instigated by well-meaning minority intellectuals, and propagated by equally well-meaning reformers and educators.

No amount of re-formulation of history can alter the fact that modern mathematics began in Western Europe, stimulated by knowledge-streams from other cultures and civilizations, and is being enriched in our own times by countless mathematicians from many countries and cultures, races and religions. Let us try to keep at least some elements of human culture mathematics and science above all beyond the poison and pollution of ethnic pettiness, and racial divisions.

V.V. Raman, Emeritus Professor, Rochester Institute of Technology

The Joys of Teaching in the Internet Age

Lawrence Evans

This from the e-mail service of the Chronicle of Higher Education:

Two instructors at City College of San Francisco have agreed to drop a lawsuit against Teacher Review, a Web site that posted anonymous, and sometimes extremely vulgar, critiques of their performance, along with reviews of other City College instructors. The two will pay $10,000 to the site's Webmaster.
The web site in question is at <http://www.teacherreview.com/>. It is operated by the students at City College of San Francisco, a two-year college. There is a disclaimer that CCSF does not support the site or endorse anything said on it.

When you visit the site, you are first given a choice between reviews of instructors at CCSF or at other institutions anywhere in the world. Then you are invited either to read reviews or to post them. Most of the activity concerns CCSF, but at the Duke page you will find one review of a local instructor. At most places other than CCSF you find no reviews, and are invited to start by posting one yourself. Over time, no one knows how many instructors in how many places will find their work "reviewed" on this site.

The two CCSF instructors who settled their suit (rather than risk paying more when the judge threw it out) teach English and physics. The English instructor (I will call him Prof. C) started the suit and was joined by the physics instructor (Prof. W) several months later.

Prof. C, openly gay, claimed he was being defamed by the postings on the site in the most vulgar and homophobic terms. Prof. W claimed the webmaster suppressed positive reviews and added negative ones, especially after he criticized the site at a faculty meeting. Both claimed that the webmaster himself wrote negative reviews about them.

The webmaster was defended by the ACLU, and claimed immunity under the Communications Decency Act of 1996, which protects webmasters from liability for injurious or otherwise offensive things posted on an open site under their control. When it appeared to the plaintiffs that the judge would not grant them the right to try to find out who wrote the reviews, they decided the case was hopeless.

I was curious to see what kind of things were said about the two plaintiffs, so I selected Prof. W's name from the list and clicked the button. There were three reviews that gave him an A, one that gave him a D, and six that gave him an F (I only looked at the first page out of three). Some of the F reviews accused him of having written the A reviews himself. Typical of the love notes accompanying the grade of F was this:

If there was a definition for BONEHEAD in the Webster's Dictionary, Mr. W's picture would be next to it. He is a waste of human flesh. I took his class a year ago and I couldn't believe this guy was allowed to teach. I don't know if you're aware of this Mr. W, but it is blatanly obvious that the A reviews were written by you. You are not fooling anyone. You should stop wasting your time writing false reviews, and spend your energy teaching your students. I don't know how you can live with yourself knowing that you are a complete failure in what is supposed to be your livelyhood. Please do all of us a favor and resign. At least that way, you can sit on your lazy ass as you have been doing all these years [Spelling by the author.]
That is mild compared to some things said about Prof. C. There were 12 pages about him. On the first page he received one A, two D's and seven F's. He was often accused of writing the A's himself. I will spare the reader the vicious rhetoric in some of the F reviews. Here are excerpts from a thoughtful one:
Professor C, I just saw the recent article about you in People magazine and it brought on a hell of a flashback to my worst memories of a few years ago. I'm not writing this as another hatchet job, but to say what I should have said eight years ago, had I not so meekly accepted your espousal of my worth as one of your literature students. The People article says you "can't help but log on" to this site. I hope you may find something here to make you rethink your essential approach toward education. There are a lot of childish and homophobic comments posted on this site. That's too bad, and obviously it discredits those writers. I do recall, though, that you couldn't seem to get through half a lecture hour without working in your "lover." I remember finding that distasteful in the same way that a straight person's constant references to their "lover," to a captive audience, would strike me as overly intimate, not to mention protesting too much. But this is besides the point, since many other educators are also openly gay and yet don't arouse the sort of hostility and rage I'm seeing in your former students Personally, I found more annoying your constant reminder to your class to the point where it became a running joke that you possess a doctorate. It smacked of defensiveness about your job at a junior college, and by extension contempt for us, your junior college students. Did it ever occur to you that your students could care less what academic credential you possess? They came to learn about literature, not to be bullied and despised by a man who let them know, twice a week for an hour, just how far beneath his station he was working.
Next I went back to the start of the web site to see if I could post a review without having to identify myself.

I picked a CCSF instructor at random (Jessica Brown, English) and clicked the button. A page opened containing a lot of forms to fill out. The first was a pop-up menu from which I had to choose a grade (A, B, C, D, F) for the instructor's performance. I was asked what classes I had with this person as instructor, and then given a large field in which I could post "Comments/Warnings/Praise" concerning the instructor. Above that field was a "Read This First!" link to a page offering guidelines and suggestions of things to comment on, and containing this item:

Please avoid slanderous, libelous or malicious material. Teacher Review will not tolerate racism, sexism, homophobia or other signs of arrested development in reviews. Accept the responsibility that comes with anonymous postings.
A similar bit of advice appeared just above the "Submit" button at the end of the form. I suspect these were added after the lawsuit was filed. The really vile stuff on Prof. C shows how seriously the site was moderated to avoid these "signs of arrested development."

Finally there were questions about the reviewer (major field, goal at CCSF, grade received in class, sex, age and GPA). All optional, as far as I could tell.

There was no check on my identity, no computer account ID or password required. I think I could have blasted away at Ms. Brown, or given her fulsome praise, with complete impunity.

Then I went to the Duke page to try the same thing. The form was not the same. There were no warnings about being libelous, etc., but there were more detailed questions about the instructor's handwriting and such things. Interestingly, on this part of the site you must open an account with Teacher Review before your comments will be posted. This seems to involve nothing more than giving your e-mail address which, they promise, will be kept secret. Secret from plaintiffs suing for defamation, at least.

In browsing around I found a few reviews aimed at N.C. State instructors. One of them had two reviews concerning his teaching of introductory calculus last spring. One gave him a A, the other a D:

He was tough but forced me to think on my own as well as understand that my limits were/are much higher than I had ever thought possible. I was really mad at him at first when I didn't understand but it forced me to buckle down and make sense of things I never thought I would get. I was in tears the second or third week when a single problem took me over an hour to solve BUT I DID IT; that was my turning point and I actually got a LOT out of the class after that moment.

This is the worst math teacher I have ever had in my life. He ignores the book and teaches based on his own personal ways of doing things and grades based on his order of operations. He is completely unreasonable and will not listen to any input from students about his teaching style. He should not be allowed to teach higher level math classes. The only way I learned anything is by reading the book and struggling to figure it out on my own. Take my advice and never, never take his course.

Same course, same instructor. Of course, it is possible that the instructor wrote the A review. It's also possible that a personal enemy wrote the other one.

Did the webmaster at CCSF manipulate the reviews and perhaps write some of them? He could have. Did Profs. C and W write some of their own favorable reviews? They could have.

I suppose the students running the site at CCSF think they are performing a service to their classmates by offering this invitation to "review" their instructors. They are also generously offering the same opportunity to anyone anywhere. The court case suggests that one has no protection against vicious and injurious things posted anonymously on an open website.

Are these reviews used in whatever process faculty at CCSF are put through in pursuit of promotion and tenure? One can hope not, but I wonder.

I also wonder when it happened that teaching became just another public activity, like entertainment or politics.