Being invited to give this FIPSE Lecture is an honor for me and has special significance because it was FIPSE that provided the funding which enabled me to experiment with what was at the time an oddball idea. Indeed, FIPSE has been very kind to me over the years. To Brian Lekander, the FIPSE representative here tonight, I say for the record that I deeply appreciate the fact that you and your colleagues enabled me to eat while I was doing the work that I am about to describe.
This work is still evolving. It is an interesting characteristic of innovative programs that, when they work, they change something--and often something fundamental--in the environment in which they operate. It is these changes which necessitate further innovation, or at least response. On the other hand, programs that are infatuated with innovation never take the time to work out the nitty-gritty details that make it possible for a good idea to work. Innovation is an occasional, periodic need. Solid program management and attention to small-scale, nitty-gritty adjustment is an everyday necessity.
Let me begin by stating the problem that we were addressing, namely, lowering the failure rate of Black students in calculus. Calculus was then, and remains, a major barrier for Black students seeking to enter careers that depend in an essential way on mathematics.
Let me ask you a question--once a teacher, always a teacher--how many degrees in mathematics, chemistry or physics do you think were awarded to Blacks and Hispanics by the California State University System in academic year 1987-1988? A hint: the system had nineteen campuses serving more than 100,000 ethnic minority students and, of course, several hundred thousand others. Your guess is 500? Yours 100? Well, you're not even close. The answer is eight! Fewer than half the campuses awarded such degrees; only eight Black or Hispanic students received degrees in mathematics or the natural sciences. It is unimaginable, but, alas, true. And it hasn't gotten any better: In 1988-89 there were only three Black students who received such degrees.
At the time we began work on this issue, the problem of Black student failure in mathematics and science was seen by many as principally a political issue, as a question of social justice, as a moral failure of the university. Finding solutions to this problem had little to do with institutional survival. The number of minority students in colleges and universities was relatively small and the number of majority students interested in mathematics and science was relatively large. Minority student failure did not effect enrollment, the life blood of public institutions.
Today we have an added problem: institutional survival in the face of fundamental demographic change. In the next fifteen years, the University of California alone will need 10,400 new faculty members. The California State University System will need even more. Who will they be, where will they come from? The answer, of course, is from today's elementary and middle-school students. If you want to get a feeling for demographic change, take a tour of the kindergartens in the community surrounding this college, or almost any other college or university near an urban area in the United States. On one such tour that I arranged for some of my undergraduates, one young woman's reaction to the extraordinary diversity she saw was: "Where do they keep the white kids?"
What started out for us as a problem of helping certain students pass calculus has become a much larger problem connected to institutional survival and, in fact, the survival of our society. As we look around the world we see country after country being torn apart by ethnic violence. It remains an open question whether we can create a democratic society which respects diversity and enables individuals to participate in all aspects of American life in meaningful numbers. The melting-pot is a great symbol but sometimes it seems like the pot's been on the stove too long. Some of the ingredients have been burned.
It now seems to me ironic that my involvement in this work was the result of an accident. I was a graduate student at the University of California, Berkeley, trying to be an algebraic geometer. I already had been in California a few years, and, as my Easterner friends said, I had become "Californicated." Evidently, they were referring to the fact that I was showing signs of needing human contact. To meet this need, I agreed to work with a faculty member, Blaine Lawson, on developing and piloting a new training program for our department's teaching assistants. The two of us were trying to improve the quality of instruction in introductory calculus at Berkeley. At that point, we were not focusing on minority students, because very few were enrolled in the course. And then a wonderful accident occurred that really changed my professional life.
It was about 1974, and I had a model section of freshman calculus. The idea was that I would teach a section as the "Great Teacher," and try out all of these wonderful innovations I had been reading about. I didn't happen to take note of the fact that I didn't actually know how to teach. But I was determined. I picked a section, and hoped that the new teaching assistants and perhaps some junior faculty would visit, get ideas, and become inspired to work on improving their instruction. The rub was that the students did not share my interest in innovative instruction, such as it was. They seemed to be interested mainly in becoming engineers, M.B.A.'s and physicians; they merely wanted to "get through" this course. I said, "You guys, you're really going to interact with each other and you're going to love mathematics." They said, "Will it be on the test?"
Now, it's three weeks into the term, and I'm pushing and they're pushing back. Then I receive a letter from two graduate students in the School of Education. It said, "We are engaged in a master's thesis study of the validity of students' teacher evaluations." (This was very controversial then: should student evaluations of instructors be considered in promotion and tenure decisions?) "Your students have identified you as either one of the ten worst or ten best teachers on this campus, and for the purposes of our study, we cannot tell you which." The great and wonderful insult was that their plan was to videotape us in action, and show these tapes to real teachers, and see if they agreed with the students' assessments of our teaching.
So let me set the scene: The classroom was set up for videotaping. Twenty-four students were working four to a table. Each table had a microphone and I had a lapel mike. The students were told that their mikes would be live only when I was interacting with them. (I, of course, had told them at the previous session that, from now on, I would give credit for classroom participation. I thought to myself, "To Hell with their research, this is my reputation, and I'm going to look good.") It's interesting to note that camera crews always film their own ideas of a good classroom, not yours. This cameraman wanted to film me in front of the room delivering a polished lecture to the students.
Well, it was as if Plato had written the script: The students were arguing heatedly about mathematics. They had rival conjectures about the behavior of the derivative of l/x when x is large in absolute value. This is stuff you see, maybe, once a decade. And I had it on film. Two men and two women are arguing away and when I walk away from them, you realize that something is wrong. What's wrong is that my mike and all the other mikes are dead except for the one at their table. Without their knowledge, everything they are saying is being recorded.
Just before I walked away from the table, I looked one of the students in the eye and said, "Gee, that's really good work." The guy next to her looks straight into the camera and he says, "Yeah, this is a really good class." As I walk away, you realize immediately that something is wrong. The students start whispering. Then a woman says, right into the mike, "Shit!" (She was from Texas, where that's a four-syllable word. I won't attempt to imitate her pronunciation.) "You ever understand anything that joker is talking about?" From there, it went down hill.
When I saw the film, I was a little depressed and demoralized. So much for the "Great Teacher". However, the next class period I got my revenge and showed the film in class.
Because of my work with the TA's, I was becoming increasingly interested in how students actually learn calculus. Do they use the text book? With whom do they speak? What do they do when they get stuck on a problem? -- the really basic questions about how students learn mathematics. I began to design projects aimed at answering these questions. One of these projects involved having each TA interview especially successful and especially unsuccessful students in his or her sections. In the TAs' reports it became clear that it was minority students who disproportionately were failing and this disturbed many of the TA's as well as myself. In fact, in the preceding decade sixty percent of the Black students who enrolled in and completed first-term calculus at Berkeley earned grades of D or F. In no year did more than two Black or Hispanic students earn more than a B- in any calculus course at UC Berkeley. Of course, at that time there were very few ethnic minority students enrolled on the campus. In the typical freshman class of the mid-seventies there were fewer than 150 Black and Latino students in a class of 3600. Today, thirty-two percent of the incoming freshmen are Black, Hispanic, or Native American. Only thirty-eight percent are white. The Berkeley campus finally looks like it's part of California.
To support our developing understanding of minority performance in calculus we sought a grant from a major foundation. In the course of negotiating we were asked to produce almost instantaneously a clear statement of our initial hypotheses. What to do? We really didn't have a clue. We had to develop our hypotheses quickly so we asked a few thousand people who didn't have a clue either and averaged their answers -- the mathematician's idea of social science research.
It will be useful for me to state what we found because I believe that these assumptions are responsible for the failure of many university intervention efforts, and because these assumptions are rarely stated explicitly and almost never publicly. The responses to our survey surfaced four widely held beliefs about the causes of minority student failure. The first was that there is a motivation gap. It's not that the minority students are unmotivated, this argument goes, but that they are not as motivated as certain groups, namely the Asians and the Jews. The implication was that small differences in motivation would have large effects in highly competitive and difficult courses. The few A's given would go to the students who, because of their high level of motivation, were willing to work extraordinarily hard. It was the students who were extraordinarily motivated who would excel and those students were disproportionately Asian or Jewish.
The second argument named inadequate preparation as the culprit. Minority students enter the university with fewer credit hours of science and mathematics from high school and with substantially lower SATs. The fault lies not in the university, but in what students bring to the university, namely motivation and prior preparation. In other words, "It's not our fault."
Several faculty pointed to the "vertical" organization of math and science. New topics depend on the topics which precede them; courses depend on the courses which precede them. This characteristic of math and science makes it difficult for students to improve their performance once they are having difficulty. Even if students are committed to improvement, the intensity and the speed of freshmen courses gives them no time to catch up.
The third problem was a conjectured lack of family support or understanding of higher education. The idea was, roughly, that since the families of these kids did not have rich educational backgrounds, how could they pass on to their kids the survival skills they would need in college? Moreover, some faculty members thought that the parents did not push their kids hard enough. Of course, we had never met any of these families, but we seemed to have clear ideas about them.
The fourth idea is a corollary of the great liberal dream: "It has nothing to do with race or ethnicity at all. It must be something else. What is it then? Income. If you control for income, all the differences disappear." Then there were a few older faculty members who had views about the effects of race and heredity and the like. They are gone now, replaced by a younger group of faculty with the same ideas. I want to mention, though, that one faculty member, who held well-known views about the genetic inferiority of Blacks, wrote the only interesting response to our survey. He said that, according to his calculations -- he was big into pseudo-statistics -- "population characteristics" (by which he meant "race") could account for only about four percent of the failure. But the observed failure was so great that only the institution's behavior could account for it. What an irony, he was the only one to assert that something might actually be wrong with the institution.
Well, these were our findings and, at the time, we believed them. Minority students' failure could be attributed to low income, low motivation, poor academic preparation and lack of family support, all factors, incidentally and conveniently, over which we had no control. Nonetheless, we were interested in how these factors worked. "On which calculus problems did these issues cause trouble?" "When and how do they actually interfere with student success?"
Our initial idea was to interview students. A typical question: "How many hours do you study?" A typical answer: "I put in two hours for every class hour." The students were telling us exactly what we had told them. They weren't being dishonest, they just didn't have an accountant's view of how they organized their time. Our next attempt was far more intrusive. We embarked on our version of a social science study, mixing, not really consciously, two different methodologies: the 1920's "industrial-style" time-and-motion study, and ethnography.
Now, picture me, if you can, boy-Margaret-Mead, out in the field. We had picked twenty Black and twenty Chinese students. The idea was that we would compare two ethnic groups, one that generally did well in our mathematics classes, and one that did not. We decided literally to move in with the students and to videotape them at work. We wanted to understand what was going on when they studied calculus, got stuck on a problem, etc.
We were struck by the enormous diversity among these students and remembered that not one person on our faculty survey had written to ask us to which minority students we were referring. No one questioned the supposed homogeneity of these groups. Some of the Black students had come from middle-class homes and had many white friends in high school. Others were the valedictorians of all-Black inner-city schools, yet others were from military families and had grown up all over the world. The Chinese students were equally diverse. There is a funny story which demonstrates this diversity.
I should tell you that I had prepared myself for working with the Chinese students by learning some Cantonese. One day, I was going to interview three young women who were deep in conversation. I approached them, greeting them in my toneless Cantonese. One of the students responded in Yiddish, "How are you doing?" It turned out that she was from L.A.'s Chinatown, and her mother, who was a nurses' aide, worked in a hospital with Jewish physicians. She had told her daughter that she could not date until she was a junior in college but when she could date, she could see only other Chinese from certain families and Jewish pre-meds. Her mother apparently had good experiences working with Jewish physicians. "They are family-oriented people" is what her mother had told her. This kid was 400 miles from home, clearly ready to date and open to exploration. So, she had enrolled in a Yiddish course. One of the wonderful ironies of all this was that we learned that our stereotypical view of Chinese students was exactly society's view of us as mathematicians: no sex, no partying, no sense of humor, and a calculator hanging on the belt.
The study was supposed to take ten weeks, but after four months we still didn't have the understanding we needed. We had gotten to that critical stage of research when one recognizes that one's hypotheses are not helping any.
We had the good luck to run into some of anthropologist John Ogbu's graduate students. They pointed out to us that our ideas were characteristically American, if not Californian, where every pop-psychology idea quickly works its way into educational practice. For example, even after the neurophysiological basis for left-brain and right-brain thinking had been refuted, workshops on learning mathematics on the left brain or right brain abounded. A small number, about three out of a hundred studies, showing that women visualize differently and describe the spatial relationships of objects differently, have been used to explain the near total absence of women in math faculties in the United States. It's truly amazing how the misunderstanding and misapplication of research influences educational trends and practice.
We were advised to step back and question our hypotheses, which was really useful. Instead of looking at what happens when students get stuck on a problem, we were encouraged to look more globally at their lives. We went up to Lake Tahoe with hundreds of hours of unedited videotape. In a weekend all of our hypotheses fell apart.
Let's look at "motivation." It is not as if our Black students thought to themselves, "Well, there's nothing happening on the streets, so let's go to Harvard, Caltech, Princeton, or Berkeley." These students were admitted to one of the premier research universities in the United States, and we had presumed that their problem was motivation! Students from the inner cities had paid a heavy price to get to Berkeley. Some were the social outcasts, the "Brainiacs," or if they were math majors, the "pervert Brainiacs." They paid a very, very high price. These kids were motivated! In fact, I believe that just about all first-year students in college are motivated for the first few weeks of their freshman term. We had been mistaking "disorientation" for lack of motivation.
The second factor was "academic preparation." We had many years of data from Berkeley that called this hypothesis into question. We found, for example, that Black students' calculus grades correlated negatively with their Math SAT scores. Many of the "strongest" students failed early. Black men with high SAT's were often facing academic dismissal. The few successes, on the other hand, came from the second quartile from the bottom. These data forced us to call into question our ideas about the role of high school background in college performance among Black students.
We studied the issue of "family support" by interviewing the families of our students. We came to appreciate quickly that many of the parents had decided before their children were ever born that their sons and daughters would go to college. There were lots of mothers brandishing heavy kitchen implements, saying "Child, you will go to college." Although teachers had helped them, these kids were, in large part, at the university because of the concerted and organized effort of adults who cared about them. We found no parental apathy and quite a few parents who were themselves college graduates.
There is a popular image of the Hispanic girl coming to the university against the opposition of her family. There were two or three young women who did face some opposition, but in a large number of cases, the families were extraordinarily supportive and had organized themselves to help their kids make it. These families had decided that their children would make it through education, and many had paid a heavy price to make that happen.
At Berkeley we had lots of the "Jack and Jillers," many of whom had grown up in largely white neighborhoods, with white friends. Sometimes their only contact with other Black children was in "Jack and Jill," or when they'd go to spend the summer with their grandparents, back in North Carolina or Louisiana. The families of these students saw college as a necessity. They respected education, and especially so for their daughters.
"Income" correlated negatively. Why? Because many of the Black students had parents who were public school employees. Some were custodians, some were teachers, some were secretaries; in any case, public school employees don't earn much. The next largest group were children of civil service workers. Typically, the parents had degrees from historically Black colleges, moved out to California in the 1950's or 1960's, and couldn't find jobs in their chosen field. So they went to work at the post office.