ALTERNATE LEARNING ENVIRONMENT HELPS STUDENTS EXCEL IN CALCULUS A PEDAGOGICAL ANALYSIS by Jerome Dancis Executive summary: "The overemphasis on testing, skill development, and fact level content ... [in high school has] inhibited [student] interest in learning, motivation, ability to work with and enjoy ideas, use creativity and attain satisfaction from an educational experience." In math, this non-intellectual approach comes from math textbooks which "never offer intellectual challenges, or chances to build confidence and problem-solving skills." This emphasis on testing, skill development, and fact level content results in entire curricula which do not include the training of pupils on how "to read critically, synthesize information, interact effectively with both peers and instructors in academic settings, and participate actively in discussions" and to "express a logical, coherent line of argumentation or to follow another's argument". It results in students going off to college with study habits which are ineffective and inefficient. The highly motivated, hard working, smart black students at U.C. Berkeley were unsuccessful in Calculus (average grade 1.5 (D+)). Uri Treisman developed a program in which minority students excelled and thrived. Training in an alternate learning environment on (i) how to learn in general and (ii)how to learn cooperatively facilitated students replacing their skill-oriented attitudes and their ineffective study habits with effective learning habits. Some of the crucial pillars of this alternate learning environment are: (i) group learning on (ii) interesting hard problems with (iii) informal interaction with an instructor rich in mathematical expertise, together with (iv) a support system for the students. There is (v) much correcting without grading and (vi) peer discussion, also (vii) major emphasis on explanations and understanding, also (viii) minor emphasis on skills and memorization of facts. It was not just groups of students doing textbook problems overseen by someone with moderate knowledge of mathematics. In 1983-84, the alternate learning environment enabled the black students to achieve an average grade of B- (2.6) in calculus in spite of their math S.A.T. average of 500. For comparison, the average for white students without this training was 1.9 (C) and they had a math S.A.T. average of 640. The good learning habits developed in the workshops carried over to success in later courses (without workshops) and to a significantly higher rate of graduation especially in math based fields . Most likely similar programs in most subjects and at many educational levels would result in considerably raising the achievement level of both black and white students. It is time to organize such programs for all students. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ At the University of California at Berkeley, most of the white students from blue collar and farm families and most of the black students were not succeeding in the calculus course for engineering and science students. In 1973-75, the average grade in Calculus 1A for Engineering and Science students for black students was 1.5 on the usual scale of 1.0 = D and 2.0 = C. Calculus for Engineers is the traditional 2 year college calculus course for freshmen and sophomores who will study math, physics, and engineering (even fire protection engineering). Students need to understand calculus on an A or B level in order to be comfortable with the calculus aspects of later math, physics and engineering courses; C is not sufficient. After only 11 weeks of college, their low grades in Math 1A dashed the academic aspirations of many black students at U.C. Berkeley. Various remedial programs were tried without success. Enter Uri Treisman. Over several years, he developed an alternate learning environment for training students how to learn both individually and cooperatively. Black participants in his alternate learning workshops exceeded the achievement levels of those white students whom he had not trained. Another result was a significantly higher rate of graduation, especially in math based fields, for the "workshop" black students over the rate for earlier black students with very similar backgrounds and very similar prior academic achievement. For the development of this program, Newsweek, in 1989, named him one of three American educators "on the leading edge of innovation" and in 1992, he was named a MacArthur fellow. How did Uri Treisman devise his winning strategy when a wide range of traditional, remedial programs had failed to help math non-achievers succeed? First, 400 math and science faculty members were polled on the question: what were the reasons for black studentsı low grades? The "off-the-cuff" faculty responses were the usual "blame the victim" type reasons: the students who flunk are (i) stupid, (ii) lazy, (iii) they do not study much and (iv) they do not know high school mathematics, etc. (Of course the faculty barely know the students.) Then, by living in the student dorms for 18 months, Uri (and 5 cohorts) observed 20 black students. He found that all the stereotypes were wrong. These black students at U.C. Berkeley were smart, highly motivated, and very hard-working; some had been valedictorians. Many of these students had even studied calculus in high school. They followed the "guidelines" by doing two hours of study for each class period and by doing the assigned work. He was the first white person to visit some of their homes; in doing so, he found that each of them had at least one parent who strongly encouraged their academic pursuits and urged them to go to college. The majority of these students had a parent who was a teacher. Since these characteristics presuppose success, why were these black students doing poorly in calculus instead of excelling? Treisman discovered that (i) these black students had good "study" habits but ineffective learning strategies. (ii) social isolation and other non-academic factors had significant negative impact on their learning; (iii) and many students attempted an ambitious academic load while working many hours each week. The Berkeley program includes important non-instructional support and it makes a real effort to persuade incoming freshmen to reduce their academic and work loads to a reasonable amount. This article will concentrate on the pedagogical aspects. A partial pedagogical analysis of high school education and how well it prepares students for college Many freshmen use the same strategies that earned them success in high school. Pseudo-good "study" habits often includes too much time spent memorizing too many formulas and prescriptions for calculations and doing lots of computations with an emphasis on getting the correct answer. These types of ³good² study habits are usually rewarded by success in high school, but they can be a trap in a college calculus class. As we will note, ineffective study habits of this kind are commonly inculcated in both black and white students in most high schools by (i) the overemphasis on testing, skill development and fact content and (ii) the underemphasis on understanding, reading critically and synthesizing information Also the skill-based instruction (which is popular in many high schools) leaves the students stymied when confronted with a problem that is slightly different from the ones they have been trained to do. That solving a large number of conventional exercises is largely ineffectual and turns misconceptions into "bad" habits has been observed by Owen and Sweller (JRME Vol. 20) and by Dr. Bernice Kastner of U.MD. (at Towson) resp.. In contrast, good learning habits include trying to gain understanding and trying to develop facility with the important ideas and techniques of the subject. At the request of the Prince Georgeıs county public school system (in Maryland), a series of discussions were held by college faculty members on the topic: What contributes to the failure of college freshmen? The participants in the initial discussions were faculty members (who have much connection with freshmen) from 10 departments of my university, together with high school teachers and college freshmen). The main conclusion (Ref. #1) was that: "The overemphasis on testing, skill development, and fact level content, etc. [in high school] seems to have inhibited [both white and black student] interest in learning, motivation, ability to work with and enjoy ideas, use creativity and attain satisfaction from an educational experience." In a later discussion among college faculty members (mostly from departments of speech and communication), it was noted that: "Entering college freshmen appear severely limited in their ability to read critically, synthesize information, interact effectively with both peers and instructors in academic settings, and participate actively in discussions." (Ref. #7) This is a natural consequence of these activities not being included in the curriculum of most school systems. Neither black nor white students read their math textbooks. Only foreign students read the math textbooks, and they do so, Uri Treisman discovered, to improve their English! That there is little value in reading school textbooks was documented in Harriet Tyson-Bernstein's book: The Textbook Fiasco; A Conspiracy of Good Intentions. In Ref. #5, Prof. Davis of Worcester Polytechnic Institute wrote: "The [high school precalculus textbook] ... is no more mathematics than the noise made by trained seals is music. But the trained seal approach abounds in textbooks and in classrooms. It never provides a foundation of fundamental ideas ... . It never offers intellectual challenges, or chances to build confidence and problem-solving skills." Of course students are able to solve those math problems for which the text has supplied cookbook-type directions, but there is little training in serious problem-solving skills, that is solving problems that are different than the examples worked out in the textbook. In this way high school textbooks "set-up" students with a wrong orientation for college. High schools and colleges together provide 8 years of education to many students. But there is little communication between them. High schools and colleges are quite different types of institutions, with different cultures, goals and views of education. Traditionally, most high school graduates went on to become clerks, secretaries or technicians; they did not become college graduates. As is appropriate for the training of clerks, secretaries and technicians, the emphasis (in many high schools today) is still on acquiring skills. By contrast, in colleges the emphasis is on acquiring understanding. This mismatch of goals results in a difficult transition from high school to college for many college freshmen. While the specific math, English skills etc. that students learn in high school are crucial for college work, the skill-oriented attitudes about learning are counterproductive in college. An excellent assessment of U.S. School Mathematics is contained in the national report on the second international mathematics study sponsored by the International Association for the Evaluation of Educational Achievement (Ref. 3). Its main conclusion was that the public school math curriculum is a repetitive, fragmented, underachieving curriculum. There is a "cause and domino effect" here, namely: (i) Many textbooks use mainly a skill development approach to learning. (ii) Teachers model class instruction on the textbooks. (iii) Students model their studying on their textbooks and on their skill-development classroom instruction . (iv) Students do calculations in a skill based manner using many memorized formulas which results in much of the mathematics being easily confused and easily forgotten over the summer. (v) So much is confused and forgotten over the summer that it necessitates (a) the Grade 6 arithmetic textbook starting with addition of integers. (b) the reteaching of much of Algebra 1 in Algebra II (c) the reteaching of much of Algebra 11/ Trig in Precalculus (d) the reteaching of Algebra 1 and Algebra II to large numbers of college students. For example: About 500 students retook Algebra 1 and another 1000 retook Algebra 2 at the University of Maryland in 1990. (Having successfully completed Algebra II (in high school) is a requirement of admission to U MD) (e) the reteaching of calculus in college to an estimated 94% of the high school calculus students (of 1982). (Ref. #9.) (f) large numbers of students enter college calculus classes with only moderate knowledge of algebra and trigonometry; often their knowledge includes many misconceptions. A major contributory cause to the high failure rate in calculus classes is that "fluency" not merely moderate knowledge of algebra and trigonometry is needed for success. (vi) The large amount of class time devoted to reteaching old topics greatly reduces the amount of time available for new topics. The content of the Algebra II/ Trig - Precalculus sequence has been cut by a third since I went to school in the 1950's. This results in an underachieving curriculum and our children being taught far less than they are capable of learning. If effective teaching methods were used the Algebra II/ Trig course would become superfluous since all its material is also taught in Algebra I and Precalculus. To be fair to the high school teachers, we note this comparison: A community college instructor of Algebra II, Trigonometry and Precalculus spends 12 hours per week in the classroom teaching. A high school teacher of Algebra II, Trigonometry and Precalculus may spend almost 23 hours per week in the classroom teaching. Thus community college instructors have almost an additional 9 hours each week for preparation. High school teachers are not allotted the preparation time needed to prepare exciting non-skill based lessons. In reaction to the ineffectiveness of precollege mathematics instruction, the National Council of Teachers of Mathematics (NCTM) is recommending a new national math curriculum (outline) called the "Standards". These NCTM Standards call for a major deemphasis on skill based learning and rote practice together with a new major emphasis on students gaining knowledge and understanding. In 1987, in reaction to the ineffectiveness of math instruction, the Maryland State Dept. of Education was wise enough to issue the following Official goals for math instruction for the State of Maryland: Goal #1 is that the students will "develop an appreciation of and a positive attitude toward mathematics". Goal #2 is that the students will develop an understanding of mathematics: concepts, properties and processes. Goal #3 is that the students will "acquire mathematical facts and skills". Goal #4 is that the students will "develop the ability to express and interpret mathematical ideas and relationships". Goal #5 is that the students will "develop the mathematical reasoning ability required in problem solving and decision-making situations". Goal #6 is that the students will develop the ability "to apply mathematics in personal, societal, technological, scientific and career settings". Unfortunately, it is probably a rare school (even in Maryland) that has started to implement these goals. Prof. Perry of Harvard Univ. (Ref. #2) has found that successful adaptation to college includes successive major reorientations of the student's approach to learning. It is a wise college that organizes its freshmen math courses in a manner which facilitates the students reorienting their approach to learning as they replace their skill-oriented attitudes and their ineffective study habits with effective learning habits. This is easy to say, but hard to do, especially with large lectures. Uri Treisman's group learning workshops do this. Prof. Clarence Stephens did this so well first at Morgan State University (a traditionally black university) and then at the State University of New York (SUNY) at Potsdam, that he was honored by the governors of MD and N.Y. The students at SUNY at Potsdam feel so good about math that 20% of the bachelors degrees awarded there are in math compared to less than 1% nationwide (This 1% is down from 5% in 1980). Unlike at most colleges, remedial math courses are not taught at SUNY at Potsdam. Basically many students study mathematics like this: They skip the reading material and just start doing problems. If they can't do a problem, they turn a few pages back in their texts in search of sample problems to mimic, a practice which worked wonderfully well with the skills-oriented high school texts. But this strategy only half works for college calculus courses, with their greater emphasis on understanding. Back to Uri Treisman Uri Treisman's team also intensively observed 20 first- generation Chinese-Americans students (who grew up speaking Cantonese) as they studied in the student dorms, and thus he could compare their behavior patterns with those of both black and white students. Most of these first generation Chinese-Americans students used a different learning strategy: they regularly spent two to three hours (per day) studying by themselves, and then would come together in groups to critique each other's work and to work on difficult problems. Separately, Professor Richard J. Light found that participation in student organized study groups was crucial for thriving at Harvard University (Ref. #11). Uri Treisman then suggested to the black students that they form study groups, but they felt that "one is supposed to be self- reliant". This was also a reason why they did not make use of the available free tutoring. As this is the American spirit of rugged individualism many white students share this attitude. Another reason is that many college freshmen do not consider their fellow students to be a useful resource (Ref. #2) Dr. Shearn of the U. MD Studies Skill Center has noted the antagonism of freshmen students (in an elementary math class at U. MD.) toward participating in study groups. As one student told her "Juniors and seniors work together all the time, but you can't expect freshmen to do it!" Dr. Shearn credits the compulsory group work both for the fact that one class of students scored especially high on the "uniform" final exam and that these same students gave their instructor an especially low evaluation. If an instructor does not "fully program" the students on how to solve every problem (the expectation of the many students at Perry's Position #1 (Ref. #2)) because the instructor wants the students to learn to figure some things out for themselves, then it is "natural" for the students to claim (on the teacher evaluation sheets) that the instructor is not explaining the material clearly. Times they are a changing. The recent introduction of group learning in high schools has resulted in 36% of the incoming college freshmen at my campus, looking forward to forming study groups. (Ref. #8.) Dr. Hight observed that many students, in remedial math classes at U MD, were study some subjects with other students, but not math. Uri Treisman noted that "I had come to question the efficacy of individualized tutoring, self-paced instruction, and short courses aimed at the development of study skills - the traditional pedagogical arsenal of special programs for minorities. I questioned also the wisdom of these programs' remedial underpinnings: the focus on minority students' weaknesses rather than on their strengths." He also observed the high level of black students suspicion to programs specifically aimed at helping them. Uri Treisman wanted a program where minority students would excel and thrive not merely survive. He believes students should both enjoy mathematics and feel sufficiently self-confident about their math ability that they will do extra mathematics problems for "sport". Over several years he developed an alternate learning environment for training college students how to learn. The core of his program was twice weekly honors-type calculus workshops where students were trained how to learn by participating in an effective and efficient learning environment. (The workshops which were composed 75% of blacks and Hispanics were in addition to the traditional "review" or "quiz" sections.) He tried aggressively to recruit all the black freshmen to join his honors- type workshops. Uri Treisman noted that some educators "considered the unabashed elitism of the new program and its willingness to enroll seemingly unprepared minority students in difficult mathematics courses to be unwise, if not downright irresponsible". As would be natural for an honors type program, he gave to these potentially flunking students problems which were as hard and harder than those given to the rest of the students. No easy problems. To quote Treisman: "Not remediation; students hate remediation." The students were asked to solve as many problems as possible individually. But when a student got stuck, instead of sitting there frustrated, he or she was to join with one to four other students to work on the harder problems. When this team could not solve the problem, they would then request help from the instructor supervising the workshop. In this way, the students spent half the time solving problems individually and half the time cooperatively. Timely intervention by the instructors saved the students from floundering, from much frustration and from going on wild goose chases. Speaking. The students were also required to explain their solutions to their peers. This is especially important since speaking is not one of the pillars (along with reading, writing and arithmetic) of the American education system. In the discussion held by college faculty members mostly from departments of speech and communication, (Ref. #7) on why freshmen have difficulties succeeding in college it was noted that: "Freshman have great difficulty in expressing a logical, coherent line of argumentation or in following another's argument." Unfortunately for American students, elocution is completely absent from their education. Clearer understanding is obtained during the "give and take" discussions when a students has to explain and defend his/her answers to others. Uri Treisman summed up a basic premise underlying the workshops: "Through the regular practice of testing their ideas on others, students will develop the skills of self criticism essential not only for the development of mathematical sophistication, but for all intellectual growth." Group learning is a non-graded, low stress, nurturing learning system which can expose and then deal with the variety of misconceptions about mathematics that students have collected during previous mathematics classes. Group work enables the student to work through more problems in a limited time period. An instructor (with expertise in mathematics) will see to it that the students avoid time-wasting inefficient approaches as well as dead end approaches to problems. Therefore the amount and variety of learning that occurs in a two hour workshop is usually far more than what normally occurs in two hours of individual study. Results in calculus at U.C. Berkeley. (1983-84) For black students whose S.A.T. math scores were 550 or higher: Average grade %earning As, Bs % earning Ds, Fs Workshops (22 students) 2.8 71 0 Non workshop 1.7 24 30 ............................................................ Average S.A.T.math scores Average grade Workshop black students 500 2.6 Non-workshop white students 640 1.9 Also, the group of black students whose S.A.T. math scores were 460 or lower but participated in the workshops had a higher percentage of A's and B's (30%) than the non-workshop black students (24%) whose S.A.T. math scores were 550 or higher. The D's and F's rates for non-workshop white and first generation Chinese-Americans students were 15% and 10% resp. Graduation and persistence rates among black students who had taken calculus at U. C. Berkeley SAT-Math Historical Workshop Non-Workshop group participants participants 1973-77 1978-79 1978-79 200-460 36% 58% 33% 470-540 47% 59% 48% 550-800 48% 77% 49% This chart counts the percentage (numbers) of black students who had taken calculus at U. C. Berkeley and then went on to graduate or were stilling enrolled at U.C. Berkeley in Fall of 1985. (Ref. # 10.) It took the ruse of an honors-type program to get the black students to learn math together, as some of their Asian peers did regularly on an informal basis. Once the black students changed their learning strategy, in a effective, efficient learning environment, they did very well, and not only in calculus, but also in later courses. Then many white and Asian students demanded to be admitted to this largely minority program! The workshops were then expanded to include more non-minority students. The moral underlying both Uri Treisman's results and those of the Underachieving Curriculum (Ref. #3) is that American school systems should abandon their practice of setting low goals. The traditional teaching till "mastery" method with its too-easily achievable goals is a prescription for frustration and boredom, as well as stress caused by perfectionism. It is a play-it-overly- safe approach to writing a curriculum. The natural result is our underachieving precollege math curriculum; This is documented in Ref. #3. Learning new things is always fun. Solving hard problems raises self-esteem. The endless repetition of teaching to mastery is drudgery, and takes time better given to expanding the curriculum. Students cannot learn what is not taught. If college courses were taught at the high school learning pace, it would take students ten years to acquire a college education! There is a further moral: Minorities are setting their sights too low when they demand that the math achievement of their children be raised merely to the current underachieving level of American white children. In contrast, Uri Treisman tried to change D and F students into A and B students not merely into C students. While he did not fully achieve this goal, 2/3rds of the black students in his program earned grades of A's and B's which was significantly better than their white peers without group learning. Of course, organizing these workshops and the increased instructor time costs money. At Berkeley, it may have taken a faculty member three hours to prepare the problem set for a single two-hour workshop. Important non-instructional support is also included in the Berkeley program. While the cost per student in these workshops is higher; the cost per student who learns the material is much lower. The workshops are especially cost effective when they results in students completing engineering degrees instead of dropping out of college. It would be highly cost effective for government to fund Treisman- type workshops in all freshmen math courses. Doing this would reduce the drop-out rate, reduce math anxiety and increase math self-confidence. It would result in students being much more comfortable with the mathematical aspects of all their courses. This would enable many students to choose their majors freely without first crossing off desired majors because of math requirements. There is an accounting question here of form versus substance. Colleges usually allocate monies to a department (for teaching) based on the numbers of students enrolled in its courses not on the numbers who actually learn the material. The workshops at Berkeley were part of a (separate) Professional Development Program. (Also the faculty at U.C. Berkeley has donated $50,000 to the program.) The funding basically needs to come from state legislatures and the general college budget. The pedagogical problem reexamined. Of course, this raises a major pedagogical question: if last yearıs students had considerable difficulty with the standard homework, how can giving this yearıs students even harder problems help them? The usual assumption is that they should start with easier problems and slowly work their way up to the hard ones. The answer: first of all, in doing interesting hard problems students get practice in all the skills they need to review. For example, doing short division exercises gives students plenty of practice with both subtraction and multiplication. Uri Treisman organized his workshops so that the students would be learning much algebra and trigonometry along with the calculus; he did this indirectly by purposefully assigning calculus problems whose solutions required "mastery" knowledge of algebra and trigonometry. In the course of trying to do hard problems, the sources of the student's difficulties become clear, and the instructor can address the weaknesses. The second part of the answer is that by working together in teams, the students help each other over all sorts of rough spots, as they fill in each other's gaps, correct each other's misconceptions and share their knowledge. Thus, four students working together can and will solve many problems that they would all give up on if working individually. In supervised group work, the instructor gives much semi-personal attention to the students in the form of "one-on-four" instruction along with individual and class instruction. The workshops at Berkeley had 20 or fewer students; with classes of 25-30 students, an instructor cannot run from one group to another fast enough to provide the needed one-on-four instruction. I can't emphasize enough how important it is that students get help with their mathematical misconceptions in ungraded situations. While I strongly believe that all seatwork should be team seatwork, this by itself is not a panacea. Group work is being treated as the current fad in some school systems. Sometimes this means having students work together in small groups on straight- forward textbook-type problems while receiving occasional guidance from the instructor. Technically this is group learning and is much better than individual seatwork, but this type of group learning bears little substantive resemblance to Uri Treisman's program. Knowing how to work effectively with one's peers is an important job and learning skill. Of course, students should be taught not to make personal remarks when another student makes a mistake. They should say "the mathematics is incorrect" and correct it, not "you are stupid". Ethnographer Dr. Asera, who works with Treisman, has noted; "False praise is never given [by the workshop instructor]. Minority students are especially sensitive to the underlying message when receiving inappropriate praise for a simple task." (Ref.#4) A college does not simply copy Treisman's program; each college must organize a variation of this program that is appropriate for its own environment. Currently 30 or more universities in the U.S. are experimenting with variations of this program. The most successful is the one at the University of Texas where a Treisman type program resulted in the average score of minority students becoming 20 points higher (on the common math dept. final exam) than the average score of the white students (who were not participating in the program). During the implementation of a Treisman type program at the University of Texas, Treisman was giving advice via telephone for more than a hour each week. Striking results were also obtained in experimental Calculus workshops at the University of Illinoisı Chicago campus and at the City College of New York (CCNY). See Ref. #6. References 1. Report by Prof. Jim Greenberg, Director of Office of Outreach Programs [to public school systems], Univ. of Maryland. (May 26, 1986). 2. William G. Perry, Jr., Cognitive and Ethical Growth: The Making of Meaning 3. Curtis C. McKnight et.al. The Underachieving Curriculum - Assessing U.S. School Mathematics from an International Perspective, A national report on the second international mathematics study sponsored by the International Association for the Evaluation of Educational Achievement (1987). 4. Rose Asera, The Mathematics Workshop [at Berkeley]: A description. 5. Paul Davis, Teaching mathematics and Training seals, SIAM News (the newsletter of the [professional] Society for Industrial and Applied Math.), (March 1987) page 7. 6. Rose Asera, The professional development program and a study in adaption, Undergraduate Mathematics Education (UME) Trends (1990) 7. John L. Brown, Curriculum Dialogues, Prince Georges County Public School System, Upper Marlboro, Maryland (1987) Page 6. 8. In/sights - Research and information about UMCP students, Spring 1991:#2 9. Don Small (Colby College) et al, Report of the CUPM Panel on Calculus Articulation. CUPM = Committee on the Undergraduate Program in Mathematics of the Math Assoc. of Amer. 10. Uri Treisman & R.E. Fullilove (1990) Mathematics achievement among African American undergraduates at the University of California, Berkeley: An evaluation of the mathematics workshop program. Journal of Negro Education 59 (3): 463-478. 11. Richard J. Light, Harvard Assessment, Kennedy School of Government, Harvard University, Cambridge, MA 02138 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Jerome Dancis is an associate professor of mathematics at the University of Maryland, College Park, MD, 20742-4015. Dr. Uri Treisman was director of the Professional Development Program, Univ. of Cal., Berkeley, CA. He wrote "A study of the Mathematics Performance of Black Students at the Univ. of Cal., Berkeley" (1985). He is currently at the Univ. of Texas at Austin.