A successful collaborative calculus program for African American and Latino/Latina calculus students at the University of Illinois at Urbana-Champaign.
Dimensions: Equity pedagogy.
Title and Location:
Mathematics Workshop Program
University of Illinois at Urbana-Champaign
Director, Mathematics Merit Program
University of Illinois at Urbana-Champaign
178 Altgeld Hall
1409 W Green Street
Urbana, IL 61801
The Mathematics Workshop Program was developed by Uri Treisman at the University of California, Berkeley. Its purpose was to reverse the low success rate in entry level calculus, and the high attrition rate in math-related fields, for African American and Latino/Latina students who entered the university interested in careers in math, science, or engineering. In no way remedial, the Mathematics Workshop Program was designed as a voluntary honors program which supplemented the students' regular calculus classes. In workshops, small groups of students were given challenging problems which they solved through collaborative efforts with their peers. The program achieved dramatic results. Highlighting that success, the Mathematics Workshop Program counts among its workshop alumni Michele deCoteau, the first African American and the first woman student at Berkeley to be awarded a Rhodes Scholarship.
Program History and Description
The Mathematics Workshop Program (MWP) operated between 1978 and 1984 at the University of California, Berkeley (UCB). It was initiated in response to the high failure and attrition rates noted for African American and Latino/Latina students who entered UCB with career ambitions in math, science, and engineering. Approximately 40 percent of the African American students who completed Math 1A-an entry-level calculus course for students with math-related majors-received failing grades of D plus or below (Fullilove & Treisman, 1990; Treisman, 1985). Furthermore, remedial programs proved ineffective in changing this situation. An initial study conducted at UCB during the 1975-1976 school year revealed that TAs disproportionately identified Chinese American students as the strongest, or most successful, students in their Math 1A sections while African American students were disproportionately identified as the weakest (Fullilove & Treisman, 1990). Subsequent investigation revealed that African American and Chinese American students applied substantially different strategies while preparing for class. African American students averaged 8 hours studying alone outside of class each week-the amount recommended by the department-and kept their academic and social lives quite separate. Chinese American students also studied about 8 hours per week, but they formed small study groups as well and thus allocated approximately 14 hours per week to their calculus course. In these study groups, difficult problems were solved collaboratively, and the students' academic and social lives became intertwined (Fullilove & Treisman, 1990; Treisman, 1990; Treisman, 1992).
Using this information, MWP was designed to adapt the best features of collaborative study strategies for use with African American and Latino/Latina Math 1A students. In weekly workshop sessions, students worked in small clusters to solve challenging problems presented on a worksheet. A TA was present to monitor the workshop and provide assistance as needed. Originally funded by a grant from the U.S. Department of Education's Fund for the Improvement of Post-secondary Education (FIPSE), the program operated on a smaller scale in 1983-1984 after funding expired. However, the results observed during both periods were dramatic. African American participants achieved high levels of success in Math 1A, and they persisted in the university system at the same rate as the general student population (Fullilove & Treisman, 1990; Treisman, 1985).
MWP was initiated with three goals it maintained throughout: (a) to help minority students in the university excel rather than simply avoid failure; (b) to emphasize collaborative learning and small-group instruction; and (c) to provide faculty sponsorship-an element considered critical for success (Treisman, 1985).
Instructional Strategies and Materials
Students met twice a week in two-hour workshop sessions which were structured around collaborative learning and small-group instruction. In no way a remedial program, MWP students were given challenging problems to solve-problems more difficult than those encountered in their regular course assignments. At the beginning of each session a problem set (worksheet) was distributed to the twenty or thirty participants. The students then clustered in groups (of five to seven students) and worked together to solve the problems. There were no set rules. Students could work alone, in pairs, or as a group. However, students were encouraged to work collaboratively, assisting and instructing each other and discussing the methods by which the proofs were derived. It was estimated that students ultimately spent approximately half their time working as a group (Treisman, 1985). While attendance was voluntary-no academic credit was given for the workshops-absences were noted and follow-up inquiries were made.
MWP did not change the curriculum or the instructional strategies used in entry-level calculus. It was an enrichment program offered alongside Math 1A, and it utilized supplemental worksheets. These worksheets contained problems which fell into one or more of the following five categories:
- "old chestnuts" that appear frequently on examinations but rarely on homework assignments;
- "monkey wrenches"—problems designed to reveal deficiencies either in the students' mathematical backgrounds or in their understanding of a basic concept;
- problems that introduce students to motivating examples of counter-examples that shed light on or delimit major course concepts and theorems;
- problems designed to deepen the students' understanding of and facility with mathematical language;
- problems designed to help student master what is known, in MWP parlance, as "street mathematics"-the computational tricks and shortcuts known to the best students but which are neither mentioned in the textbook nor taught explicitly by the instructor. (Fullilove & Treisman, 1990, p. 468)
Targeted Student Population
Approximately 80 percent of the students who participated in MWP were either African American or Latino/Latina (Fullilove & Treisman, 1990). While the program was directed specifically toward these students, efforts were made to ensure that workshops remained ethnically diverse. Substantial numbers of Equal Opportunity Program and Special Admit students were also recruited, and efforts were made to achieve gender balance in MWP as well.
The Educators: While MWP was designed and supervised by Uri Treisman, the workshop leaders were TAs who were responsible for generating the worksheets and were given additional training with regard to small-group instruction and interviewing student recruits. Leaders moderated workshop sessions in an unobtrusive manner and employed a variety of instructional methods-at times addressing a cluster of students, at times addressing the whole group, and at other times giving direction or instruction to one particular student. Frequently one student, or one cluster, would be asked to present a problem solution to the entire group-however, the student(s) would first be given time to prepare a clear and comprehensive explanation.
The School and the Community
Treisman (1992) points to the changing demographics of the university community in California-an incoming freshmen class at the University of California, Berkeley is now typically 32 percent African American, Latino/Latina, or Native American while non-Hispanic Caucasians made up about 38 percent (p. 364). Yet in the decade preceding MWP, records show that 60 percent of the African Americans who completed Math 1A failed the course (p. 364). Treisman further states that over the next fifteen years the University of California system will require 10,400 new faculty members and the California State University system will demand even more (p. 362). Filling these positions will depend increasingly on the minority student population. Math-related fields across the nation face similar circumstances.
Achievement for African American students in Math 1A was analyzed using three primary groupings: MWP participants, non-MWP students, and an historical group of students who completed Math 1A during the five years prior to the establishment of MWP. Chi-square tests were used to test the association between various membership sub-groupings and three outcome measures: (a) honors level grades of B minus or better in Math 1A; (b) failing grades of D plus or lower; and (c) persistence in the university, which was defined as either graduation or good academic standing as of fall semester 1985 (Fullilove & Treisman, 1990; Treisman, 1985). In the historical control group, 33 percent of the African American students who completed Math 1A received a failing mark of D plus or below during the five-year period prior to MWP's inception (Fullilove & Treisman, 1990). This did not differ significantly from the 40 percent failure rate for non-MWP students during 1978-1982 FIPSE-funded period or the 41 percent failure rate for non-MWP students in 1983-1984. However, the mere 3 percent failure rate for MWP participants in 1978-1982 and the 7 percent failure rate for MWP students in 1983-1984 were statistically significant differences ( p < 0.0000) (Fullilove & Treisman, 1990). Furthermore, MWP was an honors program and the proportion of students receiving grades of B minus or better showed a dramatic, statistically significant increase when MWP students were compared to non-MWP students during any of the three time periods ( p < 0.01). Notably, the smaller program size following the removal of FIPSE funds did not impact the observed change in student achievement for MWP participants (Treisman, 1992).
Treisman (1985) notes the following attributes in explaining MWP's success:
- The creation of academically oriented peer groups helped group members value academic success and achievement. As success became prized, the students worked hard to attain that success and thus devoted more time to their course work.
- In the workshops, students learned to be critical and to communicate clearly. They became aware of areas in which they had personal weaknesses which needed additional attention.
- The students developed resources for their sophomore year and beyond. They acquired both study skills and social skills in the workshops, and they developed lasting relationships with other students in their field which persisted throughout their college careers.
- Students developed leadership and collaborative skills and learned to support one another.
Michele deCoteau, a MWP alumnus, became the first African American and the first woman at UCB to be awarded a Rhodes Scholarship (Charles Dana Foundation, 1988).
MWP has been successfully adapted at several institutions in California-UCLA, the University of California at San Diego, California Polytechnic at Pomona, and the medical school at the University of California, San Francisco (Fullilove & Treisman, 1990). The University of Texas at Austin, where Professor Treisman currently teaches, operates the Emerging Scholars Program (ESP). In addition, a number of other programs around the country-biology and physics programs as well as math-have developed programs based on the MWP model.
The Charles A. Dana Foundation. (1988, Spring). Dana award winner's innovations in educating minority students in math and science attract nationwide interest.
The Charles A. Dana Foundation Report, 3 (1), 1-5.Fullilove, R. E., & Treisman, P. U. (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), 463-477.
Treisman, P. U. (1985). A study of the mathematics performance of Black students at the University of California, Berkeley. Unpublished doctoral dissertation, University of California, Berkeley.
Treisman, P. U. (1990, March 8). Academic perestroika: Teaching, learning, and the faculty's role in turbulent times. FIPSE lecture presented at California State University, San Bernadino. Available Internet: http://www.ed.gov/offices/OPE/FIPSE//Perestroika/
Treisman, P. U. (1990, November). Studying students studying calculus: A look at the lives of minority mathematics students in college. The College Mathematics Journal, 23 (5), 362-372.