Treisman's Model

In the late 1970's and early 1980's, graduate student Uri Treisman at the University of California, Berkeley, was working on the problem of high failure rates of minority students in undergraduate calculus courses. According to Treisman (1985), the African-American calculus students at Berkeley ``were valedictorians and leaders of church youth groups, individuals who were the pride of their communities. ... Thus, these students had come to Berkeley highly motivated and under great pressure to succeed'' (p. 21). Nevertheless, folklore blamed the high failure rates on the students' lack of motivation, lack of educational background, and lack of family emphasis on education (Treisman, 1992). Treisman's work (Treisman, 1985) challenged these hypotheses, and replaced the remedial approaches with an honors program that encouraged students to collaborate on challenging problems in an environment of high expectations (Conciatore, 1990).

Treisman's mathematics workshop recruited mostly African-American and Latino students having relatively high SAT Mathematics scores or intending to major in a mathematics-based field or both. Key elements of the workshop involved:

1. the focus on helping minority students to excel at the University, rather than merely to avoid failure;
2. the emphasis on collaborative learning and the use of small-group teaching methods; and
3. the faculty sponsorship, which has both nourished the program and enabled it to survive. (Treisman, 1985, pp. 30-31)

Each of these elements is discussed in more detail below.

Collaborative learning.

In his initial investigation, Treisman ``was struck by the sharp separation that most black students maintained---regardless of class or educational background---between their school lives and their social lives'' (Treisman, 1985, p. 12). He went on to compare these students with their Asian counterparts---who had a history of being very successful in the calculus courses---noting that most of the black students studied alone while the Asian students sought peers with whom to collaborate. More than merely studying together, the Asian students formed academic communities:

Composed of students with shared purpose, the informal study groups of Chinese freshmen enabled their members not only to share mathematical knowledge but also to "check out" their understanding of what was being required of them by their professors and, more generally, by the University. ...

[Treisman] observed Chinese students in their study groups ask each other questions ranging from whether one was permitted to write in pencil on a test to how one might circumvent certain University financial aid regulations. More important was the fact that these students routinely critiqued each other's work, assisted each other with homework problems, and shared all manner of information related to their common interests. Their collaboration provided them with valuable information that guided their day-to-day study. (Treisman, 1985, pp. 13-14)

Since "interactions like these were extremely rare among the blacks" (Treisman, 1985, p. 16), the key then was to build a community based in the study of mathematics, to create a merging rather than a separation of academic and social lives.

Challenging mathematics and high expectations.

In partnership with collaborative learning strategies, the mathematics employed was challenging, engaging, and meaningful. Treisman (1985) explained,

Because of their participation in [a special high school program], these students saw themselves as an academic elite group. They were accustomed to being the tutors, not the ones in need of tutoring. ... Knowing the students' sensitivities, [he] took care that the Workshop not appear to be a tutoring session. The problem sets (called worksheets) were always difficult, with near-impossible problems thrown in frequently to protect the Workshop's non-remedial veneer. (p. 26)

While "most visitors to the program thought that the heart of our project was group learning ... the real core was the problem sets which drove the group interaction" (Treisman, 1992, p. 368). The best problems were not quick, procedural applications of formulas that had one right answer; rather they were deep, thought-inspiring problems (perhaps with multiple parts) that engrossed the students. Where remediation approaches worked to reduce deficiencies, Treisman's model built on the students' already existing strengths.

Faculty sponsorship.

Critical to the success of the Berkeley program was the faculty sponsorship aspect. ``The traditional faculty response to minority students at that time was to hire someone to deal with them, create tutorial programs for them, and house them in a temporary building on campus somewhere'' (NSF, 1991, p. 4). By contrast, in the mathematics workshop model, "the significant points were to build a community around the courses and manage the courses by faculty, not tutors in temporary buildings" (NSF, 1991, p. 7). Furthermore, ``the faculty courted students, and students quickly chose mathematics as a major'' (NSF, 1991, p. 6).

Overview.

As described by Gillman (1990), the program at Berkeley

is an intensive, demanding program for talented students, particularly minority students, who are planning career[s] in mathematics-based profession[s]. ... They are told that they are among the most promising freshmen and that the program is seeking students with a deep commitment to excellence. ... The emphasis is on students' strengths rather than their weaknesses ... the direct opposite of tutoring or other remedial programs. (p. 8)

The resulting model replaces regular calculus discussion sections with workshop-style discussion sections, in which the students collaborate on non-textbook, non-routine problems. During these work sessions (which meet for larger blocks of time than traditional classes), ``[students] begin working the problems individually, then, when things get tough, in collaboration with one another. These experiences lead to a strong sense of community and the forging of lasting friendships'' (Gillman, 1990, p. 8).

The Berkeley program has been so successful that it has spread to other universities and colleges throughout the country. Modified versions have entered high schools, in forms designed to fit the particular environment and needs. As Treisman has stressed, the program is not remedial---nor should it be---and care is taken with replications that they do not revert to remedial programs.

Related Functional Links:  
                                                Studying Students Studying Calculus by Uri Triesman
                                  Advanced Placement Programs in High-School ... by Uri Triesman
                                                 About Treisman and his program
                                                 About the Emerging Scholars Program in Oregon
                                                 About the Emerging Scholars Program in Illinois
                                                 MathExcel Advantage in Kentucky

  Details from the implemented program in Kentucky:

The best calculus class at the University of Kentucky is composed almost entirely of women, minorities, and students from rural and smaller school districts. This is MathExcel, an innovative, award-winning program designed to give capable students from these groups the best possible chance to excel in this crucial course. MathExcel students enroll in special sections of calculus which encourage collaborative learning in a personal, communal atmosphere. All students in calculus take the same tests and are graded on the same standards. This is how MathExcel students compare with regular ones: