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chapter 6 Closing the Achievement Gap Calculus is the mathematical study of change. Its essence is best captured by its original name, “fluxions,” coined by its inventor, Isaac Newton. The name calls to mind systems that are ever in motion, always unfolding. Like calculus itself, this book is an exploration of change. It’s about the transformation that takes place in a student’s heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Through all these changes, they are bound together by a love of calculus. Steven Strogatz, The Calculus of Friendship In this chapter, I review how the powerful combination of committed mentors and high expectations has closed the achievement gap at a variety of institutions . We will examine data on the academic progress of disadvantaged students and study the strategies that contributed to their success. Despite the impressive student achievements, a reader of the original Treisman Berkeley report might have asked whether these workshops would be effective at other institutions. After all, the University of California at Berkeley is one of the top universities in the country, and students who are accepted there, including minority students, have already demonstrated that they are outstanding . Also, would these same effects be observed among students from other underrepresented minority groups—for example, Latinos? The Calculus Workshop Programs at California State Polytechnic Institute, Pomona One of the most extensive applications of the calculus workshop model has been at the California State Polytechnic Institute in Pomona. Martin Bonsangue conducted a thorough, systematic evaluation of this program, in which the majority of participants were Latinos. The evaluation focused upon a sample of 133 workshop and 187 non-workshop Latino American, African American, c l o s i n g t h e a c h i e v e m e n t g a p 121 and Native American students, who were followed for a five-year period.1 Both the treatment and comparison groups consisted largely of Latino students (87 percent of the workshop students and 85 percent of the non-workshop students were Latino). Both groups also contained mostly men (74 percent of the workshop students and 80 percent of the non-workshop students). The workshop program was patterned after the Berkeley experience. Students met in groups to work on calculus problems twice a week for two hours each session. Statistical comparisons revealed no significant differences between the workshop and non-workshop students in terms of their background and other pre-intervention variables such as SAT scores, high school grade point averages , and scores on a precalculus diagnostic test. Further analysis revealed that each of several workshop subgroups—Latinos, African Americans, and women—outperformed the corresponding non-workshop group. In the course of this research, Bonsangue made an important discovery. After many long hours sorting through paper forms (full course data were not available electronically at that time), he discovered that many students were failing and then retaking calculus again and again—sometimes four or five times. He then developed the course attempt ratio (CAR), in which the numerator is the number of times a student attempted a course and the denominator is the number of courses the student completed successfully (5). Additional analyses showed that the workshop effects persisted in subsequent second-year calculus courses. The CARs of groups in the second-year courses did not differ, but the workshop group successfully completed one and a half times the number of second-year mathematics courses that the nonworkshop group did, even though there were initially 40 percent fewer students in the workshop group than in the non-workshop group (8). Workshop students were significantly less likely to drop out of the institution . In the 1986–89 sample, fewer than 4 percent of the workshop minority students dropped out by spring 1991, compared with 42 percent of those not in the workshops (9). Even more impressive, “of those students still enrolled in Mathematics, Science, and Engineering, more than ninety percent of the workshop students had completed their mathematics requirements for their individual majors, compared to less than sixty percent of the non-workshop students ” (10). And workshop students who persisted in their MSE field achieved higher grade point averages overall than did the non-workshop students. However , they held only a slight advantage in terms of grades within the major, and there were no differences between the two groups with respect to number of...

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