Harvard News 10/28/83–Editorial – CURRICULUM ANALYSIS: PART 2

By E. Randol Schoenberg, Editor-in-Chief and Bart Aronson, Features Editor

In this issue, the Harvard News continues its review of the core curriculum with a look at the Math Department; in the nest issue, the News will consider the Social Studies Department.

THE MATHEMATICS DEPARTMENT

Students of mathematics at Harvard exhibit a wide variety of innate capabilities and levels of knowledge, perhaps more so than in any other discipline. For some, it is a tough climb from Mathematics I to Geometry or Pre-Calculus in eleventh grade; for others, it is an easy ride along the accelerated path to Advanced Topics in twelfth grade. Two things, perhaps, can be stated generally about math students: first, nearly everyone begins seventh grade with a different level of understanding, and second, everyone learns at a different rate. At the same time, there are, potentially, three areas of the mathematics program which do not fully provide for Harvard students’ needs: first, all students begin with the same seventh grade course, regardless of ability or experience; second, the students who drop from the accelerated program usually repeat that program’s material in another class; third, geometry is all but absent from Harvard’s curriculum.

Students enter Harvard having had different backgrounds in mathematics, and there is no doubt that some come already knowing the basic arithmetic skills taught in Mathematics I, or could learn them quite quickly. This creates an extremely difficult classroom situation. The teacher must teach at the pace of the least able student, and simultaneously keep the attention of the average and above-average students—a trying task for the best of teachers. The result is frustration for the students who learn slowly, and are learning the material for the first time, because they feel they are holding back the class, and frustration for the more skilled students, because they are not learning at all. As a consequence, though students can still follow an accelerated path and take Calculus in 11^{th} grade, tracking—beginning in seventh grade—is essential.

Mathematics is the easiest subject to test for ability. Tests, such as the SSAT or (better still) a test developed by the Math Department, could be used to divide the students into accelerated and basic levels. No test is perfect; however, presumably the SSAT is sufficiently accurate to be used in Harvard’s admission process. And certainly, any test would produce more unified classes and facilitate tracking.

Westlake School tests incoming seventh graders in August to determine which math class they will take in September. Schools such as Santa Monica High School and Walter Reed Junior High School offer accelerated tracks which allow students to take Calculus (AB and BC) in tenth grade. Such a program at Harvard would simply mean allowing outstanding seventh graders to begin with the eighth grade Unified II course. Courses would not have to change significantly—only the makeup of the classes would. The result would be classes and courses more tailored to students’ needs.

One problem in particular is the problem of students who begin in the accelerated track, and then drop out. Students who drop out after Unified III—as quite a few do—repeat the course material in Advanced Algebra with Transformations in tenth grade. In the end, they gain nothing (besides a lower grade) by taking the accelerated track. For ninth through eleventh grade, Harvard’s third track should be tailored to the students who drop from the accelerated track and the successful students in the regular track who chose not to enter the accelerated track. This proposal—which is, in sum, a change in the makeup of classes in the lower grades and grades—is both feasible and beneficial. While taking Calculus in eleventh grade instead of tenth grade might not destroy the future of any budding genius, there is no reason to slow him down.

The lack of Geometry in Harvard’s core curriculum is more of an ideological problem than those previously discussed. Geometry was eliminated from the regular and accelerated tracks by former chairman Richard Sisley, and since his departure, the Math Department has not had a chairman remain at Harvard long enough to reinstate it. Geometry in a math curriculum serves two vital functions. First, geometry is the most analytical of all mathematical areas. The use of proofs and physical models train the mind—better than any other mathematical topic—for inductive, logical thinking. Second, the standardized tests with which Harvard students are inundated, are full of geometrical questions—questions for which some of Harvard’s better math students find themselves unprepared. The general attitude of Harvard’s math teachers is that geometry should hold a larger place in our math curriculum, and it is hoped the new math chairman, Ms. Beverly Kocan, can begin to effect such changes.

Harvard’s outstanding mathematics faculty has for years taught students the necessary basic skills and, at the same time, allowed Harvard’s finer math students to accelerate beyond those basics. The changes we propose would, we hope, allow for even greater flexibility and tailoring, and in the process, enable students to learn at rates match by their abilities.