Curriculum Analysis — Math Department

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.


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 11th 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.


Curriculum Analysis — Science Department

Harvard News 10/11/83–Editorial – CURRICULUM ANALYSIS: PART 1

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

Education at Harvard is like a lone, narrow path winding up a mountain: the path will ultimately reach the summit, but there are no rest stops and no short cuts. This is not to say that the path offers no scenery and requires no skill; rather, that it has been worn, and no new ones have been made. Harvard has made the transition from a good school to a great school; Harvard should now attempt the transition from a great school to an innovative, exemplary institution. Past changes have been lateral instead of vertical; that is electives in both traditional and non-traditional fields have been added, but the core curriculum remains unchanged. The current curriculum is confining: tracking occurs too late or not at all. Few students find the curriculum frustrating because it is too hard; however, many find the curriculum frustrating because it is too easy. This is only one problem. Consequently, changes in the core curriculum should recognize students’ varied capabilities and emphasize flexibility. In the following few issues, the Harvard News will examine the core curriculum and propose changes.

Before any assessment of means is possible, an assessment of goals is necessary. Harvard is and should remain dedicated to college preparation. At the same time, two other propositions deserve our dedication: that of learning as much as possible, given our resources and our time; and that of exploring limits, with regard to a student’s potential. Harvard pursues both; we believe it could so better.

All five departments will be surveyed in the next three issues, and their order is both random and arbitrary. In this issue, we begin with a survey of the science department.


The goal of any science program is to offer the opportunity to study Chemistry, Biology, Physics, and the related sciences. We at Harvard are quite fortunate to have advanced A.P. courses in all three of these major areas. Unfortunately, advanced study in all three of these areas, for the serious science student especially, is not feasible. There are two general reasons which account for this problem. First, Harvard students begin to learn the fundamentals for the major sciences only in ninth grade. Second, the Science Department requires basic courses before A.P. courses can be taken in two of the three major courses. The Science Department’s potential—with its excellent faculty, its extensive resources, and its wealth of courses—is phenomenal; it is unfortunate that students cannot take these courses, take advantage of that potential, and fulfill their goals as science students.

The priority of the Lower School science courses should be to prepare students for study in the three major sciences: Chemistry, Biology, and Physics. The current Lower School courses do not offer such preparation. The seventh grade course could be termed pre-Biology—though it is hard to classify the Egg Drop in any scientific category. The knowledge gained in this course is at least three years away from its application in Biology, and is usually forgotten by then. The eighth grade course introduces the basic concepts of Mass, Volume, Density, and Temperature. These concepts are reintroduced in ninth grade and studied, as they should be, in more depth. Combining the useful aspects of both Lower School science courses into an Introductory Science course and then offering a Matter and Energy course in the eighth grade, is a conceivable and practical alternative. With such changes, the Lower School science courses could better serve as preparatory courses for advanced study in the three major areas of science.

Moving the basic courses back one year would help solve the problem of students not being able to take all the advanced courses, but it would not be enough. Harvard is unique in its requirement of Chemistry before A.P. Chemistry and PSSC Physics before A.P. Physics (Mechanics) and, also, not allowing Biology before A.P. Biology. Many schools allow very capable students to enroll in A.P. science courses without introductory course, and allow two-year options to the rest of the students. Harvard could certainly do this as well. In the ninth and tenth grade, students could have a choice between Biology and Chemistry, on either the normal or advanced level. In eleventh grade, students could be allowed to take Physics PSSC or A.P. Physics (Mechanics), along with a choice of many science electives. Twelfth grade would then be available for other electives or even A.P. Physics (Electricity and Magnetism). This system allows for the most flexibility and opportunity, for all students.

Under such a proposal, Harvard students would learn at least Biology and Chemistry, and could theoretically take A.P. courses in Biology, Chemistry, and Physics (Mechanics and Electricity & Magnetism). Such achievements are not impossible; one need only look at Walter Reed Jr. High School for a program at least equally remarkable. At the end of the seventh grade, IHP (Individual Honors Program) students have the opportunity to take A.P. Chemistry or A.P. Biology in Eighth grade—without a Seventh grade science course. The class, which includes students from the regular junior high school, boasts a 90% pass rate. Jeff Kurland (’84), who graduated from the IHP at Walter Reed, estimates 60% of Harvard’s students could quality for, and succeed in, the program. Harvard has the faculty, the resources, and the courses for such an outstanding program. All that needs to be done is to give students the opportunity to take advantage of such a program.