Although a statement that Harvard gives fourteen different courses in elementary mathematics--all called "Math A"--would be gross exaggeration, nevertheless present lack of uniformity among the sections gives just that impression. Resolving not to permit the slightest hint of regimentation to cast its ominous shadow over their fair course, the men in charge of "Math A" have allowed the fourteen sections to become, in practice, almost wholly independent of one another. Not only teaching methods, but organization of material, examinations, and grading standards vary from section to section, and as a result men undertaking "Math A" can never be sure of what they are in for. While initiative of individual instructors, especially of young instructors, must never be destroyed, its scope should be kept within clearly defined limits.
The problem of defining the field in which initiative is to be exercised is a difficult one. There is at present a rather definite syllabus provided for all the instructors, but many proceed to disregard it. Since each section has its own examinations, there is no effective way for preventing this; could the whole course be given identical exams the problem would be solved. This is not possible for an interesting reason. Teaching "Math A" are a number of the country's leading experts in the field, and they simply cannot agree as to the best methods of presentation; indeed, they cannot agree entirely as to what an elementary course in mathematics should contain. Thus there can be no one examination that will be fair to every student.
However, simply because there can be no single examination, there need not be fourteen different ones. If each of the three or four experts would draw up a syllabus containing what he believes to be the essentials of the course, in the order in which they should be presented, and if every section were required to follow one of these plans, the number of examinations necessary would be reduced to three, or four, as the case might be. Although this would not be a complete solution, it would be a long step toward a much-needed reform.