This article appeared in the TACT Quarterly Bulletin, LI, No. 2 (pp. 7--9)

I am writing this as a member of TACT but not as a representative of TACT or any other organization.

Last year, the legislature passed Senate Bill No. 148, which has as one of its provisions that the Texas Higher Education Coordinating Board, "with the assistance of advisory committees composed of representatives of institutions of higher education, shall develop field of study curricula. ... If a student successfully completes a field of study curriculum developed by the board, that block of courses may be transferred to a general academic teaching institution and must be substituted for that institution's lower division requirements for the degree program for the field of study into which the student transfers."

In the July issue of the TACT Bulletin, I wrote of this provision that "The field of study part of the law has the potential for even more damage to the delicate interweaving of courses and preparation of students in Texas. I believe this part of the law may cause the destruction of the best curricula this state has to offer. Of course, the precise mandate of these first-two-year curricula will depend on the wisdom of the committees appointed to prepare them. But how is a single size plan supposed to suit all of the varied needs of the students of Texas? Should all mathematics degree programs be alike?" In the next paragraph, I added "I believe that these problems will cause the common field of study plans to fail after costing the faculties of the state's institutions vast amounts of time writing them and rewriting curricula already carefully adapted to the specific students at each school."

Here, I wish to provide support for these sweeping statements. This support is followed by some suggestions, first for the mathematics community, and then for all of my colleagues.

Since I am in mathematics, I studied the mathematics degree programs in the public institutions of Texas. To keep this task manageable, I restricted my study to the institutions which offer a 4-year baccalaureate degree in mathematics. I examined recent catalogs from each of these institutions, noting the mathematics courses required of their mathematics majors during their first two years at the school, and also noting the total number of additional mathematics hours required to achieve the baccalaureate degree.

The variety of mathematics degree sequences offered throughout the state is astonishing. I tried to summarize the programs, in the hope of finding two or three common sequences that we could converge on; instead my summary showed 30 different sets distinguishable by courses and credit hours. These lower division curricula begin with any of college algebra, trigonometry, precalculus, analytic geometry, or calculus. They end anywhere from half-way through a standard calculus sequence to 12 hours past the completed calculus sequence. The number of mathematics credits in the first two years ranges from a low of 12 hours to a high of 25 hours. (The number of mathematics credits for the entire four-year program ranges from a low of 26 hours to a high of 55 hours.)

There is a block of seemingly standard courses, each of which appears in many curricula: College algebra, trigonometry, analytic geometry, calculus, linear algebra, and differential equations. These courses are usually taken in the order listed, each having the previous one as a prerequisite, except that analytic geometry is often absorbed into calculus, and linear algebra and differential equations can be taught in the opposite order. But this list is very misleading.

First, the only one of these subjects that appears in the first two years of every degree program is calculus, and even that subject is not always finished in the first two years.

Second, even the commonly-taught calculus is taught in at least six different formats, ranging from two 4-credit courses to four 3-credit courses. The very concentrated case of two 4-credit courses occurs at the University of Texas. Texas A&M University has a seemingly more relaxed three 4-credit courses of calculus, but the computer mathematics program MAPLE is taught and used throughout that sequence. For another approach to teaching calculus, Sul Ross State University teaches calculus without the theory of limits in the first year (where it is usually taught), and instead provides that theory in the second year.

Third, no degree program includes all six of these "standard" courses in its lower division sequence. At one school, differential equations and linear algebra are presented in one 4-hour course instead of the more usual two 3-hour courses. Moreover, no sequence which begins with college algebra gets as far as both differential equations and linear algebra, and most such sequences do not get past calculus.

Fourth, more than twenty of the lower division mathematics curricula include at least one course not in the "standard" list. Among these courses are discrete mathematics, modern or abstract algebra, statistics, some sort of advanced analysis, and probability and statistics. Some programs include a mathematics elective in the first two years.

All of this variety reflects the constant efforts of the faculty of the many schools throughout the state to increase the depth of understanding in their graduates and simultaneously to find new and better ways of teaching mathematics. Mathematics is universally acknowledged as a difficult subject, and we are always hoping to find ways of making it clearer, more natural, and easier for our students, without sacrificing the full understanding that they need. We experiment constantly with our courses, and when it becomes clear that an experiment has succeeded, we and others carefully and thoughtfully adopt the new methods. Since such experiments do not always succeed, they should not be carried out on a state-wide basis.

The variety of courses also conceals one essential truth. In each mathematics program, there is a small group of courses which must be completed before most upper division courses can be attempted. This group usually consist of calculus, linear algebra, differential equations, and frequently also discrete mathematics or some other course designed to give the students experience with proofs. Students whose training stops at calculus will not be ready for upper division courses at universities where this group is among the lower division courses. Thus the field of study requirement in mathematics, if there is only one, will either seriously damage the highest level sequences this state has to offer, or it will be incompatible with the sequences created for the students who need pre-calculus courses. Some group of students will suffer if there is only one field of study requirement in mathematics.

So how do we conform to the field of study portion of Senate Bill 148 without ruining the mathematics degrees of Texas? Ideally, we persuade the Texas Legislature to repeal this portion of the law. It is not workable without grievously harming the educational programs of Texas and thus the students in those programs.

But if we must live with the law, what can we do? In this case, I urge the committee selected by the Texas Higher Education Coordinating Board for the mathematics program to:

The field of study law will inevitably seriously damage our mathematics programs. However, I believe the suggestions above will allow us to recover and rebuild our sequences to give our students a selection of programs approaching the variety and quality we can offer now.

I urge my colleagues in other fields to conduct studies similar to the one I have reported here. I expect that many subjects will show similar diversity and wide-spread efforts to experiment with better teaching methods. In every field, we need a broad-based discussion of the lower division field of study issues to determine an optimal way to respond to the law. The time to act on this is now, before well-meaning but unguided committees have forced our subjects into state-wide strait jackets.

Arthur Hobbs
Professor of Mathematics
Texas A&M University