Rethinking Mathematics for Liberal Arts Students

Too often we college mathematics instructors give liberal arts and humanities students short shrift. We think of them as outsiders to our enterprise, as remedial students needing still more instruction in what we think of as the basics: school arithmetic, algebra and geometry.

The authors of
About Mathematics believe that these students deserve better. No, they are not interested in becoming mathematics majors. In fact, many of them have had bad experiences with their school math courses and have come to dislike or even fear the subject. In response to this, we should not treat them as lesser beings; rather, we should appreciate the simple fact that their main interests and abilities lie elsewhere.

This text addresses these students as honored visitors to our enterprise. We seek to give these students insights into that enterprise and in particular especially interesting insights that will improve their attitude toward our subject. There is plenty of content in this text, but the focus is on concepts, the glue that holds our subject together. It is those concepts that we wish our students to take away from their studies.

Several features of the text speak specifically to this aim. We personalize the writing by use of first person pronouns (despite the fact that there are three authors): you and I are in this together. The presentation style is unlike the usual sparse concept-proof-example-exercise format of most mathematical presentation; ours is more "wordy", that is, in the essay style more often used in the liberal arts. Well over three-fourths of the content of this text will be new to these students and they meet topics and ideas often missed by their math major friends. And a range of topics is considered that are independent of each other, thus giving these students a sense of the breadth of mathematics and at the same time an opportunity to start new topics afresh.

A major feature of this program is the regular use of pre-developed programs for the TI-84 graphics calculator, each closely associated with the text content and exercises. These programs are designed to illustrate concepts, to carry out complex calculations that too often produce errors and hide underlying ideas, and to empower these students to model and solve interesting problems. Students (and instructors) need not know anything about programming: they simply run the programs that are downloaded to their individual calculators.*

We have taught with this text in two settings: in a Buffalo State College course for lower division students and in a University at Buffalo course for math teachers. In both classes the student response has been gratifying. See the student comments page.
* Some instructors may wish to supplement instruction with About Mathematics with instruction in programming, as I did in my Buffalo State class. We have developed the separate text Program Your Calculator (q.v.) which supports that instruction.