The University of South Carolina Spartanburg (USCS), like many other liberal arts institutions in the US, has had poor success in developing effective traditional mathematics instruction for liberal arts majors. At the national summer meetings of the Mathematical Association of America in 1997, educators reported that barely more than half of the students who enter math-for-the-liberal-arts courses receive a passing grade. Many simply withdraw multiple times until they gain sufficient knowledge or they accept failure. In traditionally-taught sections of the liberal arts math course College Mathematics at USCS, the median success rate has hovered around 55% for the past five years.

During 1994 a group of faculty members at USCS began to develop and test an innovative pedagogy integrating technology and activity- or project-based instruction in mathematics for liberal arts majors. The group collected, modified and/or wrote items for a packet of activities designed to form the core of material that would be used to supplement and eventually replace the textbook in the College Mathematics course. Subsequently, M.B. Ulmer wrote a booklet to lend structure to the use of the activities, and the textbook was eliminated from use in many sections of the course. Under this pedagogy success rates have risen dramatically for students, and their subsequent performance in required statistics courses has also shown improvement.

Most of the students we try to reach in College Mathematics are products of pedagogical styles which depend on the learning of algorithmic processes for success. Few, if any, have been expected to think mathematically. As do many of their peers around the nation and the world, they view math and statistics as lists of rules to be memorized, selected and applied in response to problem types whose solutions are demonstrated in immediately adjacent sections of a text. The disciplines are seen as bearing little relation to reality and devoid of context within their own lives. Behar and Ojeda[1] observe, "[N]onstatistics majors will learn statistics only if the usefulness of it in their professional life is made clear to them." This statement can be applied in a broader context to include attempts to bolster the quantitative development of liberal arts students to prepare them for understanding subsequent quantitative disciplines such as statistics.

The textbook as primary instructional tool has compounded the problem of perceived irrelevance. Pursuing Excellence, a report on the Third International Mathematics and Science Study[2], points out some interesting differences in instructional paradigms between the US and countries such as Japan where math instruction is more successful. One of the striking differences in middle-grades instruction is the proportion of class time during which the textbook is used by students. That proportion is about two percent in Japanese classrooms but much higher in less successful countries. In the US, middle grades math classes use the textbook about fifty percent of instructional time.

The recent availability of inexpensive calculators and computers allows new options for laying mathematical foundations. We have developed a very promising approach which uses regression modeling as a tool for describing real data which students perceive as applicable to their lives. In the version of the course that makes maximum use of available technology, students have access to spreadsheets, X(PLORE), BASIC, Minitab, and the TI-82 or -83 calculator. They select appropriate technology to complete group and individual projects which range from analysis of local infant mortality rates to the construction of a personal long term financial plan. Most choose Microsoft Word to produce required reports. In addition to traditional tests and a comprehensive final exam, assessment tools include portfolios, presentations, and a term project.

For the project-based version of the course, there is no required textbook. A packet of activities and projects accompanies a forty-plus page booklet containing the topics to be covered. The booklet lends structure to the activities and projects. It contains, however, insufficient drill problems to support an instructor who might opt to spend an inordinate amount of class time in drill and practice. This intentional omission thus forces practice to occur in the context of an activity involving real data. Fewer problems are worked than in the traditional course, but, as statistics instructors such as Moore [3] have noted, the payoff is large: "[A]lthough we may 'cover' somewhat less material when we increase interaction...students appear to emerge with a greater store of usable knowledge." Student opinion of the approach has been quite positive.

With the new technology, a variety of functions or models can be introduced through regression. In completing the projects, the students are exposed to all functions traditionally taught in introductory college mathematics courses using standard texts such as that by Lial and Miller. Those functions are linear, quadratic, higher order polynomial, rational, exponential, logistic and logarithmic functions. Probability and statistics comprise a small portion of the course. Although the concept of regression is central to implementation of the course, the statistical aspects of regression are postponed for a more advanced course.

Another point of comparison in this approach involves pedagogy. The pedagogical style suggested is more student centered than that of traditional classes. Generally, a concept such as linear modeling is introduced via a small individual project before any lecture or discussion is attempted. When the project is submitted lecture/discussion is held using the project as a point of departure. Then the instructor assigns a larger group project which involves the same concepts. The individual project is graded and returned for corrections and for entry in a personal portfolio. The group project is then submitted, graded, discussed and returned for corrections and portfolio entry. Next, another individual project is assigned. Ideally, this second individual project extends understanding to more advanced concepts and the cycle continues. Much of the student's work is done out of class.

The scenario described depends heavily on the ready availability of projects or activities carefully chosen and developed to produce the desired investigations when students attempt them. At this writing, some two dozen activities constitute the activity packet that accompanies the booklet. It contains many activities drawn from liberal arts disciplines in which the students have majors, including psychology, sociology, medical fields and history as well as finance and consumer mathematics. Many of the activities were developed with the assistance of faculty or practitioners in corresponding disciplines, ensuring that students are exposed to realistic multidisciplinary thinking. This packet of activities, many of which are linked from the contents page of this web site, is now being revised. Once revised, it must be continually expanded and updated to retain the "up-to-the-minute" characteristic students find so appealing and to thwart "recycling" of project solutions and reports. This web site is a step in that direction.

Data from the first sixty-four College Mathematics sections taught since the inception of this program, of which thirty-six used the project/modeling approach, yielded the following:

• Median student success rate for traditionally-taught sections was 58%
• Median student success rate for the project/modeling sections was 75% .

(Here, student success rate for a section is defined by the number of passing students as a percent of initial enrollment in the section.) See Graph for a more recent descriptive summary.

Since we have still not solved the problem of students postponing matriculation in statistics, data on subsequent success is meager. The tracking of eighty students from traditional and project-based sections through the required statistics course reveals the following:

• Of twenty-one who succeeded in the traditionally-taught sections, sixteen (76%) succeeded the next semester in statistics.
• Of fifty-nine who succeeded in the project/modeling sections, forty-six (78%) succeeded the next semester in statistics.

If one can accept these percentages as indicative of long-term results, the projected median two-term success rates through statistics are as follows:

• For students initially entering a traditional section of College Mathematics the success rate is approximately forty-four percent.
• For students initially entering a project/modeling section of College Mathematics the rate is about fifty-eight percent.

1. Behar Gutierrez, R. & Ojeda Ramirez, M.M. (1997) A reformulation of the problem of statistical education: a learning perspective. ISI Newsletter, Vol. 21, No. 1(61), 18-19.

2. Peak, L. (1996), Pursuing Excellence - A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum and Achievement in International Context (USDE Publication No. NCES 97-198). Washington, D.C.: US Government Printing Office.

3. Moore, D. S. (1997). New pedagogy and new content: the case of statistics. International Statistical Review, 65(2), 123-137.

4. Ulmer, M. "Using Statistics and Data Analysis to Motivate Other Mathematical Topics@, Proceedings of the Fourth International Conference on Teaching Statistics, vol II, 1994

5. _"Capitalizing On Strengths in a Project Based Course for the Liberal Arts", Mathematics for Liberal Arts Students, (abstracts of Math Fest, '97), August, 1997

6. _"Regression as a Foundation for a Quantitative Elements Course for the Liberal Arts", Proceedings of the Fifth International Conference on Teaching Statistics, vol III, p.1263, 1994