Refocusing Introductory College Mathematics Courses

Vision: To provide every college student the opportunity to enroll in mathematics courses that promote mathematical and intellectual growth while supporting the mathematical needs of subsequent mathematics offerings, a wide variety of quantitative disciplines, and effective lifelong citizenship.

Problem statement: Each year, over 2 million college students enroll in mathematics courses such as college algebra and precalculus [1]. The majority of these and other similar courses (which fall under a wide variety of names) focus on developing algebraic skills to prepare students for calculus. This was an appropriate focus in the pre-technology 1960s, when these courses were developed. However, times have changed — and these courses have not kept pace with the corresponding developments in education. Enormous changes in the college student population, technology, the workplace, and society in general over the past several decades (see, e.g., [2], [3], [4], and [5]) imply an urgent need to reassess the purpose of these courses. For instance, societal changes — including the wealth of technical information recently available to the average citizen via the internet have made critical the need for every citizen to have a high level of competence when working with quantitative data [6]. Unfortunately, the level of quantitative literacy (QL) in college graduates continues to be dismally low. And, ironically, because introductory college mathematics courses at many institutions have remained unchanged, they no longer accomplish even their original goal: to motivate and prepare students to take subsequent mathematics courses. Therefore, the goals of introductory college mathematics courses need to be reassessed in light of the changing mathematical needs of students — including QL, the mathematical skills now required by other disciplines, and other contemporary needs of all citizens.

Why do so many students take introductory college mathematics courses? For many individual universities and statewide systems, a course in college algebra is a general education requirement. For many disciplines, particularly in the social and biological sciences, a course at the college algebra level is a program requirement — even though the particular algebraic skills usually taught in these courses often are not used in any subsequent courses in the discipline [5]. As such, the college algebra course becomes the terminal mathematical experience for many students. Moreover, even when mathematics arises in other disciplines, it does not look like the mathematics that students saw in introductory college mathematics courses — implying that most students do not make the connections that would allow them to apply the mathematics they may have learned. Thus, the standard introductory mathematics courses rarely provide any long-term benefits to the majority of students.

In addition, data are starting to emerge that indicate only a small minority of the students who complete these courses actually enroll in a calculus course. For instance, Dunbar [7] found, over a 12-year period, that only about 10% of the students taking college algebra at one large public institution ever enrolled in Calculus I. McGowen [8] indicates very comparable numbers at a large two-year institution. Herriott and Dunbar [9] report, based on a study at a variety of private and public universities, that only about 12% of the students enrolled in college algebra courses intend to major in a mathematically-intensive field. High DFW rates (often in excess of 50%), lack of relevant content, and instructor-centered pedagogy make traditional college algebra courses a barrier rather than a gateway. Moreover, anecdotal evidence abounds about the poor performance in calculus of students who complete college algebra courses — implying that these courses rarely serve as preparation for advanced mathematics courses. In addition, they do not adequately prepare students for study in other disciplines [5]. Finally, these courses do not provide a smooth transition for students coming to college with NCTM Standards-based K-12 experiences [4]. Therefore, the population for whom these courses are a productive learning experience is very small — perhaps even non-existent.

Since 1999, CRAFTY has sponsored (jointly with CAP, CTYC, CQL, and CSC) a series of con-tributed paper sessions on refocusing introductory college mathematics courses at the Joint Mathematics Meetings. It is clear from the large number of presentations that there is a growing realization within the mathematics community of the need for significant changes in these courses, and that the new versions of the courses offered are highly successful. However, many of the speakers have indicated frustration at being isolated within their departments, while many in the audiences have expressed even greater frustration at being prevented from offering refocused courses — by colleagues, by university-wide requirements, or by statewide mandates.

To address these issues, CRAFTY proposes the development and implementation of a new initiative for the purpose of improving introductory college mathematics courses. Specifics of this project are outlined below.

Objectives: The desired vision implies many changes in the administration of introductory college mathematics courses, leading to the following objectives:

1. refocus introductory college mathematics courses so that they are valuable both to those students who subsequently enroll in calculus and to those who choose other academic paths

2. provide alternative experiences in mathematics via courses that support a wide variety of mathematical needs

3. create introductory college mathematics courses that empower students to become confident and competent problem solvers, providing opportunities to develop the quantitative skills they will need in their academic work, in society, and in the workplace

4. promote alternative experiences in mathematics by supporting these courses as equally respectable with the traditional calculus-based mathematics sequence

5. promote best practices in teaching as part of all introductory college mathematics courses.

Project activities: A broad array of activities will be organized and implemented through a multi-year project to be led by CRAFTY and including leadership from other MAA committees, AMATYC, NCTM, and representatives from other disciplines. These activities include:

1. Conducting a comprehensive study to investigate the characteristics and subsequent enrollment patterns of students enrolled in introductory college mathematics courses. (leading group: CRAFTY)

2. Soliciting support for this project from other affected disciplines by building on the CRAFTY Curriculum Foundations project [5]. (leading group: CRAFTY and Subcommittee on Mathematics Across the Disciplines)

3. Promoting best practices in introductory college mathematics courses by identifying departments that have

   • implemented courses and programs in the spirit of the stated vision,

   • developed innovative placement systems and assessment practices, or

   • initiated novel partnerships with secondary schools, other colleges, or colleagues in partner disciplines. (leading group: CUPM)

4. Encouraging the mathematics community — via reports, publications, and presentations (both nationally and regionally)-to refocus introductory college mathematics courses to better serve all students. (leading groups: Subcommittee on Service Courses, Subcommittee on Two-Year Colleges, CRAFTY)>

5. Publishing reports and materials that support the development and implementation of refocused introductory college mathematics courses for use by individuals, departments, or institutions to influence administrators, university curriculum committees, and state-wide agencies. (leading group: CRAFTY, with support from MAA Executive Committee, AMATYC and NCTM)

6. Disseminating findings from the above work — including best practices in introductory college mathematics courses — via presentations at regional and national meetings, as well as publication of a volume in the MAA Notes series. (leading group: Subcommittee on Service Courses)

7. Developing a faculty development program that prepares faculty (particularly part-time instructors and graduate teaching assistants) to teach refocused introductory college mathematics courses. (leading group: MAA PREP project)

8. Contacting key individuals and groups at the state level to influence changes that support the stated vision and objectives for general education requirements (leading groups: MAA liaisons, regional MAA chapters, and CAP, with parallel efforts being undertaken at the school level by NCTM).

9. Encouraging the testing industry to revise placement and related high-stakes tests so that they support the stated vision and objectives. This will be accomplished by compiling assessment items that illustrate the stated objectives while supporting related activities at the secondary school level. These assessment items will then be discussed with testing agencies via connections within the mathematics community. (leading groups: CAP, NCTM)

Project implementation: Project activities will be further developed at a working meeting on October 24, 2003 at MAA Headquarters in Washington, DC. The working team assembled for this meeting includes representatives from relevant MAA committees (including the MAA executive committee), AMATYC, and NCTM. The goals for this meeting include

• identifying the specific roles and actions to be taken by MAA (and committee within MAA), AMATYC, and NCTM in this project, and

• developing a detailed outline for a grant proposal (including subcontracts to AMATYC and NCTM), to be submitted to NSF in December 2003.

Preliminary contact with the NSF-ROLE program (Research on Learning and Education) have been well-received, especially regarding activities that utilize student and course data to support a climate of change.

Conclusions: CRAFTY believes that there is an urgent need to refocus introductory college mathematics courses to provide better and more useful mathematical experiences for all students. These courses should address the quantitative needs of students in a wide variety of academic disciplines, as well as modern society and the workplace. Accomplishing the ambitious vision and related objectives outlined here will require considerable effort, both within the mathematics community and in cooperation with colleagues in other disciplines. CRAFTY and its partners are committed to making the stated vision a reality.

References

1. Lutzer, D., J. Maxwell, and S. Rodi (2002). Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States: Fall 2000 CBMS Survey. American Mathe-matical Society, Providence, RI.

2. Committee for the Undergraduate Program in Mathematics (2004, in press). Undergraduate Programs and Courses in the Mathematical Sciences: A CUPM curriculum guide, MAA Reports, Mathematical Association of America, Washington, DC.

3. AMATYC Crossroads document

4. National Council of Teachers of Mathematics (2000). Standards, Author, Reston, VA.

5. Ganter, S.L. and W. Barker (Eds., 2003). A Collective Vision: Voices of the partner disciplines, MAA Reports, Mathematical Association of America, Washington, DC.

6. Madison, B.L. and L.A. Steen (2003). Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, National Council on Education and the Disciplines, Princeton, NJ.

7. Dunbar, S. (2003). Enrollment Flows to and from Courses Below Calculus. In N. Baxter-Hastings, et al (Eds.), A Fresh Start for Collegiate Mathematics, MAA Notes series, Mathematical Association of America, Washington, DC.

8. McGowen, M. (2003). Who are the Students Who Take Precalculus? In N. Baxter-Hastings, et al (Eds.), A Fresh Start for Collegiate Mathematics, MAA Notes series, Mathematical Association of America, Washington, DC.

9. Herriot, S., and S. Dunbar