A Modeling-based Approach to College Algebra

Abstract Virginia Commonwealth University (VCU) is engaged in reforming college algebra, a course that is a gateway to the college experience for many students. The details of a modeling-based approach to college algebra are outlined in this article. An assessment of factors related to the attitude toward mathematics comparing students in this modeling-based approach with students in a traditional course was conducted. The results of the assessment, withdrawal rates of the courses, and student comments from focus groups are discussed. Introduction College algebra is a gateway course to the college experience for many students. Consequently, successfully completing the course is an important first step to obtaining a college degree. In most colleges and universities the curriculum was designed over fifty years ago and focuses on preparing students for calculus--a course which fewer than 10% of college algebra students will take (Small, 2002). This and other factors including that students have seen this material in high school and a low passing rate have a negative impact on the attitudes of students in college algebra. The attitudes developed in the course have an influence on student willingness to take other mathematics courses and on their opinion of mathematics after finishing college. The Committee on the Undergraduate Program in Mathematics (CUPM) is a group within the Mathematical Association of America who issue guidelines every decade for developing the ideal curriculum for undergraduate mathematics courses. In their most recent publication, CUPM (2004) advocates major changes to college algebra. In particular, the course should focus on content that is applicable to other academic disciplines, provide detailed study of a small number of topics, and help students develop the ability to communicate numerical ideas orally and in writing. In a series of discussions at the Algebra Initiative Colloquium (Lacampagne, 1995), mathematicians and educators reviewed all aspects of the algebra curriculum. One recommendation that emerged was that in order to prepare students for the ever-changing needs of business and industry, the curriculum "should be grounded in problem solving that reflects real-world situations and offers a variety of methods of solution" (p. 12). A college algebra course designed with these recommendations in mind has a focus on mathematical modeling. The intent is that students who complete such a course will be able to use mathematical modeling coupled with algebra skills to analyze various problems and recognize the usefulness of applying the process to real-world situations. Along the way, the educational experiences in which the students are engaged will have a significant influence on their attitudes toward mathematics. In two studies (Fox & West, 2001; Oty et. al, 2000) researchers looked at student attitudes after completing modeling-based college algebra courses. One study emphasized application problems and group projects (Fox & West, 2001). Most students wrote positive comments about their experiences in their project summaries. The negative comments reflected students' frustration with the challenge they faced through the project experiences to become critical thinkers of mathematics. The authors felt that all comments revealed that the assignments satisfied their purpose of preparing students to work with real-world problems and most of the students were positive about the experience. In a similar course featuring science-based applications, students completed a Leikert scale survey about their attitudes at the end of the course (Oty et. al, 2000). With respect to mathematics, 80% of the students in the modeling-based course expressed that their attitude had improved during the class while 55% of students in a traditional college algebra course had a similar change in attitude. Based on these studies, it appears that modeling-based college algebra experiences are a positive influence on students' attitudes. …