David M. Bressoud October, 2005
Recommendation A2: Examine the effectiveness of college algebra.
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Mathematical sciences departments at institutions with a college algebra requirement should
Few courses are taught to as many students with such disappointing results as college algebra. It carries college credit, but at most colleges and universities it covers material that we hope students would have learned in high school. For most students who take it, it is the last mathematics course that they will see, and it seldom leaves them with an uplifted view of mathematics. For many students, it is the gateway to calculus and a myriad of scientific and technical majors. But this gate too often slams shut. The list of students who begin with college algebra and succeed through the calculus sequence is short, frequently no more than anecdotal.
And the enrollments are huge. If we define college algebra as widely as possible, encompassing everything from remedial algebra through pre-calculus, then 58% of the students taking mathematics at a 4-year institution and 75% of the students taking mathematics at a 2-year college are enrolled in college algebra, two million of the three million students who enrolled in post-secondary mathematics in the fall term of 2000.[1]
The purpose of this recommendation is to get mathematical science department to look long and hard at its college algebra: Who is taking it? Why are they taking it? Is it meeting their needs? What should these students be studying? How can we improve the course or courses that we offer them?
A good course presents material that is fresh and intellectually challenging without being overwhelming. This is particularly difficult with college algebra, which often looks like what they studied and did not understand in high school, now just flying by faster. It has been my experience that all students enjoy meeting a challenge that had, at first glance, seemed daunting. When a concept begins to recur in such contexts, it becomes part of the student’s working repertoire. But when too much is presented too fast, students fall back on memorization, hoping that they have captured enough to pass the test. Our task is to create a course for our students that will engage them and force them to use the concepts we consider to be important in a variety of combinations, to begin building linkages for themselves among the pieces of college algebra. It should not be surprising that one of the most successful approaches to college algebra is to embed it into a modeling course.
Because of the magnitude and complexity of the problem posed by college algebra, the CUPM subcommittee CRAFTY (Curriculum Renewal Across the First Two Years) is focusing on these courses. This past August, CRAFTY conducted a three-day workshop on ``Redesigned College Algebra'' for teams of faculty from 11 different colleges and universities. Each of these institutions has committed to offering at least four sections of a redesigned modeling-based college algebra course and at least four control sections. They will participate in a national study to determine the success of students in these courses and their performance in subsequent courses. In addition CRAFTY is preparing a set of guidelines for College Algebra. Watch their website, www.maa.org/cupm/crafty, for more information.
If your institution is ready to start looking at alternative materials and textbooks, you can find a wealth of information in the CUPM Illustrative Resources. There are links to conference proceedings that discuss a variety of approaches to improving college algebra. There is a link to the standards established by AMATYC (The American Mathematical Association of Two-Year Colleges). And there is a long list of books and curricular materials with links to more information.
Above all, whatever solution will work best for your students will need to
be tailored for them. Student goals, preparations, strengths, and weaknesses
vary too widely for one curriculum to meet the needs at every institution. Know
your students.
[1] Tables E.2 and TYR.4 in Statistical Abstract of Undergraduate
Programs in the Mathematical Sciences in the United States: Fall 2000 CBMS Survey,
David J. Lutzer, James W. Maxwell, Stephen B. Rodi, editors, American Mathematical
Society, Providence, RI, 2002
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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at bressoud@macalester.edu. |