A summary of a study of the perceptions of college mathematics instructors concerning the preparation of students taking their first college mathematics course. (QL Home Page)
To supplement data from tests about students' preparation for college mathematics, three mathematicians at Winthrop University conducted a survey of mathematics faculty in South Carolina to assess their judgments about factors that influence beginning students' success in college mathematics courses. The survey was carried out in 1997 among full-time faculty at all public four-year colleges in the state who currently teach students who are taking their first college mathematics course. For purpose of analysis, responses were divided into two groups: precalculus and calculus courses were counted in the "Calc" group, those in other beginning courses (e.g., statistics, finite mathematics) in the "Intro" group. All the students had met a South Carolina rule that requires three years of high school mathematics (algebra I, geometry, and algebra II) for admission to a public college or university.
When asked to "grade" the precollege preparation of students in their courses, 80% of those who taught calculus or precalculus gave their students' preparation a grade of fair or poor. For those teaching the Intro courses, nearly all rated the precollege preparation as fair or poor: in these courses only 2% of the instructors considered the preparation of their students to be good. Fewer than one in twenty reported seeing any signs of improvement in the secondary school preparation of beginning students during the last five years. In many cases, poor preparation yielded poor performance: in approximately half the calculus and precalculus courses, more than 40% of the students fail to complete the course successfully.
The preparation of Intro students was even worse than the Calc students. Seven out of ten faculty reported that half or more of the students in these courses are not proficient in computational arithmetic. For example, an instructor of an elementary statistics course reported that on an arithmetic quiz fewer than half the students could determine what half of 5/16 is, or what percentage 12 out of 50 represents.
Virtually all instructors in these courses permit students to use calculators, although 60% believe that calculator use in the schools was responsible for reduction in students' arithmetic skills. In contrast, 60% of the Calc instructors report that the use of graphing calculators in high school enhanced the performance of students in subsequent precalculus or calculus courses.
Only one-third of the instructors of Calc courses reported that the majority of their students had a positive attitude about learning mathematics. Virtually none of the Intro instructors reported a similar pattern: in these courses the majority of students have negative attitudes about learning mathematics. Among them are all those who are planning to be elementary school teachers.
In written comments, many faculty cited weak motivation, poor work habits, and lack of self-direction as being at least as important in student failure as weak preparation. Others cited the mindlessness of school mathematics. Although many students fail because they cannot calculate, even those who can calculate have no idea why they perform these calculations. "They mindlessly push symbols around on the page," reported one respondent. "Even students who have demonstrated proficiency on AP Calculus cannot write mathematical sentences expressing complete thoughts about mathematical concepts."