THE PRECALCULUS-CALCULUS SEQUENCE FOR THE PHYSICAL
SCIENCES AND ENGINEERING
The basic UW Precalculus-Calculus sequence consists of four courses:
Format of classes. In all four courses students attend three 50-minute lectures given by a professor and two 50-minute ``quiz sections'' directed by a graduate student Teaching Assistant (TA). During the quiz sections, students work on assigned problems, most of the time in small groups. The TA helps students with their work and tries to answer their questions as individually as possible.
Both the lecturer and the TAs hold office hours in their offices and often in the Math Study Center. The Math Study Center provides a comfortable place and a supportive atmosphere for students to come together and study, in groups or individually. The Math Study Center is open every day except Saturday.
Overall direction and goals. In their later work in the sciences and engineering, students need more than computational calculus techniques. They need problem-solving, thinking and reasoning skills. In particular, they need the ability to ``translate'' a verbally given problem into the language of mathematics, and vice versa. All courses of the sequence focus on developing such problem-solving and reasoning skills. Right from the beginning on, students are trained in word problems and other kinds of thinking problems. The majority of test questions are of that kind. At the same time, we expect students to develop their computational skills. Fluency in computational skills is a necessary, but by no means a sufficient condition for getting a passing grade.
Our view of calculus as a problem-solving and thinking tool has led us to change the way the courses are taught and organized:
The way these developments affect our courses is described in the course-by-course description below.
Workload. The emphasis on problem solving makes the UW
precalculus-calculus sequence more challenging than a traditional calculus
course. Most students initially have difficulty with the process of
translation from a verbal description of a multi-step problem into a
mathematical description. There is no quick way to master this
material. It requires lots of hard work, and students must practice with many
examples. Students should plan on spending about 15 hours per
week on homework and other practice problems.
Effect of changes on attrition. Despite the high expectations we now have of students, overall student performance has been encouraging. The rate of attrition and the proportion of poor grades (2.0 or below) did not increase when the course became more difficult. Moreover, graduates of the course who are now taking junior-level science and engineering courses have reported that they feel well-prepared. And professors in science and engineering departments have spoken highly of the changes in our calculus program.