Calculus from 1983 to 1988
One of the main issues confronting the department at this time concerned the use of hand-held calculators in the teaching and learning of calculus.
The mathematics faculty at Grand Valley were quite interested in the use of computers in the teaching of mathematics since 1970. However, the faculty determined that it was not feasible to use computers in the teaching of calculus due to the lack of availability of computers for students and due to the fact that students would have to learn some computer programming in order to use computers in calculus.
In the late 1970’s, hand-held scientific calculators became available and some faculty became interested in the use of these calculators in the teaching of precalculus and calculus since these were tools that students could carry around with them. Although the number of students completing calculus courses at Kirkhof College was quite small, students taking calculus at Kirkhof College were required to use scientific calculators beginning in 1981. Calculators were not required in calculus courses in the College of Arts and Sciences.
When the colleges at Grand Valley State College merged into one college in 1983, the calculus sequence for the College of Arts and Sciences was the one that continued. At that time, Kirkhof College was only offering Calculus I and its version of this course was essentially the same as that of the College of Arts and Sciences with the exception that students were required to use scientific calculators at Kirkhof College. Following are the course descriptions for the calculus sequence from the 1983 – 84 catalog.
MTH 201 Calculus and Analytic Geometry I. Analytic geometry. Differentiation and integration of functions of a single variable with applications. Prerequisite: 120. Five credits. Offered fall and winter semesters.
MTH 202 Calculus and Analytic Geometry II. Integration techniques, parametric equations polar coordinates, indeterminate forms, improper integrals and vector algebra. Prerequisite: 201. Four credits. Offered fall and winter semesters.
MTH 203 Calculus and Analytic Geometry III. Partial differentiation, multiple integration, sequel and series, convergence and remainder theorems, power series and Taylor series. Prerequisite: Four credits. Offered fall and winter semesters.
The course description for MTH 201 did not change until 1990 but the descriptions of MTH 202 and MTH 203 were modified slightly in 1989. This was done to make MTH 203 a self-contained multivariable calculus course. The descriptions of Calculus II and Calculus III in the 1989 – 90 catalog were:
MTH 202 Calculus and Analytic Geometry II. Integration techniques, parametric equations and polar coordinates, indeterminate forms, improper integrals, sequences and series. Prerequisite: 201. Four credits. Offered fall and winter semesters.
MTH 203 Calculus and Analytic Geometry III. Vector algebra in two and three dimensions, partial differentiation and multiple integration, vector calculus. Prerequisite: 202. Four credits. Offered fall and winter semesters.
Even though the course descriptions did not change much, many faculty were still experimenting with ways to use scientific calculators or microcomputers in the teaching of calculus. In the latter half of the 1980’s, packaged programs started to become available that allowed students to explore concepts of calculus both graphically and numerically. This made it unnecessary for students to learn computer programming in order to use computers to explore concepts of calculus. One such program that was used at Grand Valley was MicroCalc, which was written by Dr. Harley Flanders of the University of Michigan.
Faculty still faced several problems in using such computer programs in calculus. The main problem was that any work with these programs had to be done outside of the classroom. There were microcomputer labs available on campus but it was not really possible to schedule classes in these labs. Even though these types of computer programs were now available, many faculty members required students to use scientific calculators in calculus simply because students could take them anywhere, including the classroom.
The main drawbacks to scientific calculators were that they had no graphics capabilities and were not programmable, which made it difficult to explore concepts of calculus numerically. However, in the mid to late 1980’s a new technological tool was introduced – the graphing calculator. A graphing calculator is a calculator that is capable of plotting graphs of functions on a large screen, finding approximate solutions for equations and systems of equations, and performing numerous other tasks with functions and variables. These were typically many of the capabilities of the computer graphics programs but with a graphing calculator, students could have access to these tools wherever they studied calculus. The main drawback was the additional cost to students, which was typically near $100.
Despite the added cost to students, faculty members were intrigued by graphing calculators and began to explore how to use them in the teaching of calculus. This became one of the main issues for faculty teaching calculus at Grand Valley in the next several years.