# Calculus from 1965 to 1973

The available evidence indicates that few changes were made in the calculus sequence during this period. However, there were changes in the Foundation Program that affected the calculus sequence. In addition to the Foundation Program, all Grand Valley students also had to complete the so-called Distribution Requirements, which required all students to complete 10 credit hours of study in each of the two other divisions outside of the division in which they are completing their major. Although most faculty and administrators felt this was a good academic program, after two years, it became clear that students did not find it very appealing. The main reason for this was the rigidity of the nine-course Foundation Program and that these courses had to be completed in the first year.

So in the fall term of 1966, the faculty recommended a number of changes in the Foundation Program and Distribution Requirements that were approved by the Board of Control. These changes took effect for the 1967-68 academic year. One of the significant changes was that students were given a choice of courses to complete for the Foundation Program. Students were now required to complete nine courses (three from the Humanities Division, three from the Social Studies Division, and three from the Division of Science and Mathematics) in the Foundation Program during their freshman and sophomore years. Two of the courses listed in the choices for the Science and Mathematics Division were Introduction to College Mathematics (MTH 101) and Calculus and Analytic Geometry I. This is probably why the first course in the calculus sequence was renumbered to be MTH 105, and so the prerequisite course (Algebra and Trigonometry) was renumbered also. The only catalog in which the first course in the calculus sequence was not numbered MTH 201 was the 1967-1968-1969 catalog.

**100 Algebra and Trigonometry**

An intermediate course suitable for students who wish to prepare for further work in mathematics. Not a foundation course. Prerequisite: two years of mathematics in high school.

**105 Calculus and Analytic Geometry I**

Introduction to analytic geometry, functions, limits, derivatives, applications of the derivative, and integrals. Intended for students who have completed trigonometry. May be taken as a foundation course.

This numbering scheme was short-lived, and the numbers were changed back to their original numbers for the 1969-1970-1971 catalog. However, the College Algebra and Trigonometry course was renamed Precalculus Mathematics, and the three courses in the calculus sequence had minimal course descriptions.

**121 Precalculus Mathematics**

Elementary functions, analytic geometry, real numbers characterized as a complete ordered field. Not available for foundation credit. Prerequisite: Mathematics 100 or permission of department.

**201 Calculus I**

First course in calculus. Prerequisite: Mathematics 121 or permission of department.

**202 Calculus II**

Continuation of Mathematics 201. Prerequisite: Mathematics 201 or consent of instructor.

**203 Calculus III**

Continuation of Mathematics 202. Prerequisite: Mathematics 202 or consent of instructor.** **

**The Use of the Computer in Calculus in the Early 1970’s**

Although there were no changes to these course descriptions through the 1971-72 catalog, minutes from department meetings indicate that there were some interesting discussions about the calculus sequence in departmental meetings.

At the beginning of the 1970-71 academic year, there was considerable discussion regarding the use of a computer in the calculus sequence. One probable reason for this was that several faculty members were involved in developing computer science courses in the department. The first course in computer science was taught in 1967 (MTH 195 – Introduction to Computer Science) and by 1970, the department was also teaching a course in programming in FORTRAN (MTH 192 – Computer Programming). The discussion about using a computer in teaching calculus focused on textbook selection. The department considered using a computer-oriented text developed under a National Science Foundation grant to the Center for Research in College Instruction in Science and Mathematics (CRICISAM). (Florida State University, the University of Minnesota, and Vanderbilt University were using preliminary CRICISAM materials.) The choice for a calculus text was narrowed to Breusch and Ogilvy’s *Calculus* and the CRICISAM texts. Prof. Martin explained one advantage of the CRICISAM text was that it was an excellent text for developing mathematical theory. However, several members of the department expressed concern that students would find the texts difficult to read and to omit certain theoretical portions. In October of 1970, the decision was to use Breusch and Ogilvy’s *Calculus* to be supplemented with materials and problems for the use of the computer with calculus. A committee was formed to compile course materials and problems which could be used to integrate the computer with the calculus sequence. (Members of the committee were Profs. Wiltse (chair), Johnson, Martin, Stegink, and Walkoe and two students.) At that time, however, it was decided to have the work done in the calculus sequence with the computer be optional so the difficulties for re-entering or transfer students would not be compounded.

**Note**: An article describing some of the history of the CRICISAM calculus materials can be found in the March 1971 issue of the *American Mathematical Monthly*. (“Calculus and the Computer, the CRICISAM Calculus Project – Past, Present, and Portent.” *The American Mathematical Monthly*, 78.3 (1971): 284 – 291.)

In a December 1970 department meeting, the calculus committee indicated that it was planning to submit a proposal that the department use the CRICISAM materials as well as other sources and that students would be taught a very simplified version of FORTRAN IV during the first week of MTH 201. The committee was also compiling a department workbook with problems suitable for studying calculus using a computer. However, there did not seem to be enough interest in the department for this approach and this proposal was never formally submitted to the department. In a department meeting in March of 1971, there was some discussion about the progress of integrating the computer into calculus. It was reported that there had not been as much progress as hoped in integrating the computer into calculus. As a result, since computer work in calculus had been made optional, it was agreed that instructors for MTH 201 should work more closely with students to motivate and encourage them to take advantage of the opportunity to use the computer.

It thus seems that although faculty were interested in using the computer as a tool for students to help learn calculus, the resources at that time did not allow this to happen. According to department minutes, it also appears that in 1973, the department had discussions about the possible use of terminals in mathematics courses, and it was suggested that a short seminar of about 3 weeks to learn the computer language BASIC be required of all students in 201. It appears that this remained at the discussion stage and was never implemented. One of the primary concerns was about how long students would have to wait in order to gain access to a terminal.