History of Mathematics at GVSU
Mathematics Major Since 1998


Phone: 616-331-2041
Ted Sundstrom
sundstrt@gvsu.edu

Department of Mathematics
Grand Valley State University
Allendale, MI 49401
The Mathematics Major Since 1998
The structure of the mathematics major has not changed since 1998. However, some changes have been made in the requirements for the major, including a significant change in the Secondary Certification Emphasis. Following are descriptions of the changes that have been made.
 
The Secondary Certification Emphasis
In 2001, a group of faculty members in the department, mostly mathematics education faculty, began exploring the possibility of adding a course in the curriculum specifically geared toward middle school mathematics pedagogy. The idea was to create a course that would complement MTH 229 – Mathematical Activities for Secondary Teachers. The need for such a course was in part prompted by the report Principles and Standards for School Mathematics (2000) from the National Council of Teachers of Mathematics (NCTM). The following is from page 213 of this report.
 
Special attention must be given to the preparation and ongoing professional support of teachers in the middle grades. Teachers need to develop a sound knowledge of mathematical ideas and excellent pedagogical practices and become aware of current research on students' mathematics learning. Professional development is especially important in the middle grades because so little attention has been given in most states and provinces to the special preparation that may be required for mathematics teachers at these grade levels. Many such teachers hold elementary school generalist certification, which typically involves little specific preparation in mathematics. Yet teachers in the middle grades need to know much more mathematics than is required in most elementary school teacher-certification programs. Some middle-grades mathematics teachers hold secondary school mathematics-specialist certification. But middle-grades teachers need to know much more about adolescent development, pedagogical alternatives, and interdisciplinary approaches to teaching than most secondary school teacher-certification programs require. In order to accomplish the ambitious goals for the middle grades that are presented here, special teacher-preparation programs must be developed.”
 
Other national organizations also supported specialized preparation of middle-school mathematics teachers suggesting that the mathematical preparation of middle grades teachers must include in-depth examinations of mathematical topics that provide a bridge between elementary and secondary mathematics. So in the fall of 2001, the following course was proposed.
 
MTH 329 Teaching Middle Grades Mathematics. Emphasis on what mathematics is, how students learn mathematics, planning and instruction, assessment, and professional decision making. Conceptual, constructivist, and cooperative activities assist middle grades teachers in helping their students learn mathematics connecting algebra, geometry, number, measurement, statistics, and probability. 20 hours of service-learning with middle grades students required. Prerequisites: C or better in MTH 202, MTH 210, and one of MTH 229, 321, 322, or 323. Junior standing. Three credits. Offered fall and winter semesters.
 
Although there was consensus about the need for such a course, the problem was deciding how to incorporate this course into the requirements for the Secondary Certification Emphasis. Faculty governance was (and always has been) very concerned about adding requirements to any program. The message from the university and faculty governance was that undergraduate programs should be four-year programs. To accomplish the goal of adding this course without increasing the number of credits, the department considered the following three options for the Secondary Certification Emphasis.
 
  1. Have MTH 329 replace the upper level elective.
  2. Have MTH 329 replace one of the two courses in the upper-level sequence and thus to not require a two-course upper level sequence.
  3. Have MTH 329 replace the cognate course selected from the list of courses from other disciplines.
 
Most members of the department wanted to retain the upper level elective and the upper level sequence for the Secondary Certification Emphasis, and so in the fall of 2001, the department submitted a new course proposal for MTH 329 and a Program Change Request in which MTH 329 would replace the cognate course selected from the list of courses from other disciplines.
 
One of the requirements for any program change request is to contact any department that might be affected by this change. The departments of physics and biology raised concerns to the University Curriculum Committee. They argued that having MTH 329 replace the cognate requirement would effectively add 4 credits to the degree requirements of mathematics majors who select either physics or biology as their teachable minor. Consequently, the University Curriculum Committee approved MTH 329 as a new course but only as an elective in the major. They did not approve the program change request.
 
The department now had the choice of leaving MTH 329 as an elective, having MTH 329 replace the upper-level elective, or having MTH 329 replace one of the two courses in the upper-level sequence and thus to not require a two-course upper level sequence in the Secondary Certification Emphasis. In the fall of 2002, the department decided to submit a new program change request using the option of having MTH 329 replace one of the two courses in the upper-level sequence. The following is taken from the Program Change Request submitted by the department:
 
The change to the major consists of replacing the choice of MTH 410, Modern Algebra II or MTH 431, Non-Euclidean Geometry, in the required courses category with MTH 329.
 
MTH 410 and MTH 431 are very worthwhile courses and will continue to be contained in a list of elective courses, one of which each student must select as an elective.   However, the student preparing to teach secondary mathematics will be better served by the direct relevance and necessary content knowledge of MTH 329. This does not increase the number of hours required for the major.
 
This proposal was approved and the new requirements for the Mathematics Major with Secondary Certification Emphasis became effective with the 2003 – 04 catalog. In addition to the core, the requirements for this emphasis were now as follows:
 
A minimum GPA of 2.8 is required in the major for recommendation for teacher certification. In addition to the core, students who are seeking a mathematics major with secondary certification must complete the following requirements:
 
a. Required Mathematics Courses
MTH 203       Calculus and Analytic Geometry III    4 credits
MTH 229       Math. Act. for Sec. Teachers             3 credits
MTH 329       Teaching Middle Grades Math.         3 credits
MTH 341       Euclidean Geometry                         3 credits
MTH 345       Discrete Mathematics                        3 credits
 
b. One additional course from the following list:
300, 304, 327, 360, 400, 402, 405, 408, 409, 410, 431, 441, 465, 495, 496
 
c. Cognate Requirement: STA 312 and one course from the following: PHY 230,CS 162,ECO 480, GEO 440,GEO 470,STA 314,STA 316,STA 412,SS 300,BIO 355,BIO 375, or CHM 351.
 
d. School of Education requirements for secondary certification must also be met.
 
Renaming the Courses in the Calculus Sequence
In 2003, the department renamed the courses in the calculus sequence from Calculus and Analytic Geometry to Calculus. The reason for this change was that from the course descriptions and course syllabi, it was clear that the three courses formed a sequence of calculus courses covering the basics of single variable and multivariable calculus with no significant amount of analytic geometry. It was felt that the titles of these three courses should reflect that fact.
 
Changes in the Cognate Requirements
 When the major was redesigned 1998, for the courses that could be used as an option in the cognate requirements, the department identified courses offered by other departments that had a significant mathematics prerequisite and that could potentially fit into a minor program. For the 2004 – 05 catalog, the department proposal to add more courses to the list of options for the cognate requirements was approved.
 
The following courses were added to the list.
 
  • CS 160 – Programming in Visual Basic
  • ECO 342 – Strategic Games
  • HSC 201 – The Scientific Revolution
  • EGR 304 – Creativity
  • PSY 300 – Research Methods in Psychology
  • STA 345 – Statistics in Sports
 
With the exception of CS 160 and PSY 300, the motivation for expanding the cognate list was not to add more courses that could be used in a minor program (as we did before) but to add courses that could be used within a theme for the general education program. The process used by the department was to develop a list of potential courses by examining the courses within each theme. Information was then requested from the departments offering these courses. Based on the expertise of the faculty in the department and the responses from the other departments, courses were chosen that involved a mathematical prerequisite or involved enough mathematics or mathematical reasoning to be appropriate for mathematics majors.
 
The rationale for adding PSY 300 was that this course was the Department of Psychology’s version of SS 300, which was already in the list of cognate courses for mathematics major. The department also felt that CS 160 would be just as appropriate as a cognate course as CS 162. CS 162 had become the first course in the computer science major and the department felt that it would not be appropriate as the only computer science course taken by a student who will not be a computer science major or minor. Since the Department of Mathematics has always included a computer science option in its list of cognates. (A computer science course is required for students not seeking certification), and  CS 160 – Programming with Visual Basic, was a course that dealt with the aspects of programming and computer science that are appropriate for mathematics majors,  it was felt that CS 160 would be an appropriate course to add to the list of possible cognates for the mathematics major.
 
The last course in the list (STA 345) would be added only to the major with a secondary certification or elementary certification emphasis. These courses would be added to the cognate lists in different ways for each emphasis as follows:  (additions are underlined)
 
Mathematics major for students not seeking teacher certification: STA 312; CS 160 or CS 162;  and one course from the following:  PHY 230,  ECO 342, ECO 480, GEO 440, GEO 470, STA 314, STA 316, STA 412, SS 300, PSY 300, BIO 355, BIO 375, CHM 351, HSC 201, or EGR 304.
 
Mathematics major with an elementary certification emphasis: STA 312 and one course from the following:  PHY 220, PHY 230,  CS 160, CS 162,  ECO 342, ECO 480, GEO 440, GEO 470, STA 314, STA 316, STA 345, STA 412, SS 300, PSY 300, BIO 355, BIO 375, CHM 351, HSC 201, or EGR 304.
 
Mathematics major with an secondary certification emphasis: STA 312 and one course from the following:  PHY 230, CS 160, CS 162,  ECO 342, ECO 480, GEO 440, GEO 470, STA 314, STA 316, STA 345, STA 412, SS 300, PSY 300, BIO 355, BIO 375, CHM 351, HSC 201, or EGR 304.
 
 
The Prerequisite for MTH 496 – Senior Thesis
When the department redesigned the mathematics major and introduced the two capstone courses in 1998, it was expected that most of the students would complete the capstone course MTH 495 – The Nature of Modern Mathematics rather than the capstone course MTH 496 – Senior Thesis. This has proved to be true, but by the fall of 2003, some faculty members were not sure that MTH 496 was an appropriate capstone course due to the focused, specialized nature of the course. This idea was discussed quite a bit during that semester. The department, however, decided to keep MTH 496 as an option for the capstone course, but this discussion led to another discussion dealing with the prerequisites for the capstone courses.
 
The prerequisite for MTH 495 was (and is): MTH 210, MTH 227, MTH 310, and at least three other 300–400 level mathematics courses.
 
In 2003, the prerequisite for MTH 496 was stated as follows: Open to senior mathematics majors in good standing.
 
One of the problems with the prerequisite for MTH 496 was that a student could be a senior as defined in the catalog without having completed many courses toward a mathematics major. So the department decided to make the prerequisites for MTH 496 similar to the prerequisites for MTH 495. In the end, the prerequisites were given in a somewhat complicated manner by giving different prerequisites for those using MTH 496 as their capstone and those using MTH 495 as their capstone. The approved prerequisites for MTH 496 are now stated as follows:
 
To use MTH 496 as the capstone course in the major: Completion of at least 27 credits of mathematics courses in the major, and a GPA in the major (as indicated by SIS) of 3.0 or better. Consent of instructor required.
 
For majors not using the course as the capstone course: MTH 495 with a grade of B. Consent of instructor required
 
 
The Elementary Certification Emphasis
In 1992, the department introduced three new courses specifically designed for the Mathematics Major with the Elementary Certification Emphasis. These courses were:
 
MTH 321 Number Systems and Structures.
MTH 322 Geometry for Elementary Teachers.
MTH 323 Statistics and Probability for Elementary Teachers.
 
These courses have remained a vital part of this emphasis since then. 
 
At the time these courses were introduced, the only mathematics course that all students, regardless of major, seeking elementary certification were required to complete was MTH 221 – Mathematics for Elementary Certification I. Consequently, the only prerequisite for MTH 321, MTH 322, and MTH 323 when they were introduced was MTH 221. This made these courses available to students other than mathematics majors.
 
Since 1996, all students seeking elementary certification have been required to take MTH 221 and MTH 222 – Mathematics for Elementary Certification II or they could complete MTH 223 – Mathematics for Elementary Teachers III, instead. The combination of MTH 221 and MTH 222 was seven credits. MTH 223 was a five-credit course covering the same topics as MTH 221 and MTH 222, but it was designed for students with a stronger mathematical background since its prerequisite was Calculus I.
 
Because of these changes in the requirements for elementary certification, it made sense to consider changing the prerequisites for MTH 321, MTH 322, and MTH 323. In the fall of 2003, the department proposed changing the prerequisites to MTH 223; or MTH 221 and MTH 222. In these courses, students were expected to participate in a supervised and structured tutoring experience in a local elementary school in which they assessed a child’s understanding of mathematical understanding and then planned appropriate tutoring activities. This would then make it possible for instructors in MTH 321, MTH 322, and MTH 323 to build on this experience and not have to repeat it in these three courses.
 
In addition, the faculty teaching MTH 321 also felt that students needed a stronger mathematical background than MTH 221 and MTH 222. After several years of experience with MTH 321, it was found that even though the prerequisite was only MTH 221, most of the students in the course were indeed mathematics majors or minors. In addition, those few students who came into MTH 321 with only a background of MTH 221 and MTH 222 were not prepared to study the mathematical content of these courses that the faculty wanted to include. One particular aspect of the course was that MTH 321 students studied functions in depth, in particular how a change in one variable affects another and how this change can be represented in different forms. The instructors felt that in order to do this, MTH 201 – Calculus I should also be a perquisite for MTH 321 since the concept of the derivative would help give students insight into understanding the behavior of a function and would provide a tool for analyzing and representing change.
 
For the 2004 – 05 catalog, the following prerequisites were approved.
 
Course
Prerequisites
MTH 321
MTH 201 and MTH 223; or MTH 201, MTH 221, and MTH 222
MTH 322
MTH 223; or MTH 221 and MTH 222
MTH 323
MTH 223; or MTH 221 and MTH 222
 
  Last Modified Date: December 6, 2007
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