MTH 110 History
Viewing the History of the University through MTH 110 (Algebra)
By Edward Aboufadel and Ted Sundstrom
Department of Mathematics, GVSU
As the University celebrates fifty years of educating students and shaping lives in west Michigan, this is an opportunity to view the history of the university through the development of curriculum. In particular, in this article we will discuss the history of an important mathematics course – MTH 110 (Algebra) – noting how its evolution matched that of the university. Currently, MTH 110 is a Basic Skills requirement for graduation, and although many students waive the requirement due to completing a higher-level course or having sufficiently high ACT scores, about half of the students enroll in MTH 110 while at Grand Valley. So it touches the education of a significant portion of students on campus. The course is also a pre-requisite for courses in departments such as Chemistry, Economics, Computer Science, Finance, Physics, and Statistics. The history of the course – how it has fit into the overall curriculum of the University and how faculty have modified their pedagogy and the use of technology – offers a unique opportunity to view the development of the University.
Grand Valley State College opened its doors to students in September 1963. During the 1963-64 academic year, only one mathematics course was taught, which was “Mathematics 1: Introduction to College Mathematics.” (This course has evolved into the current MTH 131 – Introduction to Mathematics, which is part of the Mathematical Sciences category in the General Education Program.) In fact, during that first academic year, only courses that were part of the so-called Foundation Program were taught. The Foundation Program was a set of nine courses that all students were required to take. The Foundation was considered by its designers as a centerpiece for a public, liberal arts college. Some of the other courses in the Foundation program were “English 1: The Art of Self Expression”, “History 1: History of Greece and Rome”, “Natural Science 1: The Foundations of Life”, and “Philosophy 1: Introduction to Moral Philosophy”.
Following is the course description of Mathematics 1 from the first Grand Valley catalog (1963-64):
Mathematics 1 – Introduction to College Mathematics. This course will review important steps in the history and development of mathematics, designed to familiarize all students with the logical bases of mathematics and to introduce some simple applications of mathematical concepts.
It was indicated in the catalog that “programmed course materials” would be made available for students needing a review of high school mathematics, but it is not clear if this really occurred. Marvin De Vries taught Mathematics 1 in 1963-64. He was one of the original fifteen faculty members at Grand Valley and he started his career at Grand Valley as an Assistant Professor of Mathematics and Economics. He was, however, an economist and so the original faculty did not have a mathematician. GVSC hired two mathematics faculty members for the 1964-65 academic year: Dan Clock and Don Vander Jagt, and the Fall 1964 enrollment count was 530 freshmen and sophomores.
During the first two academic years, Grand Valley did not have a course such as MTH 110 or even any precalculus courses (courses equivalent to the current MTH 122 – College Algebra and MTH 123 – Trigonometry). Any student was able to enroll in the first calculus course independent of her or his mathematical background. In an article he wrote for the Grand Valley Review (“Field for Dreams”), Prof. Donald Vander Jagt indicated that about half the students in calculus failed during the fall quarter in 1964, which led to the creation of a precalculus course, MTH 121 Algebra and Trigonometry, for the 1965-66 academic year. There was still no course such as MTH 110.
The establishment of MTH 110
MTH 110 was first offered in the fall of 1969, the same year that Arend D. Lubbers succeeded James H. Zumberge as President of GVSC. At that time, the course was numbered MTH 100, and it was “intended for students who sought admission to MTH 121 [Precalculus]” according to the course description. The course description did not specify the content of the course, but it was noted that admission to 100, 121, or MTH 201 (Calculus I) was granted “after consultation with a member of the mathematics faculty and is usually based on the student’s performance of a Qualifying Examination.” MTH 100 was basically a remedial course at that time, with students earning five credits in the quarter system that was used by GVSC. The course number was changed to MTH 110 for fall 1974, when MTH 109 (Elementary Algebra) was introduced. (MTH 109 is now MTH 097.) A new course description, with actual mathematics content, also debuted that semester:
Content is equivalent to most second-year high school algebra courses. Topics include the properties of real numbers, operations with polynomials and rational algebraic expressions, exponents, radicals, equations and inequalities of first and second degree, linear functions and graphs and systems of linear and second-degree equations.
As enrollments exploded at universities in the 1960’s and 70’s, schools turned to large lectures to deliver courses, and GVSC was not immune. During the first half of the 1970’s, MTH 110 was taught in a large lecture format and there were a few discussion sections. The evidence that we have indicates that there was just one large section of MTH 110 each semester, meeting in a large lecture hall such as in Lake Huron Hall. However, faculty questioned the wisdom of teaching in this way, and changes occurred at the beginning of the 1980’s. More on this later.
Ensuring Basic Skills in All of the Colleges
By September 1973, GVSC had become Grand Valley State Colleges, with the opening of College IV (later called Kirkhof College) that fall semester, and William James College two years before. There were now four “cluster colleges” (the other two being the original College of Arts and Sciences (CAS) and Thomas Jefferson College, established in 1968), and GVSC enrollment was almost 6000.
In the late 1970s, the administration directed each of the four cluster colleges to develop basic skills requirements that would ensure that their students “possessed basic skills.” In CAS, the largest of the four colleges, this was distinct from the mathematics requirement in what was known as the “Distribution Program.” There was, and continues to be, a mathematical or quantitative analysis requirement in the general education program that is distinct from the Basic Skills Mathematics requirement. Courses in that category typically have had MTH 110 as a pre-requisite.
CAS began requiring MTH 110 as a basic skills requirement in fall 1980. The writing skills requirement and the Supplemental Writing Skills (SWS) requirements were also implemented at that time. It is interesting to note that the Department of Mathematics and Computer Science in CAS did not support MTH 110 as a basic skills mathematics requirement, and the department was on record opposing requiring students to complete MTH 110. In an interview with Ted Sundstrom for the History of Mathematics web site, Bruce and Georgianna Klein indicated that Bruce was representing the department in the CAS Faculty Senate at that time, and that he was charged by the Department of Mathematics and Computer Science to argue against MTH 110 as being a basic skills requirement. However, the CAS faculty senate approved the basic skills requirement and MTH 110 has been a requirement since then.
As to the other colleges, Kirkhof College already had a set of Competency Requirements for graduation and had “Competency Readiness Courses” that were designed to prepare students for the competency tests. A basic skills mathematics course was also set up in that college. The course was “5915: Quantitative Applications”, which was described as follows: “An analysis of statistical and other quantitative concepts and methods used to interpret data.”
In William James College, the 1979-80 catalog simply stated the following: “Entering students must take a series of diagnostic tests in reading and quantitative skills. Remedial work may be recommended or required.” Specific courses were not mentioned. Students of Thomas Jefferson College could demonstrate their knowledge of basic skills through testing (as we now make available for all students), and otherwise were referred to the Development Skills Institute (DSI). The DSI was first mentioned in the two-year 1977-79 GVSU catalog, and one of its purposes was to enable students who did not meet the admission criteria of a degree-granting college to pursue a college education, by completing developmental courses in composition, reading, mathematics, science, academic skills, and other topics. MTH 110 was one of the courses in the DSI list.
January 1980 – December 1983: Dramatic Changes
The history of Grand Valley in the early 1980’s is full of incredible changes in the midst of a deep economic recession, and MTH 110’s evolution at that time reflected those changes. In the four year period, the four cluster colleges were merged, the College (singular) moved to a semester system, fall enrollments fell from 7142 in Fall 1979 to 6366 in Fall 1982 (and recovered by Fall 1984), the Fieldhouse dome collapsed and was demolished, and plans were made to establish a presence for GVSC in downtown Grand Rapids. A new Department of Mathematics and Computer Science came to be in the new Division of Science and Mathematics.
MTH 110 emerged by the end of 1983 as a four-credit course in the semester system, and students had a choice between MTH 110 and MTH 115 to satisfy the new Basic Skills mathematics requirement for graduation for all GVSC students. The course description was the same for MTH 110, while MTH 115 was a descendant of a course from Kirkhof College:
MTH 115 – Quantitative Applications: An introduction to various statistical and quantitative concepts and methods used to interpret data, solve problems, and make decisions. Practical examples using financial analysis and elementary statistics will be used. Many of the techniques may require the use of graphs, algebra, calculators, and computers. Not recommended for students who will take additional mathematics, computer science, physics, or chemistry courses.
Notable was the use of “calculators and computers” in this course, and it harkened back to Kirkhof College’s competency requirements from the previous decade. One of those, “Quantitative Applications”, was the following: “Demonstrate the ability to solve typical quantitative problems facing people in today’s world, demonstrate the ability to use a calculator, and demonstrate an understanding of the capacities and limitations of computers.” By the time College IV was renamed Kirkhof College in 1978, Kirkhof College began offering scheduled classes as well as continuing to offer self-paced, modular courses. Most of the self-paced modular courses in mathematics were designed and developed by Carl Arendsen, Phil Pratt, and Ted Sundstrom with assistance from two visiting faculty members: James Kaput and Leon Ablon. During the first few years of College IV, Carl Arendsen was the only mathematics faculty at the college. Phil Pratt, from CAS, provided some assistance, and both had student assistants to help them with the development of the modules for the mathematics courses. Interestingly, one of those assistants was Patricia Videtich, currently an Associate Professor of Geology at GVSU. Two of the traditionally scheduled mathematics courses at Kirkhof College were the first at Grand Valley in which a calculator was required. The use of graphing calculators in MTH 110 came later.
Also by 1983, placement procedures were updated so that all entering students were required to complete the Mathematics Qualifying Exam. As a result of the exam, students were advised whether or not to enroll in MTH 110, or one of the four other entry-level courses in mathematics, from pre-algebra to calculus. The following advice, which still makes sense today, was included in the catalog, “Students are advised to review their high school mathematics so their performance on the examination reflects their background accurately.” Pre-requisites were not enforced at that time, so placement results were advisory.
Also by 1983, MTH 110 was being taught in classes of pedagogically-sensible size, going from six sections in fall 1980 to 22 sections in fall 1985. In 1986 and a few years afterwards, along with sections of 30 students (recommended by mathematics professional societies), a large-section offering returned.
Finishing the Millennium: Growth, Technology, Pedagogy
The years from 1983 to 2000 were a period of astounding growth at Grand Valley. Fall enrollment in 1983 was 6710. In fall 2000, there were 18,279 students enrolled. GVSC became GVSU in 1987, the Eberhard Center opened in 1988, and new programs were established and grew. By fall 1995, the new Padnos science building was ready to go in Allendale, and the University was becoming known as one of the “most wired” campuses in the country. MTH 110 continued to be a Basic Skills requirement, but the course continued to evolve.
The most obvious change is that the number of sections continued to grow. This was due to a number of factors. The tripling of enrollment just described above was the biggest driver of growth. The mathematics proficiency profile of incoming classes wasn’t changing much, so a similar percentage of new students were being placed into MTH 110. In addition, MTH 115 was discontinued sometime in the early 1990s, due to poor enrollments, as it was not a pre-requisite for any other course, while MTH 110 became a pre-requisite for several courses, such as STA 215. This was a reflection of the increased importance of mathematics in a variety of disciplines – a good example being the rise of genomics in biology. The purpose of MTH 115 turned out to be the seeds of its destruction: “Not recommended for students who will take additional mathematics, computer science, physics, or chemistry courses.” By fall 2001, 69 sections of MTH 110 were offered!
(This was back when sections were identified with a single letter, a pair of letters, or a letter with a number. MTH 110 sections were labeled A to Z, followed by ZA to ZZ, then Z2, Z3, etc. The Department of Mathematics cleaned up the letter designations in 2002, and then the University switched to numerical designations in 2007 with the new Banner system.)
With thoughtful intention, mathematics faculty carefully but surely became a “wired” department. Graphing calculators, computer programs such as Maple, and other technological tools were infused into our courses, including MTH 110. Graphing calculators, such as those manufactured by Texas Instruments, became a required tool for MTH 110, and students became more adept in the numerical and graphical analysis of functions, along with symbolic algebraic manipulation. The curriculum for the course also featured a greater focus on applications and mathematical modeling. The course description was modified to reflect these changes.
Viewing the MTH 110 classroom from year to year during this time period, an observer would also see other important changes. Graphing calculators put more mathematical power in the hands of the students, and facilitated the movement to more student-centered classrooms that were called for in the late 1980’s by the National Council of Teachers of Mathematics. Faculty members were moving away from the “stand and deliver” approach to teaching mathematics, and towards an approach where students were more active in class, and more collaborative. While this approach was seen as benefiting all students, faculty such as Cathy Gardner recognized that this environment would be particularly welcoming for non-traditional students. As new classroom building were built or expanded (to match the tripling of enrollment), faculty called for tables and chairs, rather than tablet desks, in new classrooms, to make it easier for students to work together. In the 1998, 2002, and 2008 expansions of Mackinac Hall, most classrooms are set up in that way.
Mathematical placement methods evolved during this period, too, as it became unwieldy to administer Qualifying Exams to the growing wave of new students each summer. A statistical analysis was done by students working with Mary Ellen Barber, looking for correlations between Qualifying Exam scores, ACT scores, high school grades, high school mathematics courses, and other criteria. They determined that the number of high school mathematics courses and students’ ACT mathematics subscore were the best predictors of performance on the placement test. Consequently, a grid was created to determine if students should start in MTH 096, MTH 097, MTH 110, or to waive MTH 110 as a graduation requirement, based on these two factors.
Bringing this time period to a close, one final point needs to be made: in order to staff 69 sections of MTH 110, many adjuncts needed to be hired. The number of tenure-track faculty focusing on the course did not grow as the University did, and in fact, with the greater emphasis on scholarship by the faculty, and with the comparable growth in the number of sections for courses in the major, new faculty were being assigned to teach courses like calculus and beyond. This would be an issue for MTH 110 after 2000, along with the following “suggestion” from the 1999 NCA accreditation report: “The institution should seriously investigate how to link the multiple sets of data concerning students, particularly data concerning student learning, and do a more comprehensive analysis of this information, in order to improve the basis for conclusions in the assessment program and for making various academic and non-academic decisions.”
The Last Ten Years
In 2002, a new type of faculty began to appear on campus – the affiliate faculty member. This is a full-time position, with benefits, on a three-year renewable contract, and a terminal degree is not required, at least in the Department of Mathematics. Because we wanted a committed, continued faculty presence in MTH 110, some of our adjuncts were promoted to affiliate status that year, and because these were full-time positions, we needed fewer adjuncts going forward. Affiliate faculty now bring years of experience to this and other 100-level mathematics courses in our department, and they, along with our tenure-track faculty, establish an on-going commitment to the course.
Assessment has been eponymous on our campus the last ten years, as courses and programs are analyzed for evidence of student learning and accomplishment. Since the Department of Mathematics has seven courses in the General Education program, in 2007 an assessment was conducted for these courses as part of the new three-year cycle of General Education assessment. Curiously, MTH 110 is not part of the General Education program. Like Writing 150, it is in a different basket – Basic Skills – a basket that has become a bit of an orphan in faculty governance. Nevertheless, an assessment of MTH 110 was done by our department in 2007, and in our analysis, the course is meeting its goals and objectives.
In the 1990’s, a MTH 110 Coordinator position was established as a way to help manage the large number of sections we have been offering. The position has been critical in maintaining consistency among the instructors, and to facilitate communication between instructors. Recently, the MTH 110 Coordinators led an initiative to identify and articulate the student objectives and instructional practices in the course, many of which were referred to above. This initiative reflects a growing system on campus to clarify what is important and what we do.
MTH 110 instructors continue to adapt the changes in technology. In the past few years, we have begun to experiment with on-line homework systems and on-line “delivery of instruction”, although in a way that embraces the department’s mission, vision, and values (which were also written in the past ten years). This year, we are starting to face the question of smart phones and pads with graphing and algebraic “apps”, and we continue to discuss how the power of technology in our students’ hands actually gets in the way of learning at times.
The course description was last updated in the late 1990’s and it now reads as follows:
A symbolic, numeric, and graphic approach to intermediate algebra with an emphasis on applications. Topics include operations, equations, and inequalities of linear, exponential, logarithmic, quadratic, rational, and radical functions.
Today, the course is a pre-requisite for most courses in the Foundations: Mathematical Sciences category of the current General Education program. In addition, meetings with Unit Heads of several departments during the summer of 2008 indicated the continued need for algebraic thinking throughout the curriculum. This is emphasized by the following wording in the current catalog:
Grand Valley State University is concerned that all graduates have the skills for understanding numerical data and mathematical reasoning, for writing lucidly and expressively, and for reading critically and actively. To achieve these goals, the university requires specific competency levels in mathematics, writing, and reading as indicated by the completion of specific courses or by scores on placement tests.
GVSU continued to grow the past ten years, but not at the same incredible rates of the 1980’s and 1990’s. This has been due to a number of factors, both external and internal. Externally, the economy in Michigan has sputtered since 1999, as Michigan didn’t share in the 2002-07 national economic expansion. This has led to GVSU moving from a “state-sponsored” institution to a “state-assisted” institution, with a greater part of the budget coming from tuition. It is not the environment for robust growth. Internally, questions have been asked for quite a while as to whether we could continue to keep our student focus if we get too large. Consequently, in fall 2009, enrollment was 24,408, which is still over 30% larger than in 2000. However, this fall, there are only 40 sections of MTH 110. What happened?
The percentage of students needing to enroll in MTH 110 has been dropping, which reflects the rising profile of our incoming classes. In fall 1999, 27% of incoming students waived MTH 110 due to their ACT scores and number of mathematics courses in high school. For fall 2009, it was 47%. The percentage is expected to continue to grow over the next two years for two reasons. One is the stronger high school graduation requirements that were championed by Gov. Jennifer Granholm. Beginning in 2011, students must successfully complete four years of mathematics in high school in order to get a diploma, and that should lead to more students with higher ACT scores. The other is a change in math placement procedures implemented over the past two years, which puts GVSU in line with other universities as to the cut-off scores for waiving MTH 110, and also makes it more transparent to students how they can pass a proficiency test once they arrive on campus to waive the MTH 110 requirement. We anticipate that two-thirds of our incoming freshmen will waive the MTH 110 Basic Skills requirement by 2013, and is fair to say that we can now make it an expectation that incoming students to have already demonstrated proficiency in MTH 110 when they have arrived.
What can we expect in the future? There are on-going discussions in faculty governance to fold Basic Skills into the General Education program, and proposals are being considered to no longer require MTH 110 as a graduation requirement, but for it to remain an important pre-requisite for mathematics, statistics, and other courses. What is certain, though, is that MTH 110 will continue to evolve in focus, format, enrollment, and pedagogy, mirroring changes on the campus of Grand Valley State University that will occur during its second fifty years.