Annual Assessment Report for the

Mathematics Department

April, 2003

Introduction

As part of our continuing assessment program, the Mathematics Department performed an extensive transcript review of all mathematics majors who graduated between 1991 and 2002.  The goal of this review was two-fold:
There was a general feeling in the department that most majors were taking a minimal number of mathematics courses to complete the major, and that this was not the case in the past.  We wanted to confirm or discredit this intuition.
The department wanted detailed information on what courses students were taking.  We plan to examine and possibly revise the mathematics major in the next few years, and this information will help with that process.

Assessment Activities

The Mathematics Department obtained transcripts of all mathematics major who graduated between 1991 and 2003.  These years were chosen because they correspond to the department's growth in recent years, and the addition of most of the current faculty.  The transcripts were reviewed by the preparer, summarized in spreadsheets, and presented to the department for review.  After considerable time for review and individual reflection, the department met to discuss the information.  Conclusions were drawn by consensus, and future plans were discussed.

Assessment Results and Conclusions

The information on the transcripts is included in the table at this link.  The raw data was organized by catalog year and by graduation year.  We have not included this data due to privacy concerns for the students involved.  A few comments are in order.

The majority of the graduating class of 2003 will graduate under the 1999 catalog.  When they have graduated, the data for the 1999 catalog will be updated to reflect their course choices.
Math 450 is Independent Study, and some students took more than one independent study in their course of study.  Therefore, rather than compute the percentage of students that took an independent study, we computed the number of independent studies per student and multiplied by 100.
Dark horizontal lines indicate changes in the structure of the mathematics major.  A summary of the majors follows.

pre-1989:  36 credits above Calculus II including Differential Equations and Analysis I (Real Analysis)
1990-1993:  36 credits in mathematics, including Calculus I, Calculus II and Linear Algebra, one of Real Analysis or Abstract Algebra, and one sequence.  Sequences were Analysis I-II, Discrete Structures-Abstract Algebra, or Probability-Statistics. Remaining electives had to be numbered over 200.
1994-1997:  38 credits (2 cr. senior seminar) including Calculus I, Calculus II, Linear Algebra, Discrete Structures plus one from each group and both from one group.  The groups were Multivariate Calculus -Differential Equations, Abstract Algebra I-II, Analysis I-II, Probability - Statistics. Remaining electives had to be numbered over 200.  While this major was in place, Senior Seminar was reduced to 1 credit.
1998-present:   37 math credits including Calculus I, Calculus II, Linear Algebra, Discrete Structures, Real Analysis, Abstract Algebra, plus three electives numbered above 200.
 

The following conclusions were drawn from the data.

The number of mathematics majors taking the minimum number of courses is indeed increasing
The average number of mathematics courses taken by the mathematics majors is decreasing.
The average number of mathematics courses taken at Carthage by mathematics majors is decreasing.
Some courses (Math 112 and Math 306 in particular) show decreasing numbers of students.

Some explanations and conclusions were drawn from the data.

Students are receiving more AP credit for calculus.  This could by why fewer majors are taking Math 112 at Carthage.
In the 1990s, the number of mathematics-chemistry double majors was very high.  This could explain why fewer students are taking Math 306.  In addition, the structure of the major in the 1990s made Math 306 a more desirable option.  Now, more mathematics majors double major with computer science, making other courses more appropriate.
We can no longer assume that Math 112 is the first course that most mathematics majors will take at Carthage.  Math 113 and Math 121 should also be considered entryways into the program.

Use of Findings

The data collected and the findings summarized above will be extremely valuable as the department proceeds with plans to consider re-structuring the mathematics major, and in fact the entire curriculum.  We have already learned that the new major (if we indeed decide to revise) must have multiple entryways.  In addition, we must  be sure that a minimal major covers all topics we deem essential to a mathematics curriculum.  Even the best students are opting for fewer courses rather than more.  Rather than increasing the size of the major, initial discussions have moved us toward a re-structuring that includes essential topics in fewer courses, then options to explore more ideas in significant detail.

Overview of Assessment Activities and Findings

Various problems were encountered as we reviewed the transcripts.

We found that we needed to organize the data by catalog year rather than graduation year. 
Course numbers were a big problem.  Over the years, Abstract Algebra has been numbered 322, 321, 320, and 300.  Discrete Structures has been numbered 121, 210, and 321 (in conflict with Abstract Algebra).  There used to be a course called Discrete Mathematics that was taught at a lower level, but some majors still took it voluntarily early in their course of study.  This course was numbered 120, then 103.  Calculus II used to be numbered 201, and is now 113.  Linear Algebra used to be 302 and is now 200.  This made transcript evaluation somewhat challenging.

The Registrar's Office was very efficient and timely in providing transcript information, even though some of this information was difficult to obtain and distribute.  Some information was in the new system, some was in the old system, and some was distributed over multiple systems.

Next Year

In the future, we wish to engage in more activities that will help us as we examine and evaluate our current major.  We are particularly interested in the computer skills of our students, particularly spreadsheet use.  In addition, we need to assess the technical writing skills of our majors.  In the past, we have reviewed senior theses and journal articles.  Next year, we tentatively plan to assess writing through an activity administered as part of senior seminar.

Report Prepared By:  Mark Snavely
Date:  4/15/03
Academic Year:  2002-2003