Department of Mathematics
Knowledge and skill goals for this undergraduate degree program are recorded in the most recent CU-Boulder catalog.
In some summaries of assessment activity, goals are referred to by number (e.g., K-2 is knowledge goal 2).
In 1989-90 the department used test questions embedded in the mid-term and final exams of three upper-level courses to evaluate selected knowledge and skills goals. The test questions were developed by a committee of faculty members. They were graded for outcomes assessment by the members of the departmental Undergraduate Committee, independently of the course instructors. 57% of the answers to the assessment questions for MATH 2400 (Calculus 3) were scored in the "satisfactory" to "perfect" range, as were 78% of the answers in MATH 3130 (Linear Algebra) and more than 80% in MATH 4310 (Advanced Calculus). The department concluded that Calculus 3 instructors "...should be informed that setting up multiple integrals, including the preliminary sketching, needs to be worked on more."
In 1990-91, the department began using the Major Field Achievement Test (MFAT) in mathematics to assess all its goals. The MFAT is a nationally standardized test, based on the GRE, designed to assess knowledge and skills in the major. Students entering the major since 1991-92 are required to take the MFAT as seniors.
CU-Boulder students' overall MFAT performance has been consistently above the national average for institutions, varying between the 64th and the 99th percentiles, but has usually been close to the 80th percentile. Their rankings in calculus and algebra are similar to their overall ranking, but in applied mathematics it is a little bit lower. Although the fluctuations in the results from semester to semester make it exceedingly difficult to measure progress, in general the results are reassuring, but it should be noted that a great many of the institutions using the MFAT would not be considered to be our peer institutions, and so we would be disappointed if our students' performances were merely average.
CU's performances were best during semesters when very few students took the MFAT, and a small number of outstanding individual performances thus carried considerable weight. The number of students taking the test in the last couple of years (2000-2001 and 2001-2002) is much higher due in part to an increase in the number of mathematics majors. It also appears that in some past years some students found a way to avoid taking this test. Procedures have now been tightened so that all major requirements will be strictly enforced. After discovering instances of students taking the examination but not attempting to obtain the correct answers, the department has reinstated the rule that the students must pass the exam. This rule had previously been removed to alleviate students' anxiety. The passing score is to be determined by the department's Undergraduate Committee. With these changes it is expected that results will be more consistent from semester to semester and be more reliable asessment indicators.
The structure of the mathematics MFAT indicated that the exam's writers believed that mathematics majors should study more modern algebra than the CU-Boulder program required in 1990-91. Because this belief was also held by a majority of the mathematics faculty, MATH 3140 (Modern Algebra) is now on the list of required courses for one of the two tracks in the major. In addition, the calculus sequence has been redesigned, and some traditional calculus courses are offered in small sections.
Other changes made since the department began using the MFAT include strengthening the major requirements to make them comparable to those at universities to which the department would like to be compared, and offering an alternative major plan which has a more applied emphasis. New undergraduate courses that have been introduced include courses in Precalculus, Calculus with Computer Applications, Mathematics for the Environment, Topology, Operations Research, Fourier Analysis, Differential Geometry, Time Series, and Coding and Cryptography.
An exit survey begun in 1993 asked graduating seniors to rate the department's courses on a D to A scale, with C indicating "of average quality" and A indicating "outstanding". A little less than half of the seniors responded. In recent years the average ratings have been in the B range.
Last revision 07/19/02
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