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University Mathematics Program
Last updated 9/16/1998

Quantitative reasoning and mathematical skills (QRMS) competence can be demonstrated by passing a special exam given at the start of each semester or by passing an approved course. Only a few students take the exam; most acquire or improve these skills in courses. For example, students in majors that require three or more credits in Mathematics or Applied Mathematics meet QRMS requirements by fulfilling the standards of their majors and are assessed within their majors. Other students take one of several special courses designed to teach QRMS skills. The University Mathematics Program (UMAP) assessment focuses on these courses.

The UMAP Program offers the college's main quantitative reasoning and mathematical skills course (QRMS1010/MATH 1012) as well as mathematics courses (MATH 1000 through 1100) given in a self-paced module format.

Mathematics Module Program: Students in this program take various numbers of one-hour mathematics modules (e.g., college algebra, college trigonometry, etc.). The modules are mastery oriented, and students can make several attempts at different versions of each module's exams. In 1990-91 and 1991-92, students needed an average of 1.9 attempts to pass each exam, indicating that, in general, students were achieving minimum mastery levels without having to take exams an excessive number of times. In addition, students taking math module courses in 1991-92 and 1992-93 were surveyed to discover how the program could better provide services to them. In response to these statistics and other concerns regarding the number of attempts allowed, we will be reducing the number of repeated attempts at exams in Fall 1998 semester.

Students from every department in the college take math module courses, each for his or her own reason. Further, students in any given module course can have widely varied backgrounds and preparations. The program's faculty advisory board planned to develop ways to group students coherently so that tailored sets of assessments can be used. As a first attempt, in Fall 1994 and Spring 1995, the program offered three sections of traditional nonmodular college algebra, specifically designed for students who have dropped math module courses several times in the past because they were unable to manage the self-paced module format. About half of the 66 students in these sections had previously withdrawn from or failed self-paced math modules. Only 4 dropped the instructor-paced course, and the average grade for those who had previously been unsuccessful in self-paced modules was C+ in this course. Beginning in fall 1997, UMAP will again be offering this kind of traditional College Algebra course to meet the needs of those students who find the module method unworkable.

Further attempts at reintroducing the traditional course structure have been unsuccessful. This is undoubtedly due primarily to the lack of resources that the program has to implement such a program without jeopardizing the current one. Pursuit of such resources will continue in hopes of achieving this goal.

Currently, the administration of this program is trying to provide students with additional learning resources via the world wide web. We hope that response to this addition will be positive and will continue development in this direction as much as possible.

Since fall 1996, the Math Module Testing Center has been offering two Math Placement Examinations on a walk-in basis. The first determines readiness for entry level mathematics courses and the second is tailored to the first five Math Modules (college algebra and college trigonometry). In both cases, the scores of the students who take the exam are compared with their final exam scores in the corresponding Modules. Analysis of placement scores versus completion rates will be used to advise students in future semesters. Two additional placement examinations, Finite Mathematics and Business Calculus, are planned to be offered in the same manner to assist in assessing student performance in the six Business Mathematics Modules as well.

QRMS 1010: In 1990-91 and 1991-92, pre- and post-testing assessment was used in QRMS 1010. At the start of the term, a pre-test of QRMS skills was given. The same questions were embedded in the final exam to serve as a post-test. The questions were written by teams of faculty members. Pre-test and post-test scores of students who completed the course and took both exams were compared. In 1990-91, the minimum pre-test score was 3 of 25 questions answered correctly, and the average score was 16.3 correct answers. The minimum on the post-test was 11 correct answers, with a mean of 19.1, showing that the students' skills had improved. 1991-92 results were similar.

The UMAP Program suspended assessment of QRMS 1010 in 1992-93 and 1993-94 because of ongoing administrative and curricular restructuring of the course. The large lecture/lab format was dropped and replaced with one involving multiple small sections.

Specific goal statements were developed for the revised course. These are:

  1. Development of basic mathematical skills including facility with arithmetic, with algebraic equations (principally linear, exponential, and logarithmic) and their graphs, and in introductory topics from probability and statistics.
  2. Integration of these mathematical skills into students' reasoning about topics of interest from their own fields of study.
  3. Alleviating students' antipathy to, and even fear of, the discipline and its methods.
  4. The development of graduate student teaching skills with regard to grading and assessment, classroom presentation, course content, and ethics.
 

Several assessment methods were piloted in 1994-95. The plan calls for assessing the skills mentioned in the first goal by including specially-written questions in the final exams of the various sections of QRMS1010. Exams and exercises were constructed cooperatively by all the instructors to keep evaluation fairly consistent across course sections that varied in their extra-mathematical content. In 1994-95, across sections, 95% of the students who enrolled completed the course, 55-60% with grades of B or better. In 1995-96 across sections, 93% of the students who enrolled completed the course, 54% with grades of B or better.

In assignments related to the second goal, students are asked to write papers devising questions from their own fields of study calling for quantitative analysis with the mathematical skills they have learned. A sample of these papers was evaluated by all QRMS instructors. Each instructor independently rated each paper in the sample, and their ratings were quite consistent with each other. Some students were very creative in thinking quantitatively within their own areas of interest; others were much less so. There did not seem to be any relationship between the students' mathematical skill levels (goal 1) and their creative application of their skills to their own fields of study. In 1995-96 sample papers were again independently rated by instructors. Surprising regularity was demonstrated this year as well.

As a first attempt to evaluate progress toward the third goal, alleviating math anxiety, students in one fall 1994 QRMS 1010 section made pre- and post-course self-evaluations. At the start of each term in the past, QRMS 1010 students have been asked to comment on their own attitudes toward mathematics in general and this course in particular. In the selected section, a similar self-evaluation was made at the end of the term. Students' responses were categorized as negative, neutral, or positive. There were far fewer negative responses at the end of the term (2, vs 11 at the start) and far more positive ones (9 vs 1). This pilot comparison seemed promising. In 1995-96 pre- and post-course surveys were conducted in six of the nine sections. Three sections found the 1994-95 trend repeated: fewer negative responses (11, vs 40 at the start) and more positive ones (37, vs 18 at the start). Three other sections reported only changes in attitude: 34 students reported that their attitude improved, 17 that it remained the same, and 8 that it was worse as a result of taking the course. In future, an attempt will be made to extend the survey to all sections and to unify the style of reporting.

Achieving the fourth goal, increased graduate student teaching skills, has been complicated by the fact that graduate instructors are assigned to the program for only a short time. Because only three of nine instructors continue from the Fall through the Spring, teacher training tends to focus on familiarizing new instructors with the goals and methods of QRMS 1010. With a constantly changing staff, there is little or no time to develop finer points of teaching style with those who do continue. To provide more stability, the QRMS 1010 director has suggested hiring at least two instructors that are not graduate students and requested that graduate student instructors be assigned to teach the class for two full years before rotating to other assignments.

QRMS 1010 assessment was suspended in 1996-97 because of administrative changes in the program, and will resume in 1997-98.

Due to further administrative changes occurring for 1997-1998, continuing the evaluative procedure outlined above proved difficult. Attempts to reinstate the meaningful methods used in previous semester are being made.

In addition, much time has been exhausted on attempting to develop new methods of effective material presentation. Since these methods are still in development, full assessment of their effectiveness is not possible. As one example, an instructor, who taught one section in both Fall 97 and Spring 98, began moving towards a strictly web-based course. The intent is to provide the same skills as traditionally covered in the course and to open the door to further pursuits in various areas of interest, thereby addressing all 4 goal statements above. Although full implementation of the web has not been achieved and thus assessment of this method not yet possible, initial reactions from both students and instructor seem positive. It is hoped that a sound assessment can be created and, assuming positive response, that other sections might also incorporate this format for a larger assessment pool.

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Last revision 07/12/02


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