Quantitative Reasoning Requirement
Assessment Plan
Coordinator of QR Requirement for 2007-2008:
Dr. Joe Stickles, Associate Professor of Math
Quantitative Reasoning (QR) is a non-sequential requirement in the MPSL. All Millikin students are required to fulfill this by taking a designated QR course. A goal of this program is that through quality advising, students take a QR course that fits the needs of the student’s academic area.
Quantitative Reasoning Learning Outcome Goals
The learning outcome goals for students taking a course that fulfills the quantitative reasoning requirement are that students will be able to:
- use deductive reasoning in a formal, symbolic, axiomatic system, and
- apply the theorems of the system.
2007 Snapshot
Select courses in Mathematics, Philosophy, and Behavioral Sciences meet the QR requirement. The number and types of courses taught are detailed in Table 1. All of these courses were chosen because they fulfill the requirement of manipulation of symbols according to rigorous inference rules or algorithms.
2006-2007 Courses meeting the QR requirement:
Course |
Title |
MA 112 |
Mathematical Content for Elementary School Teachers |
MA 114 |
Functions |
MA 117 |
Finite Mathematics |
MA 120 |
Elementary Probability and Statistics |
MA 125 |
Mathematics and the World |
MA 140 |
Calculus |
MA 208 |
Discrete Mathematics |
PH 213 |
Critical Thinking: Logic |
PS201/SO201 |
Statistical Methods in the Behavioral Sciences |
IN 207 |
Honors Seminar in Mathematics |
Academic Programs QR Traditions:
The QR courses serve all programs of the university. Some programs have designated courses to meet the requirement. Majors in the Behavioral Sciences (Human Services, Sociology, Psychology) and Nursing meet the requirement with PS021/SO201. Majors in Philosophy meet the requirement with PH213. Tabor School of Business students meet the requirement with MA120.
The Learning Story
Most of Millikin’s programs of study have particular QR needs. The QR course provides the kinds of experiences in symbolic, deductive reasoning required for professional success in these areas. Examples of QR topics in action include statistics in nursing, business and the behavioral sciences, calculus in the natural and physical sciences, and logic in the humanities. In addition, students of the arts gain experiences in symbolic, deductive reasoning that will enhance their ability to grow as educated democratic citizens (e.g., financial mathematics, voting models, and resource analysis).
The particular nature of the experience varies from student to student according to their educational, professional, and personal goals. Not every student needs to learn calculus or statistics or symbolic logic. Nevertheless, every Millikin student will have an experience that challenges him or her to apply rigorous deductive reasoning. The QR requirement provides this experience in the context of the student’s major field or in the context of the student’s participation in a democratic society.
The QR requirement is seen in action when a biology student successfully applies the integral and differential calculus in modeling the growth of a population of field mice, when a business student successfully argues for the marketability of a new product based upon a sound statistical analysis of a survey, when a pre-law student successfully answers a LSAT question involving syllogisms, or when a musical theatre major successfully obtains a loan for a new car after knowledgably negotiating rates and terms.
Assessment Methods
The QR goal is a meta-goal encompassing a wide variety of fields and techniques that falls under the broad heading of formal, symbolic axiomatic systems. Hence, the assessment method is equally wide and encompassing. The key to success is the content of the QR courses. Does the course provide the student with experiences in symbolic deductive reasoning?
Two Program Review Processes:
- Syllabi review. Usually, a quick examination of the syllabus is sufficient.
- Review what QR courses are being offered that academic year, which ones students are taking, and whether or not the courses they are taking are the best for their majors. These reviews will be used to help advisors understand the connections between QR courses and their areas.
One Assessment of Student Performance:
Samples of final exams will be evaluated, rating how well students demonstrate the ability to use deductive reasoning in a formal, symbolic, axiomatic system, and to apply the theorems of the system to solve appropriate problems.
2007 Report Assessment Data
The following data were collected by the QR task force.
1. The QR assessment team collected and reviewed the syllabi for all QR courses offered in Spring 2007. Final exams for some of these courses were collected, but not a large enough percentage were obtained to be used for assessment.
2. The QR assessment team collected data about QR course offerings and student enrollment trends (which courses are students taking from various disciplines) for the academic year 2006-2007.
3. The QR assessment team collected student data from nine quantitative reasoning courses offered in Spring 2007. Data from three courses, MA 120 02, MA 120 03, and MA 120 04, were not collected because Dr. Lee left the country for a conference before we could get data from her sections. We asked the instructors of these courses to identify one problem on their exam that could be used to assess the deductive reasoning learning goal and to identify one problem on their exam that could be used to assess the theorem application goal. The instructors then randomly selected five students’ final exams and assessed each student’s work according to the assessment rubric.
2007 Report Analysis of Assessment Results
1. The review of the syllabi for all QR courses revealed that all QR syllabi included topics that directly addressed the QR student learning outcomes. However, most syllabi did not explicitly state the QR learning outcomes. This is not surprising because the learning outcomes were not distributed to QR instructors before they prepared their syllabi.
2. The student enrollment data reveal the following.
- 77.4% of the students in MA112 were education majors. The course was specifically created for these majors.
- 64.3% of the students in MA114, MA140, and MA208, collectively, were science and mathematics majors. These courses are designed for these majors.
- 37.4% of the students in MA120 were business majors. This course is required of business majors. However, MA120 was also quite popular across the University.
- 37.7% of the students in MA125 were fine arts majors. This course also had wide appeal. The course was created to provide QR skills to non-science and non-business majors.
- 97.9% of nursing majors chose a statistics course. 60.8% of these chose SO/PS 201 over MA120.
- 53.7% of students majoring in areas that we’ve grouped under “Other” chose a statistics course.
Overall, it seems that students are taking the appropriate QR course.
3. The evaluation of random samples of completed final exams concluded the following status of student performance with respect to the QR student learning outcomes.
(1) use deductive reasoning in a formal, symbolic, axiomatic system.
Learning Goal (1) Rating
Comment: Nearly 90% of the assessed student completed finals were rated good or average by the instructors.
(2) apply the theorems of the system to solve appropriate problems.
Learning Goal (2) Rating
Comment: Seventy-one percent of the assessed student completed finals were rated good or average by the instructors. The majority were rated good. The number assessed as poor (29%) is greater that we would like. It would seem that we need to attend to theorem application a little more.
2007 Report Improvement Plans
We are pleased that the data indicate that the QR goals are being met. Nevertheless, we see room for improvement in several areas.
- QR instructors should be instructed to list the QR goals on their syllabi.
- The assessment team needs to inform QR instructors early in the semester the team will need copies of their final exams.
- The theorem application goal, while being met, seems to need more attention. Chairs should emphasize this to QR instructors.
- The next assessment report should include QR courses taught in the PACE program.
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