Mathematics Discipline Assessment 2006-2007

Scope of assessment activities

___√__Course-embedded assessment

___√___ Pre- and post-testing

______ Outside the classroom

______ Across the discipline

Direct measures of student learning

___√__ Capstone experience

______ Portfolio assessment

___√__ Standardized tests

______ Performance on national licensure, certification or

preprofessional exams

______ Qualitative internal and external juried review of

of comprehensive senior projects

______ Externally reviewed exhibitions and performances in

the arts

______ External evaluation of performance during internships

Discussion and Description

Discipline goals, direct measures, and improved student learning

1. Mathematics discipline goals

· to help students develop competence in mathematical techniques and methods

· to sharpen students’ mathematical intuition and abstract reasoning as well as their reasoning from numerical data

· to encourage and stimulate the type of independent thinking required for research beyond the confines of the textbook

· to provide students with the basic knowledge and skills to make mathematical contributions to modern society

The curriculum prepares students to enter graduate school, pursue careers in applied mathematics, or teach mathematics

2. Math senior seminar

The senior seminar is the principal assessment vehicle in the mathematics discipline. The seminar has been assessed annually since the 2003-2004 academic year.

Each student majoring in mathematics works for two semesters under the guidance of a faculty advisor to produce a piece of individual research. Students are expected to

· extend a mathematical concept from a primary paper in the literature

· use multiple references to obtain an understanding of a mathematical concept

and

· strive for some degree of originality in their project.[1]

The research product is a ten-to-fifteen page paper and a forty minute public presentation.

The mathematics faculty works closely with each student during the run-up to the presentation. Student and advisor meet periodically. Prior to the presentation, the entire mathematics faculty reads near-final drafts of all of the papers, then meets as a body with each student to critique and encourage the work, and to offer suggestions for the presentation and/or paper.

Although the faculty advisor assigns the final grade, the entire mathematics faculty meets to discuss the presentations and to ensure consistency in grading. Students receive feedback through two vehicles: the advisor’s evaluation of the paper; and the assessment sheets filled out by audience members at the presentation, which provide opportunities for both numerical ratings and evaluative comments.[2]

The faculty meets at the end of the academic year to evaluate the most recent round of papers and presentations. This is the touchstone for improved student learning. The author of the 2006-2007 assessment report writes, “All students showed mathematical growth by the end of their senior seminar experience. Overall, the faculty feel that this was a very successful year of senior seminar.” The annual critical assessments of the senior seminar have led to the mechanisms that made possible the growth and success noted in the two quoted sentences, viz., the explicitly detailed guidelines and timeline, the close-mentoring by one faculty member and the wide-mentoring by all faculty. Two changes are planned immediately based on this ongoing assessment.

3. Course-embedded assessment

The 2006-2007 report gives examples of how three instructors of Calculus I used course-embedded assessment to improve student learning. One instructor used an assessment/feedback/reassessment model to improve student understanding of functional notation. A second required that students demonstrate proficiency in four areas before receiving any credit whatsoever for an exam. A third used a glossary quiz at the beginning and end of the semester to assist students in using mathematical nomenclature precisely.[3]

A fourth instructor of calculus sought to improve student learning in the subject by making the use of Mathematica, a powerful software tool in mathematics, more appealing.[4] Overall his assessment showed more frequent use of and a better attitude towards Mathematica, but the cognitive impact was not measured.

4. Putnam Mathematical Competition

The Putnam is a national exam. Two UMM students took the exam in 2006, having prepared for it by taking the Problem Solving Directed Study. They ranked 747^th and 1089^th out of 3640 participants.

5. Placement in Beginning Mathematics

The mathematics discipline makes recommendations on whether beginning students should enroll in basic algebra, precalculus, first- or second-semester calculus. The recommendation is based on student success with a placement exam administered during summer registration and on the students’ high school record in mathematics. In the fall of 2006 the discipline collected data correlating the recommendation, the course actually taken, and success in the course. It believes that any change would be premature based on this data set alone, and will continue to collect data annually. It is anticipated that the placement exam will be “revisited” in the near future.

6. Course Planning

During the 2007-2008 the mathematics faculty will discuss its freshmen and sophomore level courses with an eye to increasing their number and variety for both majors and non-majors.

General education categories spanned by the discipline

Mathematics courses all bear the M/SR, mathematics/symbolic reasoning, general education designator with the exception of a few courses bearing none (basic algebra, precalculus, directed study, history of mathematics).