Assessment of Student Learning


SPRING, 2000

Phase I.

Unit Mission/Goal(s)

Please state your unit’s mission/goal(s):

To advance the knowledge of mathematics and statistics: by teaching mathematics/statistics and their processes, by research in mathematics/statistics and mathematical/statistical pedagogy, and by dissemination of this knowledge to our students and the community we serve.

Please describe how your unit mission/goal(s) relate to the institutional mission

Historically, the study of mathematics is central to the liberal arts education. The mathematics/statistics curriculum serves as an integral part of students’ active pursuit of liberal arts education. The discipline’s mission concentrates on the three main components of the institutional mission, namely, teaching, research, and outreach. The mathematics/statistics curriculum is currently serving students who major/minor in mathematics, seek secondary mathematics teaching licensure, major/minor in disciplines which require a mathematical background, aim to complete pre-professional programs, and the whole campus through its general education courses in areas such as abstract systems. The mathematics discipline also guides students who choose to design their own major/minor which is in the direction of the institutional mission which says "...students can shape their own education." The discipline’s mission also involves dissemination of mathematical knowledge to the community which supports the institution’s mission "(UMM) is an educational resource and cultural center for citizens of west central Minnesota (and it has) strong sense of community."

Student Learning Objectives/Expected Outcomes

Learning Objective 1.

Students will gain the basic knowledge and skills to make mathematical contributions to modern society, whether in the form of pure mathematics or mathematics applied to the other disciplines.

Expected Outcome 1.

Demonstrated basic knowledge of calculus, analysis, algebra, probability, statistics, and ability to describe these areas of mathematics and see importance of this in their mathematics education. (A detailed learning objectives and expected outcomes for these topics will be prepared during the process.)

Learning Objective 2.

Students will sharpen their mathematical intuition and abstract reasoning as well as their reasoning from numerical data.

Expected Outcome 2.

• Demonstrated ability to model and solve real-world problems, formulate a problem mathematically, and determine an appropriate approach towards its solution.

• Demonstrated ability to write, read and construct proofs of key results in various courses taken.

Learning Objective 3.

Mathematics and statistics curriculum will enhance students’ critical thinking in domains involving judgments based on data and stimulate the type of independent thinking requiring research beyond the confines of the textbook.

Expected Outcome 3.

• Demonstrated ability on how to deal with theoretical and applied mathematical problems whose solutions do not fit exactly into any existing mathematical knowledge. For instance, the student should try to embellish it or solve some special cases.

• Demonstrated ability to interpret results of a mathematical/statistical analysis.

Learning Objective 4.

The curriculum will prepare students to enter graduate school, pursue careers in applied mathematics or statistical fields, or teach mathematics and statistics.

Expected Outcome 4.

Students should be able to document and prove their mathematics/statistics background to get a job or admission to graduate schools. Also, they should be able to meet the requirements for professions such as teaching and actuarial science.

Learning Objective 5.

The students will be able to see and communicate mathematical and statistical ideas effectively.

(The students will be able to see and communicate how the development of mathematics has been part of the development of several civilizations and is intimately interwoven with the cultural and scientific development of these societies.)

Expected Outcome 5.

Demonstrated ability to describe and explain a theorem, mathematical/statistical formula/model, and a solution of a problem in broad terms to a non-specialist audience.


Assessment Methods & Tools

Method(s), Measure(s), and Instrument(s) for Expected Outcome 1.

• Mathematics Major Student Portfolio(*)

• Mathematics Placement Exam

• Gateway (proficiency) tests on basic skills courses such as Pre-Calculus, Calculus, Linear Algebra, and Statistical Methods

• Some examinations in these courses will be designed to measure students’ pre-determined skills and/or knowledge. The mathematics faculty will jointly review a sample of these examinations annually and determine the degree to which these detailed objectives are met. These exams will be also a part of the "Mathematics Major Student Portfolio."

Outcome 1

Starting Date for the Implementation:

• Mathematics Major Student Portfolio:

Spring 1997

• Mathematics Placement Exam: In Progress

• Gateway Tests: Spring 1997

• Special Examinations: Spring 1997

Anticipated Date for the First Results:

• Mathematics Major Student portfolio: Spring 1998

• Mathematics Placement Exam:

Spring 1997

• Gateway tests: Spring 1998

• Special Examinations: Spring 1998

Method(s), Measure(s), and Instrument(s) for Expected Outcome 2.

• Survey of graduates

• Mathematics Major Student Portfolio (projects, papers, specially designed exams)

• Final Project (senior seminar presentation)

• Putnam performance

Outcome 2

Starting Date for the Implementation:

• Survey of Graduates: In Progress

• Putnam Performance: In Progress

Anticipated Date for the First Results:

• Survey of Graduates: In Progress

• Putnam Performance: In Progress

Method(s), Measure(s), and Instrument(s) for Expected Outcome 3.

• Mathematics Major Student Portfolio (course projects, MAP/UROP/Campus Compact reports)

• Specially designed exams

Outcome 3

Starting Date for the Implementation:

Spring 1997

Anticipated Date for the First Results: Spring 1998

Method(s), Measure(s), and Instrument(s) for Expected Outcome 4.

• Survey of Graduates

• Graduate school acceptance rates, GRE exam scores

• Success rate on professional exams

• Success rate on obtaining teaching licensure

Outcome 4

Starting Date for the Implementation:

Acceptance Rates: In Progress

Success Rates: In Progress

Anticipated Date for the First Results:

Acceptance Rates: In Progress

Success Rates: In Progress

Method(s), Measure(s), and Instrument(s) for Expected Outcome 5.

• Student papers from various courses

• Student presentations in some courses with attendance of faculty from and outside the mathematics discipline (including community representatives in some cases)

• Senior seminar

• Student publications, UROP and MAP reports

• An essay giving an example of a development of a mathematical/statistical idea and its impact on the cultural and scientific development of society

(Most of these materials will become a part of the student portfolio)

Outcome 5

Starting Date for the Implementation:

Spring 1997

Anticipated Date for the First Results: Spring 1998


(*) Mathematics Major Portfolio will have the following sections:

A. Characteristics of Entering Students

High school mathematics courses, mathematics placement score, ACT mathematics score

An essay written by students on their expectations and academic plans

B. Learning Development of Students in Mathematics During Their Stay at UMM

Gateway/proficiency tests from basic skills courses

Specially designed examinations from the core courses

Course project reports

An essay on development of mathematical ideas

A self-report of learning by students on each mathematics course that they have taken (which will include answers to questions like: What did you learn? Why do you think that this course is important in your mathematics education? How will you be able to use the knowledge that you have gained in this course after your graduation?)

C. After graduation

Survey of Graduates

After the review of the mathematics faculty, the results of the assessment and the portfolios prepared by the students will be delivered to the external consultants/reviewers for input. Mathematics discipline is planning to continue to have the ties with St. Olaf and Grinell College from which a group of faculty carried out disciplines 5-year review.

Phase II.

Use of Observed Outcomes and Possible Actions

Please comment on the possible use of the findings of your assessment plan.

(In responding to this question you may want to consider the following issues: How would the results of the assessment be communicated to faculty in you own and other disciplines? How could the results be used to improve the student learning and programs? How could the results produce input to other related processes (e.g., academic and nonacademic planning, curriculum review)? How could the results of the assessment change your unit’s mission/goal(s)? With which other units would you like to share the results of your assessment?)


Each math faculty member will examine the student portfolios and other relevant data and give comments to the Math Assessment Committee.

The Math Assessment Committee will assemble and distribute a report to the math discipline and to other departments by paper, e-mail, or web posting.

We propose to produce a report every two years.

This process will help identify areas that are successful and ones that need further work. These areas will be identified and communicated back to the math discipline for possible course or program changes.

The Implementation Needs

Please comment on the information and assistance necessary for the successful implementation of your assessment process.

(In responding to this question you may want to consider issues like; what are the other units (e.g., other disciplines, programs, administrators and/or committees that should produce input for the successful completion of your assessment cycle? what type of input do you need from other units? what should be the function of the Assessment of Student Learning Committee and Coordinator to increase the effectiveness of your unit’s assessment process? what type of support might your unit need for the planning and application of your assessment cycle?)


We need convenient access to GRE and other professional exam results of our students.

We need convenient reporting of the Career Center survey of past graduates.

We need convenient access to the graduating senior survey that will be conducted by the UMM Campus Assessment group.

We need convenient access to Mathematics Placement results given by the counseling and testing service to track our majors and others.

We need some sort of convenient mechanism for getting input from outside the math discipline. For example, a survey filled out by other disciplines regarding the math program.

We need institutional support for outside reviewers to evaluate our program on a periodic basis.

We need an e-mail list, and a paper list of all math majors so that we can communicate better.

Release time for a faculty member to coordinate senior seminars and portfolio collections.

Many of us believe that to properly assess the learning in the mathematics program, it is crucial to measure the extent of their mathematical preparation prior to joining us in classes. We need to know their prior preparation and knowledge of mathematics. We are currently lacking baseline measurements to compare with. A convenient system for obtaining this information is needed. Many of us believe a computer software testing system would be most helpful. We also point to page 9 of our assessment plan for other support services that are needed for our plan. These have not changed.

Phase III.

Application: Observed Outcomes

Please comment on your findings of the implementation of the assessment methods and tools.

In responding to this question you may want to summarize your findings, provide data that supports your interpretations, discuss the validity of your results, and suggest ways of improving the methods and tools that you have used.


Winter ‘98 was the first implementation of a pre- and post-test instrument in the Introduction to Statistics course. All indications are that this will be an effective means for assessment in that course. More precise quantitative and qualitative evidence will be available after the post-tests are collected and evaluated.

We have a long history of successful graduates in high school teaching, graduate school in mathematics, graduate school in statistics, and careers in industry and actuarial science.

Proficiency exams in the calculus courses have revealed a deficiency in skills necessary for successful completion of the calculus program. The system for administering these exams is currently being refined to improve uniformity across sections and quarters.

The results of Winter Quarter proficiency test data are given below. We note that the scores tend to increase/improve over time.

Trigonometry Test

(exam) Exam 1 Exam 2 Exam 3

(average) 6.78 8.81 8.58

Elementary Functions Test

(exam) Exam 1 Exam 2 Exam 3

(average) 8.85 11.00 12.54


Actions Taken

Please comment on the actions that you have taken or planning to take based on your findings.

In responding to this question you may want to consider the following issues: What other units were involved with the actions that you have taken? What was the impact of the actions that you have taken on the students’ learning? What other structures do you propose to increase the success of you actions?


Only action taken was to revise the scheduling and implementation of proficiency exams in the calculus courses.

Several of us encouraged Math majors (two years ago) to start preparing portfolios of their work. This effort was not successful due to the difficulty maintaining contact with majors, and with there being very little incentive for students to undertake the portfolio creation process.

The discipline needs to establish a periodic and regular informing mechanism for majors. This process will involve messages from student advisors and also announcements at the beginning of required and elective courses in the math major. This way even those students off student teaching or learning abroad will be informed of the portfolio system and requirements.


You may want to provide the following optional information that may be relevant to your unit’s assessment of student learning plan.

Number of degrees granted within the past 5 (or more) years.



Area of Concentration


Teacher Education


**Please contact Registrar’s Office for this data.**


Please list the graduates of your program who are (were) in the graduate programs and provide approximate acceptance rate for your graduates.

(Since last self-study report in 1995)

Brett MacAlpine (94) graduated, MS, University of Minnesota, Statistics

Michele Johnson (95) University of Minnesota, Statistics

Lee Ann Wirth (95) University of Iowa, Statistics

Matthew Diersen (??) North Carolina State, Mathematics

Michelle Mathiason (97) Oregon State University, Statistics

Ross Dierkhising (97) Iowa State University, Statistics

Lisa Hollerman (97) Iowa State University, Computer Science

Keith Vertanen (97) ??, Computer Science

Ben Winchester (97) University of Missouri, Sociology

Eric Nordberg (96) Texas A & M, Mathematics

Joanna Turner (96) University of Wisconsin, Statistics

Amy Hoffman (95) University of Georgia, Mathematics

Wen Hong Wong (98) University of Iowa, Statistics/Actuarial Science

Jessica Stoering (99) Purdue University, Mathematics

Brent Heeringa (99) U. Massuchusetts, Amherst, Computer Science

Nic Hopper (99) Carnegie Mellon University, Computer Science

Dan Wolters (99) University of Minnesota, Mechanical Engineering

Matthew Soukup (99) University of Virginia, Statistics.

Please list the post graduate activity of your students and provide approximate percentages for each group.

Math/Statistics Related Career (20%)

Andersen Consulting:

Jessica Rybaski (97)

Shanyn Bain (95)

Deanne Nordberg (99) Unisys

Actuarial Career:

Craig Schwaegerl (91-92)

Melissa Ahman (95) Alliance Life Insurance Company of America

Daniel Seyfield (96) Lutheran Brotherhood, Minneapolis

Brad Zarn (99) St. Paul Companies

Statistics Career:

Mayo Clinic/Allina Health System Ryan Bolduan (97 Emphasis Statistics)

Ross Dierkhising (97) Mayo Clinic

Jeff Thostenson (99) Mayo Clinic

Gina Garding (99) (Statistics Concentration) Mayo Clinic

Debra Kielhold (99) (Statistics Concentration) Mayo Clinic

Eric Bass (98) (Statistics Concentration) Mayo Clinic

Aaron Koelman (98) (Statistics emphasis) Augsburg Publishing/?


Math Teachers: (50%)

Jennifer Wirth (97)

Michelle Smith (97)

Joel Pautzke (97)

Michelle Bierbauer (98)

Paula Wiemer (99)

Julie Plahn (98)

Laurie Plahn (99)

Dave Berntson

Graduate School: (10%)

See above

Please list student publications in your program that took place within the past 5 (or more) years.

(Since self-study)

Lora Martin (98) "Classroom Scheduling Problem: A Discrete Optimization Approach"

Anderson, Kershner, Long, Garding (99) "Violence Against Women in

West-Central Minnesota. CURA Reporter, 29, 13-19.


Please list student projects in your program that have been implemented within the past 5 (or more) years, such as UROP, MAP, etc.

(Since self-study)

Lisa Martin (98) MAP with Peh Ng (96-97)

Lora Martin (98) UROP with Peh Ng (96-97)

Ross Dierkhising (97) MAP with Jon Anderson (95-96)

Ross Dierkhising (97) UROP with Jon Anderson (96-97)

Eric Bass (98) MAP with Jon Anderson (96-97)

Ryan Bolduan (97) UM Graduate School Grant with Jon Anderson (96-97)

Gina Garding (99) UM CURA Grant with Jon Anderson (97-98)

James R. Johnson (99) MAP with Peh Ng (98-99)

Helen Wollan (01) MAP with Peh Ng (99-00)

Please list student presentations/performances/artistic exhibitions in your program that took place within the past 5 (or more) years.

(Since self-study)

Lora Martin - Mathematical Association of America Conference, Atlanta, 97

Ryan Bolduan - SAS Users Group Conference, San Diego, 97

Dan Wolters & Matt Kelm - To present at the Minnesota Academy of Science meeting in May 98

Please list honors and awards that the students in your program earned within the past 5 (or more) years.


Craig Schwaegerl, 91-92 Kauffman-McCree Award

Lisa Hollerman, 96-97 Kauffman-McCree Award

Please comment on the success of your graduates on professional and graduate program exams.

Actuarial exams typically take our students two tries. This is a reasonable performance.

Graduate school exams must be going fairly well because our graduates who wish to go to grad school are not having any difficulty.

Our teaching licensure candidates also seem successful.


Please list participation of your students in special programs such as study abroad, internships etc.

Please present some case studies that present other learning outcomes not reflected elsewhere.

Jessica Rybaski (97) and Lisa Martin (98) worked on "Routing Problems for the Ottertail County Recycling Management" with Peh Ng (96-97).

Laura Eisenmenger was an MAI (Morris Administrative Intern) winter, spring quarters 1999. She organized local MAA meeting, and organized the local student chapter of the MAA.