Office of the Provost and Vice President
for Academic Affairs
Department of Mathematical Sciences
Academic Year 2014-15 Assessment Report
MISSION STATEMENT
The Department of Mathematical Sciences at The University of Montana is dedicated to excellence in
teaching, research, and service in mathematics, statistics and mathematics education. Our mission is
threefold: to teach mathematics, to advance the mathematical sciences by research, and to serve the
university, state and nation by sharing our mathematical expertise through outreach, consultation and
collaboration.
In teaching, we seek to provide students with the training in mathematics, statistics, and mathematics
education necessary for success in their careers. The instructional mission of the department is to
provide: 1) a quality program of mathematical specialization at the undergraduate and graduate
levels leading to B.A., M.A., and Ph.D. degrees, 2) the mathematical background for students
preparing for careers in fields other than mathematics, and 3) quantitative literacy to undergraduates
in the framework of general education.
In research, we attempt to extend the frontiers of knowledge in mathematics, statistics, and
mathematics education by producing quality research with original results, by supervising students’
research at the graduate and undergraduate levels, and by conducting interdisciplinary research with
researchers in other fields. Our research mission complements our teaching mission.
The department is committed to service to our colleagues, the people of the state of Montana and our
nation. An important responsibility is to provide mathematical resources for researchers and graduate
students in other disciplines at the university. Other examples of service include outreach programs
for K-12 teachers and students, leadership and advice on K-12 and college mathematics education
issues, assistance in regional and state mathematics competitions, service on University committees,
involvement in national mathematical organizations, and editing and refereeing for professional
journals. In our public presence we hope to foster understanding of the power of mathematics and its
role as a fundamental mode of human thought.
The department’s mission is closely aligned with the mission of The University of Montana as given in
the University mission statements.
1
DEPARTMENT OBJECTIVES and ALIGNMENT WITH STRATEGIC ISSUES
1. Teaching
In teaching, we seek to provide students with the training in mathematics, statistics, and mathematics
education necessary for success in their careers. The instructional mission of the department is to
provide:
• A quality program of mathematical specialization at the undergraduate and graduate levels
leading to B.A., M.A., and Ph.D. degrees.
• The mathematical background for students preparing for careers in fields other than
mathematics.
• Quantitative literacy to undergraduates in the framework of general education.
(In support of Strategic Issues: 1. Partnering for Student Success; 2. Education for the Global
Century; 4. Dynamic Learning Environment; 5. The Planning-Assessment Continuum)
2. Research
In research, we attempt to extend the frontiers of knowledge in mathematics, statistics, and
mathematics education by producing quality research with original results, by supervising students’
research at the graduate and undergraduate levels, and by conducting interdisciplinary research with
researchers in other fields. Our research mission complements our teaching mission.
(In support of Strategic Issues: 1. Partnering for Student Success; 2. Education for the Global
Century; 3. Discovery and Creativity to Serve Montana and the World)
3. Service
The department is committed to service to our colleagues, the people of the state of Montana and our
nation. An important responsibility is to provide mathematical resources for researchers and graduate
students in other disciplines at the university. Other examples of service include outreach programs
for K-12 teachers and students, leadership and advice on K-12 and college mathematics education
issues, assistance in regional and state mathematics competitions, service on University committees,
involvement in national mathematical organizations, and editing and refereeing for professional
journals. In our public presence we hope to foster understanding of the power of mathematics and its
role as a fundamental mode of human thought.
(In support of Strategic Issues: 1. Partnering for Student Success; 2. Education for the Global
Century; 3. Discovery and Creativity to Serve Montana and the World)
2
STUDENT LEARNING GOALS AND MEASUREMENT TOOLS
The undergraduate mathematics major is intentionally very flexible, giving students the opportunity to
develop, in conjunction with their tenure-track advisor, a program of studies suitable for their particular
interests and goals. The department offers a significant number of capstone courses at the 400-level,
and each major must take at least three of them. The department’s assessment of the student learning
goals is based on an individual assessment of all math majors in these advanced courses.
Student Learning Goals
1. Calculus. Students will learn the
standard results of calculus, and will be
able to use them in a variety of
applications.
Measurement Tools
The student learning goals for math majors will be
assessed in each of the 400-level math courses aimed at
math majors, namely
M 412, 414, 429, 431, 432, 439, 440, 445, 472,
473, 485, and 491, and STAT 421, 422 and 452.
2. Proof and logical reasoning. Students Each math major takes a minimum of three of these
courses, and often more. Every faculty member teaching
will develop clear analytical thinking skills
one of these courses selects three of the four learning
as demonstrated by rigorous reasoning in
goals, and separately assesses the performance of each
mathematical arguments.
individual math major in the course with respect to the
selected learning goals on a scale from 0-10, using the
departmental assessment rubrics developed for each
learning goal (see appendices), and submits this
3. Writing and communication.
information to the departmental Undergraduate
Students will develop the ability to clearly
Committee. The latter compiles these individual
communicate mathematics in writing.
assessment reports in two ways: both by individual math
majors (using data from several years, where available)
and by the individual learning goals (for math majors who
graduated during a given academic year). Based on this,
4. Specialized knowledge at an
the Undergraduate Committee then assesses the student
advanced level. Students will learn the
learning goals, and determines, where applicable, which
standard results of one or more
corrective actions need to be taken to improve
specialized area of mathematics at a level
performance.
appropriate for advanced undergraduates.
3
RESULTS AND MODIFICATIONS
The following tables show the assessment results for the Student Learning Goals. Here “very good” corresponds to a score of at least
8.0, and “satisfactory” to a score between 6.0 and 7.9, on the 0-10 scale used in the rubrics (see the appendix).
LG 1: Calculus
Academic Year
Very Good
Satisfactory
Needs Improvement
2010-11
57%
43%
0%
2011-12
14%
64%
21%
2012-13
60%
33%
7%
2013-14
38%
52%
10%
LG 2: Proof
Academic Year
Very Good
Satisfactory
Needs Improvement
2010-11
35%
50%
15%
2011-12
13%
73%
13%
2012-13
40%
60%
0%
2013-14
54%
42%
4%
LG 3: Writing
Academic Year
Very Good
Satisfactory
Needs Improvement
2010-11
54%
42%
4%
2011-12
27%
60%
13%
2012-13
45%
50%
5%
2013-14
52%
44%
4%
LG 4: Specialized Knowledge
Academic Year
2010-11
Very Good
46%
Satisfactory
54%
Needs Improvement
0%
2011-12
20%
67%
13%
2012-13
30%
60%
10%
2013-14
41%
52%
7%
4
The data show some variation from year to year, which
is clearly to be expected given the relatively small
number of majors. It would be surprising if the
performance were more uniform than it is. In particular,
note that small differences in percentages do not seem
to be statistically significant.
Overall, the assessment shows a steady, good
performance over several years. In particular, for each
Student Learning Goal, the combined categories “Very
Good” and “Satisfactory” are usually in the 90% range,
while the “Needs Improvement” category usually hovers
around 10% or lower (which usually represents 0-2
students and never more than 4 students).
In light of the steady, good performance, at this point the
assessment outcomes do not mandate curricular
adjustments. The Department of Mathematical Sciences
is, however, constantly working to improve its programs,
and in the sequel we list some of the significant
curricular changes we implemented during the last few
years.
RESULTS AND MODIFICATIONS (continued)
Other Program Modifications:
1. Mathematics is mostly applied in other fields. Because of this, adding a minor or a second major
is particularly appropriate and useful for math majors. In light of this, our degree requirements
are already modified for students completing a minor or a second major. Over the last two
years, we revised the requirements for math majors to give further incentive to students to add a
minor or a second major (or else to study math in a bit more detail).
2. Some of our upper-division courses come with an optional computer lab. These are extremely
useful for our majors, since mathematics is nowadays mostly used via computer programs.
While not making these labs required, we changed our major requirements to give students an
incentive to take one or more of these computer labs.
3. We updated the Computer Science Requirement for math majors by adding a new course to the
list of courses students can use to satisfy this requirement.
4. Over the past two years, we collaborated with the Departments of Management Information
Systems and Computer Science to develop the new Big Data Analytics Certificate, which is
currently awaiting approval by the Board of Regents. Big Data program educational activities in
our department are aimed at preparing the qualified workforce for hi-tech industries both in the
State of Montana and in the USA. Our participation in the development and teaching of the
courses which count towards the certificate requirements aligns well with at least three Strategic
Goals of the University of Montana: Education for the Global Century; Discovery and Creativity
to Serve Montana and the World, and Dynamic Learning Environment.
5. Prof. Brian Steele together with other permanent and visiting faculty members developed three
new courses in support of the Big Data Analytics Certificate (M 461, 462 and 467).
6. The department’s Undergraduate Committee is currently deliberating curriculum changes to
make it easier for math majors to earn the Big Data Analytics Certificate (by modifying the
Science Requirement for math majors).
7. Prof. Mark Kayll developed and tested the new general education course “M 118 Math for Music
Enthusiasts”, aimed, to some extent, at music majors. This complements our general education
course “M 104 Numbers as News” for journalism majors.
8. Professor Dave Patterson and Associate Dean Jenny McNulty developed and offered the
Global Leadership Initiative (GLI) seminar M 191 “Fairness and Social Justice” this fall.
9. Several math faculty jointly offered the 2-credit special topics course “Coaching MathCounts” in
Fall 2012. This course was aimed at both elementary education majors and math-ed majors.
10. After careful deliberation, the department decided to convert the sequence of math courses for
elementary education majors from a 9-credit two-course sequence (M 135/136) to a sequence
of three 3-credit courses (M 132, 133, 243). It is expected that this will increase student
retention, provide for better preparation of future teachers of K-8 mathematics and allow for
greater compatibility within the MUS system.
11. Dual delivery courses, i.e., the courses which are taught simultaneously face-to-face in the
classroom as well as online, were developed and successfully offered (for example, one of our
modeling classes, M 445, is being taken every academic year by 10-15 students from University
College Cork in Ireland; a Math Ed class taught by Prof. Jim Hirstein was taken online by 13
students / middle school teaches located all over the State of Montana).
12. We combined the Applied Math and Statistics seminar to make it more vibrant and more
interesting for the graduate students working on the projects in these areas.
13. Although not a curricular issue, we need to mention that substantial improvements were made
to the room Math 306 (computer lab) that is now used to teach classes requiring substantial use
of technology (mathematical software, programming, computation, modeling, etc.).
5
APPENDICES
1. Mathematics Curriculum Map
2. Department of Mathematical Sciences Policy on the Assessment of Student Program Learning
Goals. (This document includes the rubrics for assessing the learning goals.)
FUTURE PLANS FOR CONTINUED ASSESSMENT
The plans for future continued assessment are outlined in the section “Student Learning Goals and
Measurement Tools”, and are detailed in the departmental policy in the appendix.
In addition, each academic year assessment issues will be discussed at several meetings of the
departmental Undergraduate Committee, and at a departmental Faculty Meeting.
6
UM Curriculum Map
B.A. in Mathematics Degree
11/24/2014
Required Core
Courses
M 171 or 181
M 172 or 182
M 210*
M 221
M 273*
M 307
6-7 Required
Electives, with 3
at the 400-level
M 301
M 311
M 326
M 361
M 362
M 381
STAT 341
M 412
M 414
M 429**
M 431
M 432
M 439
M 440
M 445
M 472
M 473
M 485
STAT 421
STAT 422
STAT 452***
KEY:
Outcome 1:
Calculus
Outcome 2:
Proof and
Logical
Reasoning
I
D
D
I
D
I
Outcome 1:
Calculus
Outcome 2:
Proof and
Logical
Reasoning
M
D
M
D
M, A
M, A
M, A
M, A
M
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
Outcome 4:
Outcome 3:
Specialized
Writing and
Knowledge at an
Communication
Advanced Level
I
I
I
I
I
D
Outcome 4:
Outcome 3:
Specialized
Writing and
Knowledge at an
Communication
Advanced Level
D
D
D
D
D
D
D
M
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M
M, A
M, A
M, A
M, A
M, A
D
D
D
D
D
D
D
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
M, A
* = not required for students in the Mathematics Education Option
** = Most majors take this course (default for Upper Division Writing Req.)
*** = not yet assessed; counts only beginning with the 2014-15 Catalog
I = Introduced
D = Developed/reinforced, with opportunities to practice
M = Mastery
A = Assessment evidence collected
NOTE:
I
I
Instructors of 400-level courses must only assess 3 of the 4 Outcomes;
the table reflects which Outcomes were assessed most recently.
Department of Mathematical Sciences
Policy on the Assessment of Student Program Learning Goals
Adopted March 3, 2009
Revised, February 1, 2010
The undergraduate mathematics major is intentionally very flexible, giving students the opportunity to
develop, in conjunction with their tenure-track advisor, a program of studies suitable for their particular
interests and goals. Because of this, common capstone courses and exit exams for all math majors
would be impractical and even counterproductive. The department offers, however, a significant
number of capstone courses at the 400-level, and each major must take at least three of them. In light
of this, the department’s assessment of the student learning goals is based on an individual assessment
of all math majors in these advanced courses.
This assessment strategy was developed during the academic year 2008/2009 and will be used starting
with the academic year 2009/2010.
Student Learning Goals:
1. Calculus. Students will learn the standard results of calculus, and will be able to use them in a
variety of applications.
2. Proof and logical reasoning. Students will develop clear analytical thinking skills as
demonstrated by rigorous reasoning in mathematical arguments.
3. Writing and communication. Students will develop the ability to clearly communicate
mathematics in writing.
4. Specialized knowledge at an advanced level. Students will learn the standard results of one or
more specialized area of mathematics at a level appropriate for advanced undergraduates.
Outline of the Assessment Procedure:
The student learning goals for math majors will be assessed in each of the 400-level math courses aimed
at math majors, namely:
M
412, 414, 429, 431, 432, 439, 440, 445, 472, 473, 485, STAT 421, 422
MATH 412, 414, 406, 421, 422, 431, 471, 475, 452, 451, 485, MATH 441, 442
In addition these learning goals will also be assessed in those special topics courses (M 491/MATH 495)
which count towards the “six course requirement” for math majors.
Each math major takes a minimum of three of these courses, and often more. Every faculty member
teaching one of these courses selects three of the four learning goals, and separately assesses the
performance of each individual math major in the course with respect to the selected learning goals on
a scale from 0-10, using the departmental assessment rubrics developed for each learning goal (see
below), and submits this information to the departmental Undergraduate Committee. The latter
compiles these individual assessment reports in two ways: both by individual math majors (using data
from several years, where available) and by the individual learning goals (only for the academic year for
1
which the individual assessment reports were written). Based on this, the Undergraduate Committee
then assesses the student learning goals, and determines, where applicable, which corrective actions
need to be taken to improve performance.
Assessment Procedure Used in the Individual 400-level Courses:
When an instructor of one of the 400-level mathematics and statistics courses assesses one of the
program student learning goals, he or she selects a representative sample of relevant assignments. The
performance of each math major in the course on each of these assignments is then assessed using the
rubrics below. At the end of the semester, the instructor submits a report to the departmental
Undergraduate Committee, listing, for each math major, his or her average performance on the selected
assignments for each of the assessed program student learning goals.
Assessment Rubric for Student Learning Goals 1, 2, and 4:
The performance of a student on an individual assignment will be assessed as follows:
10
8-9
6-7
4-5
0-3
Exemplary
Complete; minor details may be missing
Satisfactory, but with significant, albeit minor flaws
Major flaws, but significant progress towards the solution
Inadequate; no significant progress towards the solution
Assessment Rubric for Student Learning Goal 3 (Writing and Communication):
Depending on the nature of an individual writing assignment (e.g., proof writing, report writing, or
expository writing), the criteria used for assessment address some or all of the following areas:
•
•
•
•
•
•
Clear sequence of arguments
Clearly stated assumptions and conclusions
Complete and grammatically correct sentences
Conciseness
Correct use of mathematical notation
Reasoning
The performance of a student on an individual assignment will be assessed as follows:
10
8-9
6-7
4-5
0-3
Exemplary
Minor shortcomings in at most two areas
Satisfactory, but with significant shortcomings in one area
Acceptable, but with significant shortcomings in two areas
Inadequate
2