Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
Primary Contact Name/Info:
Dr. Kathy M. C. Ivey, Head
Belk 391 (Stilwell 426A beginning Fall 2006)
227-3831
kivey@email.wcu.edu
Department Mission Statement
The Department of Mathematics and Computer Science serves as a community of scholars
involving students and faculty in a broad range of intellectual and aesthetic activities. Its
undergraduate programs include the B.S. in mathematics and the B.S. Ed. in mathematics education.
Related graduate degrees include the M.A.T. and M.A. Ed. in mathematics education and the M.S. in
Applied Mathematics. We also offer a “4+1” program in Applied Mathematics for students to
complete a B.S. and an M.S. in five years.
The most significant of the department’s activities are the teaching and learning processes that take
place between students and faculty in classrooms and field locations (e.g., student teaching). The
department provides curricula for majors in mathematics and mathematics education. To prepare
university students for participation in society, the department also offers courses that provide basic
intellectual skills and essential perspectives for all university students. In addition, the department
offers specialized courses that serve other undergraduate and graduate degree programs of the
university.
Scholarly productivity through a variety of discipline-related activities is essential to the vitality of the
department. For this purpose, the faculty engage in research, creative activities, and publication.
Students are directly involved in many of these scholarly activities.
The department also engages in numerous service activities internal and external to the university.
These include faculty participation in university governance, student advisement, sponsorship of
student activities, leadership in professional organizations, and a variety of intellectual and problem
solving services to others.
Statement on Alignment of Program Mission with University and College Mission
The most significant departmental activities are the teaching and learning processes that occur in the
classroom, labs, and field locations. The departmental mission statement also describes activities
which complement the teaching mission, including scholarly creativity and service activities. Taken
as a whole, the goals and objectives of the department are designed to produce educated citizens
who have the potential to become responsible members of society.
7/28/2006
Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
Program Goals/Objectives
Outcome Delivery Matrix*
Mathematics and Secondary Mathematics Education
Intended Outcome
1. Students will demonstrate
an understanding of the
following fundamental
concepts and mastery of the
following fundamental skills in
mathematics:
Course/Experience/Activity
1. Students acquire
fundamental concepts of the
major through a prerequisitebased mathematics curriculum.
The specific courses which
address the concepts and skills
listed in the first Program Goal
are discussed here.
Course/Experience/Activity
1. In conjunction with MATH
479, we have developed a brief
test of overall program content
material that will be
administered during this course
and will be reviewed and revised
over the next several years. Also
in MATH479, students have an
opportunity to research and
demonstrate their
understanding of one or more
of the following areas of
mathematics.
a. understanding the
derivative concept in terms
of slope as well as “rate of
change,” with procedural
fluency in evaluating
derivatives.
a. Students learn about the
derivative in MATH153 and
256 (Calculus I and III).
a. In most of the Calculus I
sections, students must
demonstrate their mastery of
evaluating derivatives by
passing a “gateway” exam.
b.
understanding the
definite integral as a limit
process for evaluating sums,
with procedural fluency in
evaluating integrals.
b. Students learn about the
integral in MATH255 and
256 (Calculus II and III).
b. Many sections of
Calculus II make use of a
“gateway” exam to insure
student proficiency in
evaluating integrals.
Note: Understanding of the
calculus concepts is reinforced
in other classes, such as
MATH320, MATH422,
MATH441, and PHYS230-231.
Although none of these classes
are requirements in our current
curriculum, almost all of our
students enroll in at least one of
these courses.
c. understanding differences
c. Algebraic systems are
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Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
and similarities between
various algebraic systems,
such as groups (including
non-commutative systems),
fields, and vector spaces,
with the ability to correctly
operate within these
algebraic systems.
addressed in MATH361
(Abstract Algebra) and
MATH362 (Linear Algebra).
Some students elect to enroll
in a follow-up course (461 or
462) for more depth.
d. understanding
applications of matrices in
mathematics, with the ability
to set up and solve matrix
equations.
d. Matrix applications are
addressed in MATH362
(Linear Algebra) and the
optional follow-up course,
MATH462.
e.
understanding
probability as a
measurement of likelihood,
with the ability to use
probabilistic arguments in
statistical reasoning.
e. Concepts of Probability
and Statistics are covered in
MATH270 (now required of
all of our students), and most
of our students also take one
of: 370, 375, or 470 for
additional depth.
f. understanding graphs as
discrete mathematical
models, with the ability to
apply graph theory in
applicable situations.
f Graph Theory and
Combinatorics are the subject
areas of the required course
MATH310 (Discrete
Mathematics).
g. understanding
combinatorial arguments,
with the ability to distinguish
situations in which various
combinatorial methods, such
as use of combinations,
permutations, the inclusionexclusion principle, or
recurrence relations, are
applicable.
g. Graph Theory and
Combinatorics are the subject
areas of the required course
MATH310 (Discrete
Mathematics).
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Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
h.
In addition, students
in the B.S. Ed. program will
demonstrate an
understanding of the
axiomatic development of
geometric systems, and
students in the B.S. program
will demonstrate
understanding of the use of
either partial differential
equations, computer
algorithms, or methods of
operations research for
modeling and problemsolving.
2. Be able to effectively use
inductive and deductive
reasoning, with the ability to
formulate mathematical
conjectures and then use
appropriate mathematical
methods and logically valid
arguments to prove or
disprove those conjectures.
h. The B.S. Ed. students
study the axiomatic
development of geometry in
MATH411 (Foundations in
Geometry), and the B.S.
students gain additional
experience in mathematical
modeling in MATH320
(Intro. to Ordinary
Differential Equations), 350
(Operations Research), or
441 (Intro. to Numerical
Analysis).
2. Related to the second
program goal, students are
formally introduced to the
logical structure and the nature
of proof in Math 250 (Intro. to
Logic and Proof). Several
upper-division courses build
upon this foundation with a
strongly proof-oriented
structure, including MATH361
(Intro. to Abstract Algebra),
362 (Intro. to Linear Algebra),
and 422 (Advanced Calculus).
Of course, mathematical
arguments form a substantive
part of the entire curriculum,
although the presentation may
be less formal in some of the
other courses. Students in the
teaching certification track
(B.S. Ed. degree or B.S degree
with teaching certification)
have an additional opportunity
to experience the nature of
mathematical discovery,
including the process of
making a conjecture and then
7/28/2006
Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
3. Be able to communicate
undergraduate-level
mathematical concepts
correctly and clearly, both
orally and in writing. Students
will make use of mathematics
as a language, i.e., they will use
standard, accepted
mathematical notation for
concise, clear communication.
proving or disproving that
conjecture, in the MATH300
(Problem Solving) course. The
culminating “proof experience”
is the Capstone course,
MATH479, described in
further detail in the next
section of this report.
3. Related to the third program
goal, the use of correct,
standard mathematical notation
is emphasized throughout the
MATH curriculum. In
MATH250, students learn the
common mathematical
shorthand for representing
Boolean operators (and, or,
not), quantifiers (for every,
there exists), and implications
(if, if and only if), and students
gain experience translating
mathematical sentences into
symbolic form and vice versa.
Throughout the curriculum,
students routinely justify their
work in written form, which
may range from showing the
steps of a numeric
computation in lower division
courses to extensive proofs
(either in full prose or using the
symbolism learned in
MATH250) in upper-division
courses. Students also have
numerous opportunities to
orally justify their reasoning.
Our Calculus instructors have
made a commitment to
devoting extensive time in the
MATH153, 255, and 256
courses to student
presentations at the blackboard
(which involves both writing
and discussion on the part of
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Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
the students). This experience
at the lower level of the
curriculum builds our students’
confidence and trust in the
faculty, so that they are more
willing to make verbal
contributions in our upperlevel classes, as well. Again, the
Capstone course (MATH479,
described in the next section of
this report) serves as a
culminating experience for
students to communicate their
mathematical findings (of
independent mathematical
research) both orally and in
written form.
4. Be able to use technology as 4. Related to the fourth
program goal, many of our
part of a problem-solving
classes, including MATH153,
process.
255, 256, 270, 370, and 362
require the use of a graphics
calculator. All of our students
are required to take at least one
course involving the use of
computers: EDEL466
(Computers in Education) for
those students pursuing
teaching certification, and
CS340 (Introduction to
Scientific Computing) for
students in other tracks.
Students pursuing teaching
certification experience
multiple uses of technology in
their professional certification
courses (including the use of
calculators, spreadsheets, and
the World Wide Web in the
mathematics methods course,
MATH415), and the B.S.
degree students experience
additional use of technology in
their required additional
7/28/2006
Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
computing/modeling course
(MATH320, 350, or 441).
5. Be able to use mathematics
to analyze events and solve
problems that occur in
numerous areas of human
endeavor.
6. Be prepared to become a
highly qualified secondary
teacher of mathematics, to
continue studies at the
graduate level, or to enter the
workforce in a position which
requires analytical thinking
skills, depending upon the
option selected by the
individual student.
5. Related to the fifth program
goal, applications from various
aspects of life are incorporated
into our mathematics
curriculum. In just MATH153
alone, students will solve
problems from areas as diverse
as physics (projectile motion),
biology (population models),
economics (optimization of
profit), and chemistry
(radioactive carbon dating).
Students’ exposure to “real
life” applications of
mathematics deepens as they
experience a diversity of
courses (including statistics and
discrete mathematics) in the
curriculum. In the Capstone
course, MATH479, students
may choose an area of
application in which to apply
their mathematical study.
6. As the sixth program goal
indicates, the Mathematics
curriculum is designed to be
flexible enough to meet the
needs of three broad
constituents: students whose
goals are to teach high school
mathematics, students whose
goals are to enroll in graduate
school after receiving the B.S.
degree, and students who wish
to enter the workforce after
receiving the B.S. degree.
Certain courses taught by our
department, including
MATH400 (History of
Mathematics), 411
(Foundations in Geometry),
and especially 415 (Methods &
7/28/2006
Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
Materials for Teaching Math.),
are designed specifically for the
benefit of our future teachers
(although all of our majors can
benefit from MATH400 and
411). In conjunction with the
professional education
sequence (28 hours specified
by the College of Education),
the curriculum prepares our
future teachers with depth in
subject area as well as
knowledge of pedagogy and
“best practices” in education.
Students receive first-hand
experience through field
observations in several
education courses, and the
culmination of the program is
the student teaching
experience.
To meet the needs of those
students who wish to pursue
graduate studies in
mathematics after completion
of the undergraduate degree,
the B.S. program includes
coursework to give students
critical background knowledge
for their graduate studies:
calculus (153, 255, 256),
abstract algebra (361), linear
algebra (362) and analysis
(422).
To meet the needs of those
students who wish to enter the
workforce upon graduation,
the modeling courses (320, 350,
441) and statistics courses (270,
370, 470) give students
experience in problems that
might be useful in research or
7/28/2006
Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
industry.
7. Those students choosing to
become secondary teachers
(B.S. Ed. students and B.S.
students with teaching
certification) will
a. exhibit behavior
characterized by integrity,
responsibility, and
sensitivity to diverse
people and cultures (a
desired outcome for all
WCU students), with the
desire to similarly
encourage honest,
responsible, sensitive
behavior from their future
students.
b. have an awareness of
the contributions of
mathematics to our social,
economic, philosophic,
and artistic heritage.
7. Related to the seventh
program goal, students address
issues of sensitivity, integrity in
the classroom, and the learning
needs of diverse students in the
professional education
sequence.
a. Many of these ideas are
addressed in the Math
Methods (415) class. Issues
discussed in the classroom
are reinforced by the various
field experiences and the
student teaching seminar
which is paired with the
student teaching field
experience.
a. Mathematics Education
students complete a Work
Sample as part of their
Student Teaching Portfolio.
In this Work Sample,
students must show how to
accommodate the needs of
diverse learners in the
classroom.
b. MATH400 was designed
to heighten our students’
awareness of the
contributions of
mathematics to our social,
economic, philosophic, and
artistic heritage.
*Adapted from Bresciani, M.J., 2003, Identifying Projects that Deliver Outcomes and Provide a Means of Assessment: A Concept
Mapping Checklist, NASPA NetRESULTS.
Statement on Alignment of Program Goals/Objectives with University and College Mission
The program goals given above for the B.S. in Mathematics and the B.S. Ed. in Mathematics
Education are closely tied to the University's mission statement. The alignment of our undergraduate
program goals with the aspirations of Western Carolina University (page 5 of the 2005-2006
Undergraduate Catalog) is emphasized below:
a. Goals 1, 2, 3, and 5 provide discipline-specific objectives concerning communication,
problem solving, and critical thinking. These goals are aligned with the first aspiration of the
university.
7/28/2006
Office of Assessment
Western Carolina University
Program Assessment Plan
Mathematics and Mathematics Education
Arts and Sciences
Assessment Plan for 2006- 2007
b. Goals 1, 2, and 4 encompass the intellectual and technical skills of the discipline, in
alignment with the second aspiration of the university.
c. Goal 7b (of the B.S. Ed program) seeks to connect mathematics to other academic areas
including the creative and performing arts, in alignment with the third aspiration of the
university.
d. According to Goal 7a, not only are our prospective teachers expected to exhibit important
traits of citizenship during their own studies, they are expected to go further by encouraging the
next generation of students to exhibit these traits also.
e. As an extension of Goals 2 and 5, it is hoped that our students not only exhibit the ability to
reason logically, but that they gain an appreciation of the problem-solving process, and that this
appreciation leads to a life-long interest in learning, in alignment with the fourth aspiration of
the University.
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Office of Assessment