TEACHING PORFOLIO
James P. Peirce
Department of Mathematics
University of Wisconsin – La Crosse
Spring 2006
Table of Contents
1) Teaching Responsibilities
2) Teaching Philosophy
3) Teaching Strategies and Methods
4) Teaching Through Advising Undergraduate Research
5) Student Evaluations
6) Efforts to Improve Student Learning
7) Future Goals
8) Appendices
Teaching Responsibilities
My teaching responsibilities fall into two broad categories: service, general education
courses intended for students outside of mathematics and classes in the mathematics
major.
Service courses include Math 150 College Algebra and Math 175 Applied Calculus. I
have taught College Algebra for two semesters and Applied Calculus for one. The
algebra course is used to review and build the tools needed for students to take an algebra
intensive class such as Applied Calculus. The College of Business Administration
(CBA) requires their students to pass the Applied Calculus course. Consequently, most
students in Math 175 are students majoring in a department housed in CBA. Enrollment
in these classes average about 35 students per class.
In addition, I also teach classes directed toward students working on their mathematics
degree. I have taught Math 207 Calculus I, Math 353 Differential Equations. Calculus I
is typically the first class a math major takes towards earning a mathematics degree.
Students in the differential equations class come from both math and science majors.
Enrollments in these classes are about 20-25 students per class.
Teaching Philosophy
My strongest quality as a teacher is simply my passion for mathematics, which I believe
is contagious in the classroom. My primary goal as a teacher is to use my enthusiasm for
mathematics to motivate my students. I project an upbeat attitude when I am in front of
the class; I take pauses in the lecture to interject math anecdotes; and I provide short
historical accounts of the mathematicians who discovered the material. I also continually
tell students that I am willing to spend extra time working with them. I believe that this
commitment and attitude inspires my students to put more effort into the course. I felt
proud that I had achieved this goal when I received a student evaluations that said, “I
heard math classes were hard no matter what teacher you get. Dr Peirce, you made it a
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little easier to understand. I am glad I stuck through this class.” (See Appendix A) The
principle at work here is simple: motivated students work more and hence learn more.
I believe that a good instructor must invest time in preparing a clear, precise lecture. Like
a good story, a lecture needs to have a beginning, middle, and a well-constructed end
(including a climax if possible). These parts of a story are crucial to capturing the
student’s attention and sustaining their interest during the lecture. I do this by
constructing appropriate examples, finding applications that are interesting to students,
and anticipating difficult areas in the material. When commenting on the class, students
are quick to mention the usefulness of the examples: “You covered the material
thoroughly and gave many examples, which helped a lot.” and “Examples in class were
very, very helpful!” (See Appendix A)
When preparing a lecture, I carefully construct examples that review the recent ideas and
present the students with a concrete, often visual example. I practice these illustrations
beforehand to ensure that during lecture I am able to reproduce the clearest picture of
what I want to demonstrate. Beyond preparing simple examples that demonstrate basic
math techniques, I have also made a habit of presenting real-world application in my
classes. Math students come from various departments on campus, so I keep on hand an
arsenal of real-world examples from a wide range of fields, from Business to Population
Biology. For instance, in my differential equations class, I noticed that a particular topic
was the source of confusion for many students. Now when we study that topic, I
introduce the material in terms of a Mathematical Ecology problem, and have my
students read a supplemental review I've developed on how the concept at hand is used to
model the dynamics of the HIV virus as well as a fun model about the ups-and-downs of
love. I hope my rich collection of real-world examples helps students connect to and
remember the material, feel motivated to continue in math by seeing how math can be
used, and maybe catch a glimpse of the beauty of mathematics. I know that this is
approach is working when a student comments, “I love how he relates math to every day
life.” (See Appendix A)
Another important aspect of lecture preparation is anticipating difficult areas and
common errors, and preparing a strategy to address those questions in a way that
encourages students and accommodates different learning styles. When I spot a topic that
will be difficult for students, I devise a series of questions, each question following from
the previous answer, which leads the students to the correct conclusion. This technique
involves students actively in the lecture, and gives them the feeling of discovery and
accomplishment. Anticipation of difficult area becomes easier the more I teach a class. I
think that this was evident in my college algebra course during the 2004-2005 academic
year. In the Fall semester, I taught College Algebra for the first time in my career. Some
lectures went better than others and I created notes on places to make improvements.
During the following semester I acted on these improvements and my student evaluation
of instruction scores increased from 3.83 to 4.35. (See Student Evaluations section
below)
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I believe that active involvement in class increase students' confidence and give them the
experience to work problems on their own. When I take questions from students, I
always keep three things in mind: I involve the whole class in thinking about or
addressing the problem; I emphasize the progress that the question-asker has already
made on the problem and the progress that the class makes in solving the outstanding
question; and I take as much time as is needed, either during the lecture or after class. I
hope that students are comfortable asking questions during class. However, I know some
students prefer asking questions one-on-one during office hours and I strongly encourage
them to stop by my office by having an open door policy.
I try to be as approachable as possible outside of class. I know students in my lower level
classes have trouble with math and are math phobic. I try to encourage them to work on
problems on their own and come see me when they are stuck. I enjoy helping students
during office hours. I know I am doing this well when students comment, “Dr. Peirce has
been very understanding and helpful when it comes to needing further help outside of
class” (see Appendix A)
Finally I believe that any instructor should always strive to be a better teacher. There is
never a point when I believe I know all there is to know about teaching. I constantly
work to be a better educator by seeking out opportunities to teach in different settings, by
asking my colleagues to observe and evaluate my teaching, by noting teaching styles
whenever I am listening to an accomplished instructor, and by keeping notes from one
course to the next...all in an effort to continually update and improve my teaching
method. My ultimate goal in teaching mathematics is to use my passion for mathematics
to inspire my students in the same way I was inspired when I was a student.
Teaching Strategies and Methods
Course syllabi (see Appendix B) reflect my teaching philosophy and strategies, and
evolve through self-evaluation and the input I receive from peer evaluations. In the
syllabus I clearly state the goal of the course and give the students a list of steps
suggesting how they should study for the course.
When teaching general education courses, I stress applications. The students in college
algebra have seen most of the material in the course before and benefit greater from
seeing the applications as a review of their algebra skills. The students in the applied
calculus class on the other hand, are learning calculus for the first time. Most of the
students are business majors who need to know how calculus can be applied to their
discipline. Therefore we discuss how to maximize revenues and minimize costs rather
than the (beautiful) theoretical results stressed in the calculus course for math majors.
During office hours I work to involve each student. I ask them to work their problems on
the chalkboard and encourage other students to offer help. I use office hours to note
where my students are struggling and also to observe their distinct learning styles. I pay
attention to which alternative approaches really click with different learners, so that I can
incorporate those approaches into my lectures.
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In my upper division math courses, I have required multiple writing assignments. As
with any discipline, students need to practice communicating their work to others. I
firmly believe that the act of writing mathematics can enhance student learning. The
depth of understanding required to produce a lucid mathematical explanation is generally
deeper than that demanded by traditional homework assignments. As students write their
solutions, and therefore as they discover how much harder it is to explain than merely to
solve the problem, they deepen their own understanding of the mathematics underlying
their solution. Finally, projects are by their very nature open-ended and therefore
difficult, demanding that students develop and practice the problem-solving skills that are
the hallmark of mathematics. Examples of written project from Calculus I and
Differential Equation can be found in Appendix C and D.
In Math 353 Differential Equations, I get the pleasure of teaching a class in the area of
my research. I try to discuss each major topic from three viewpoints: theoretic, analytic,
and geometric. For example, one of the first subjects in the class is the study of first
order differential equations. I motivate the equations by deriving common physical
models such as chemical mixtures and population growth. We discuss when the
differential equation a realistic model of a physical process. In other words, we talk
about the theoretical concerns of when the solutions to our equations remain unique and
stable. After the students know when solutions exist, we explore the many techniques
used to solve first order differential equations. Unfortunate we quickly realize that not all
the equations are solvable by hand and I show them two ways to geometrical visualize
the solutions using computer simulations. I think each of the three viewpoints build
breath to their understanding of differential equations.
Teaching Through Advising Undergraduate Research
Undergraduate research is an important opportunity for students to dive deeper into the
beauty of mathematics. Guided research projects require students to apply knowledge
learned in a structured classroom to a particular problem modeling a real life situation or
phenomena. By designing, implementing, and completing a research project (with a
written summary), students learn the ups and downs of the research process. A student
must persevere through the difficulties, thus gaining self-confidence and responsibilities
for their own learning.
In the spring and summer of 2005, I advised Devin Bickner on an undergraduate research
project. Devin is now a senior majoring in mathematics. The goal of the project was to
introduce Devin to an area of math that he had never studied. Since he is minoring in
Music, I asked him to develop a model for the motion of a plucked guitar string. After
reading material on the wave equation, he proposed an equation that included the effects
of dampening and he proved that the total energy of the model decreases as we expect
from a real guitar string. Devin presented his work at the Pi Mu Epsilon Undergraduate
Research Conference at St. Norbert College on Nov. 4, 2005. Devin has decided to
continue his study of mathematics in a Ph.D. program at Iowa State University.
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Student Evaluations
The mathematics department uses a standard evaluation of instruction (SEI) form. The
scores are registered on a scale of 1 to 5, with 5 being the highest rating. There are 10
questions on the SEI form (see Appendix E). Although we are given the scores for every
question, the mathematics department only records the weighted average of the median
score from the final question. The chart below shows the ratings for all of the courses I
have taught at UW-L. I have included the department median for comparison.
Term
Fall 2005
Course
Applied Calculus
Differential Equations
Spring 2005
College Algebra
Differential Equations
Fall 2004
College Algebra
Calculus I
Fractional Median
on #10*
4.3026
4.7857
4.3468
4.6111
3.58335
4.5455
Overall Dept. Median
4.4286
4.43
4.3571
4.29
3.8485
4.18
*Question #10: On the basis of the factors considered above (student-teacher relationship,
teaching ability, and testing policy), how do you rate this instructor?
Efforts to Improve Student Learning
In June 2005, I was selected as a Project NExT fellow and participated in the summer
2005 workshop at the University of New Mexico. Project NExT (New Experiences in
Teaching) is a professional development program for new or recent Ph.D.s in the
mathematical sciences. This national program addresses all aspects of an academic
career: improving the teaching and learning of mathematics, engaging in research and
scholarship, and participating in professional activities. It also provides the participants
with a network of peers and mentors as they assume these responsibilities. The core of
this year's program is two workshops in the summers of 2005 and 2006 and a series of
special courses at the Joint Mathematics Society Meetings in January. During the
summer workshops, fellows explore and discuss issues that are of special relevance to
beginning faculty. These topics include innovative approaches to a variety of
introductory and advanced courses, ways of using writing and reading to help students
learn mathematics, involving undergraduates in mathematical research, alternative
methods of assessing student learning, getting research off to a good start, and balancing
teaching and research. Past participants in the Project NExT program have gone on to
receive national awards in mathematics and are now taking leadership roles in the
mathematical community.
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Future Goals
 Develop a course in mathematical biology.
 Research and use methods to access student learning in classes I teach semester to
semester.
 Quarry more frequently the experience of previous instructors to the courses I am
teaching.
 Keep a better log of the effectiveness of specific lectures.
 In corporate more inquiry based learning into my lecture style.
Appendices
Appendix A: Course Evaluation—Student Comments
Appendix B: Sample Syllabus
Appendix C: Sample Writing Project for Calculus I
Appendix D: Course Project Description for Differential Equations.
Appendix E: Student Evaluation of Instructor (SEI) Form
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Appendix A: Course Evaluation – Student Comments
Fall 2006
Math 175 Applied Calculus
 Dr. Peirce was an awesome professor. He was so helpful with my questions and
took the time to make sure I was understanding the material. I learned a lot from
him and Math 175 was honestly my favorite class. Dr. Peirce also went out of his
way to answer any of my last minute questions before a quiz or exam and he
would always make time for myself and other students by extending office hours
and answering e-mails. I would take another course from him again!
 Dr. Peirce has done an excellent job thru this semester. He is always more than
willing to help you. I like that he responds to his emails so quickly, especially
near test time with answers to my questions. I feel like I would not have enjoyed
calc with a different professor as much as I did with Dr. Peirce.
 He is an excellent professor.
 I think Dr. Peirce is an excellent professor and I really have no complaints.
However, I have kept up with all my assignments and rarely miss class but I still
do not do well. I feel this may be because I do not have enough time to complete
the questions and recheck my work.
Spring 2005
Math 150 College Algebra
 “You covered the material thoroughly and gave many examples, which helped a
lot.”
 “Dr. Peirce has been very understanding and helpful when it comes to needing
further help outside of class”
 “Dr. Peirce really seemed to know his stuff and showed enthusiasm for the
content.”
 “I heard math classes were hard no matter what teacher you get. Dr Peirce, you
made it a little easier to understand. I am glad I stuck through this class.”
 “One of the best math teachers I’ve had. Really made me understand stuff in
class.”
 “Keep doing what you are doing. I find you to be an excellent math instructor.
Writing everything on the board and proving why certain properties work is very
helpful. If I have to take another math class, I will definitely look for you. “
Math 353 Differential Equations
 “I love how he relates math to every day life. He has a genuine concern when it
comes to his students success.”
 “I think that the prof. did an excellent job of breaking down the math problems
and explaining them.”
 “Great instructor. Teaches at a level that is not over my head.”
 “Examples in class were very, very helpful! He also was available for extra help
whenever we asked.”
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