Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
Teaching Philosophy: “Here is the mathematics go solve the problem”. Think about how
powerful and effective teaching can be if as educators we change this philosophy to: “Here is the
problem. Let us find the mathematics to solve it!” This is what I practice and this is what I
preach! Not only has this helped me shape myself to become a good teacher but has also helped
me to understand the importance of teaching and learning being two sides of the same coin. I
have always had the interest and a strong commitment to become a successful teacher. To me,
teaching is an exciting, challenging, rewarding and multi-faceted profession. I believe that my
role as a teacher is the essential element in the path to success of every student I meet, as I
engage them in the learning process, provide the feedback and guidance they need to improve
their academic performance, and motivate them to pursue life-long learning. The primary
educational frontier in Mathematics in any institution is to design efficient scientific tools that
incorporate innovative methodologies for transforming the educational experience. In order to
provide students such an engaging experience the pedagogy should go beyond traditional forms
of teaching and should include inquiry-based approaches that naturally increase the cognitive
demand in the lesson being delivered. To accomplish this, one of the non-traditional forms I
employ includes active learning in class where the students are made to learn by doing as
opposed to passively listening and understanding. This effort requires cooperative learning,
simulation-based research and learning by discovery. It involves motivating the students to
participate in my classes by asking them questions, extra-credit work and group-assignments. In
particular my classroom assessment techniques help the students to learn about multiple problem
solving strategies including algebraic, graphical, verbal, pictorial, tabular and many more ways. I
always take the approach of teaching mathematics by developing and making explicit for
students, the mathematical ideas they might have already picked up and used in informal settings
and other practical scenarios. I believe this has helped students better their understanding of the
subject matter and develop strong mathematics fundamentals. I have also found that such
teaching efforts allow the students to become confident with their own abilities to master new
technologies and applications. I strongly feel that one's learning cannot be complete without the
proper blend of theory and its practical applications. Thus I have always encouraged my students
to learn various mathematical software packages such as MATLAB for computation and
visualization to enhance the understanding of both fundamental and advanced topics in
Mathematics, while enabling the student to actively put theory into practice. I not only enjoy
working with students at all levels but I also constantly work as a mentor for junior faculty. I also
understand that by learning more one becomes a better teacher and by teaching more one
becomes a better learner.
Education and Outreach: I currently direct the GMU Center for Outreach in Professional
Mathematics Learning and Educational Technology (COMPLETE) that was recently established
through multiple grants from the Virginia Department of Education. One of the mission of this
center is to develop STEM based educational programs for students and teachers to solve realworld problems that focus on 21st Century Skills including critical thinking, problem solving,
communication, collaboration and creativity, careers, technology and innovation. Through this
program I have been able to successfully establish partnerships with six school districts in
Northern Virginia and two school districts in Hopewell and Petersburg. These grants have also
given me an opportunity to work with several undergraduate students at GMU to provide
sustained, intensive and high-quality K-12 teacher mathematics professional development
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
through systemic approach that provides unique opportunities for students to increase their
knowledge and access to rigorous curriculum aligned to the Virginia standards of learning. The
programs developed through this center in the past three years that include ACT Now (Algebraic
Connections and Technology); IMPACT (Improving Mathematical Practices in Algebraic
Connections and Technology) and ESTEEM (Expeditions in Science Technology Engineering
Education through Mathematics) have impacted over 500 K-12 teachers and over 1000 students.
In particular, in 2010 program IMPACT received the "Program That Works" awards from the
Virginia Mathematics and Science Coalition for being an exemplary program in the State that
has demonstrated evidence of a positive impact on student or teacher learning. I have also
initiated several key educational outreach and professional enrichment programs in the last
decade for K-12 students. They include a Summer Mathematics Academy, which was an
innovative and intensive two-week summer academy in Mathematics and its applications that
attracted talented highschool students and their teachers. I have also organized a program that
brings mathematics and world-component together called “Calculations across Cultures and
History”. Another similar program that I directed was the New Horizons Math Mania Camp for
two years and the Paul Robeson Academy in collaboration with the African American Studies at
GMU. I have also participated in the Sally Ride Science Festival for girls at Mason as a
presenter. This year I have also had the opportunity to engage in global outreach by participating
in a visiting lecturer program at the Nelson Mandela African Institute of Science and Technology
in Tanzania. This program was sponsored by the Developing Countries Strategy Group of the
International Mathematics Union (IMU) , in cooperation with International Center for Pure and
Applied Mathematics (CIMPA) and the U.S. National Committee for Mathematics.
New Course Development: At GMU, I have had the opportunity to develop four new graduate
classes that include:
1. MATH614: RATIONAL NUMBERS AND PROPORTIONAL REASONING. This was a special
graduate course that was developed as a part of a Math Science Partnership grant from the
Virginia Department of Education. This class enhances middle school teacher content
knowledge of rational numbers, ratios and proportional reasoning through (a) Quantitative
Proportional Reasoning (QPR), (b) Algebraic Proportional Reasoning (APR), and (c) Spatial
Proportional Reasoning (SPR). This course covers Virginia SOL strands in fractions, ratios
and rational numbers. Instruction covers interpretations, computation, and estimation with
fractions, ratios, proportions, decimals, and percents through a coordinated program of
activities that develop rational number concepts and skills. This course engages participants
in a coordinated program that includes hands-on activities and in-depth discussions that
develop both rational number concepts and proportional reasoning. Attention will be given to
K – 8 students’ development and understanding of fractions, ratios, proportions, decimals
and percents, and ultimately rational numbers and proportional reasoning. Special attention
is given to interpreting and assessing students’ work and learning.
2. MATH610: NUMBERS AND NUMBER THEORY. This was a special graduate course that was
developed as a part of a Math Science Partnership grant from the Virginia Department of
Education. This course is designed to develop a comprehensive understanding of our number
system and how its structure is related to computation and problem solving. Special attention
is also given to children’s thinking, how they learn the fundamentals of number systems,
their problem solving strategies, and how they construct their understanding of various
number systems and arithmetic.
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
3. MATH600: ALGEBRAIC CONNECTIONS AND TECHNOLOGY. This was a special graduate
course that was developed as a part of a State Council of Higher Education in Virginia Grant
to enhance the mathematics content of elementary and middle school teachers. This unique
graduate class takes the teachers through a content-focused summer institute where the
teachers grapple with rich mathematical problems and try to make algebraic connections.
This summer institute is followed by an ongoing professional development for teachers
through school based lesson study as well as online e-webinars where the teachers form
collaborative lesson plans and deliver it in various schools. Also, special attention was given
to articulating big ideas, analyzing problem-solving strategies, identifying and using
appropriate models, multicultural education, examining technology connections and learning
about assessment tools. The course has had a great impact on the teachers and has already
attracted the attention of the Virginia Department of Education.
4. MATH689: CLASSICAL/MODERN NUMERICAL ANALYSIS. This is a new multi-disciplinary
graduate course that has been developed for students from a variety of disciplines including
engineering and science. The purpose of this class is for students to actively learn to: (a)
Develop the ability to mathematically formulate problems from a nonmathematical
description; (b) Identify features relevant to a model and be able to analyze the model using
analytical techniques and (c) Perform simulations using state-of-the-art mathematical
software such as MATLAB and Maple to interpret the results and suggest recommendations.
This course provides a unique experience of how mathematics is applied outside academia
and also broadens the horizon beyond what is usually presented in graduate education.
Teaching, Research and Mentoring: I also recognize the importance of the integration of
teaching and research in improving the quality of teaching effectiveness and student learning. I
have served as the Principal Investigator of two successful REU programs: TTU (Summer 2006,
2007) and GMU (Summer 2008, 2009). Since 2000, I have directed/co-directed five doctoral
dissertations, several masters thesis (one of these being a high school teacher), multiple
undergraduate research projects (including several REU, UAP and URCM projects) and high
school senior projects. These have included students in the McNair Scholar Program (which
prepares low-income, first-generation and minority undergraduates for graduate study at the
doctoral level); Mason Dream Catchers Program (that provides an opportunity for at-risk youth
enrolled in alternative education programs to work with a faculty from Mason). I am also a
Project-NExT Fellow and currently serve as a consultant for mentoring new assistant professors
in mathematical sciences across the country. I also served as a mentor in the Association for
Women in Mathematics (AWM) Teacher Partnership that is intended to link teachers of
mathematics in schools, museums, technical institutes, two-year colleges, and universities with
other teachers working in an environment different from their own and with mathematicians
working in business and industry. I was the organizer and chair of a session on “Using the web
effectively in teaching” at the MathFest 2001 (MAA) meetings at University of Wisconsin,
Madison in August 2001. I was also the principal organizer of the Redraider mini symposium in
November 2003 on “Mathematical and Computational Modeling of Biological Systems” with the
objective of enhancing the awareness of the ever-increasing utility of mathematical and
computational approaches in understanding biological systems. I was awarded conference grants
from the National Science Foundation, the Whitaker Foundation for hosting this minisymposium. It greatly contributed to the scientific development of 161 participants who came
from 34 different Universities from 27 different states in the United States and two countries
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
outside USA. The participants included undergraduate, graduate students, early career scientists,
junior and senior faculty, who had the opportunity to interact with some of the most outstanding
leaders in biological system modeling and to learn about new research venues and open
problems.
Teaching Awards and Recognition: National recognition of my commitment to teaching was
provided when I was selected as one of the 72 new mathematics assistant professors in the
United States, for a Project Next Fellowship in 2000, by the Mathematics Association of
America (MAA). This prestigious award is given only to individuals with strong scholarly
credentials and outstanding potential for both graduate and undergraduate teaching in the United
States. In 2001, I was also selected as one of the two Texas Project Next Fellows to improve
quality of education and research in the state of Texas. Prior to joining GMU, I have been
honored several times as one of the top educators at Texas Tech University for my professing
excellence and outstanding teaching contributions. Some of these awards include Tribute to
Teachers Outstanding Teacher Award (2002); Texas Tech Alumni New Faculty Award (2003);
SIAM Graduate Professor of the Year (2002 and 2004); Outstanding Faculty Award (2004) for
being one of the top five educators given by the Mortar Board and ODK societies. In 2005, I was
inducted as a member of the Texas Tech Teaching Academy. I am a member of Who's Who in
America; and also to the Phi Kappa Phi National Honor society. I am proud to be one of the
original signing members of the Phi Kappa Phi Chapter at George Mason University that was
initiated this year. In 2010 and 2011, I was selected as one of the Nifty Fifty Speakers which
includes a select group of noted professionals who were chosen from over 500 submissions from
4450 partner organizations. All these teaching accomplishments have helped me to achieve the
highest award in Teaching Excellence at two different institutions (Texas Tech University and
George Mason University). I am also fortunate to be the first recipient of the College of Science
Teaching Award from George Mason University this year.
The five-minute teaching moments: Let me now share with you some aspects of my teaching
that encompasses various exciting five-minute teaching moments that I have experienced as a
faculty that has helped me to be where I am today! So…Sit back, relax and enjoy the read!
SETTING: My office. A student from an undergraduate mathematics class I was teaching that
semester knocks on my office door…Knock, Knock!
Padhu: Please come in! (I have an open door policy. Students may walk in anytime besides the
office hours to talk with me. However busy I may be, I always make it a point to talk to the
students for at least five minutes!)
Student: (He is upset, I can tell from his face!) Dr. Seshaiyer, I was wondering if you have some
time to go over one of the questions in the exam. You marked the question wrong.
(I can now tell from the student’s voice that this is going to be an interesting five-minute teaching
moment. In fact, any time a student makes such a bold statement as “you marked a question
wrong”, as a faculty I embrace this confidence in the student. I was looking forward to what was
about to happen next!)
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
Padhu: I will be happy to discuss this. Can you explain to me where I have taken off points?
Student: Here is the test. You have taken off some points in this question. I don’t think I did any
mistake!
(I look over the student’s work. It was an involved problem and the student had
done a decent job at presenting his work. However, towards the end of his solution,
he was expected to divide the number 33 by 3 and what he wrote on his paper
shown on the right surprised me for which I had taken off points.)
33
3
3
Padhu: Can you please explain this step (pointing to this division step)? Does this step make
sense?
Student: Yes, it makes sense. My middle school teacher taught me that if I see some number on
the top and the same number in the bottom, I can cancel.
(This was a profound statement and I realized why the student made the mistake. Whatever the
student said would have made perfect sense if the numerator was a 3 times 3 instead of 33. So
here was my five-minute teaching moment and I was not going to give up on this!)
Padhu: Ok, tell me if you and two of your buddies go to a bar (it was a college student and so I
thought taking an example of going to a bar was ok!) and the bill comes to $33, how much do
each of you owe?
Student: $11.
Padhu: How did you say that?
Student: I divided 33 by 3.
Padhu: (I looked at him pointing to the division on paper) Now tell me do you think this step
makes sense?
I now see a sly smile on the student’s face! He seems to have realized his mistake. He thanks me
for the clarification and leaves the office!
As I saw him walk out, I remember an ancient Chinese Proverb, “Give a man a fish and you feed
him for a day. Teach a man to fish and you feed him for a lifetime.” I felt great about what just
happened and also I felt that was an important lesson for every teacher to recognize that
students come into an educational system such as a university with preconceived notions from
their middle and high school system that may be true or false. As a faculty, I feel it is our duty to
recognize this and turn those opportunities into rich teaching moments to help guide students to
clarify any misconceptions in the content they come with!
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
SETTING: An elementary school classroom
I was invited to visit the school as their Pi-Day speaker. The topic I was discussing was
multiplication. At the beginning of my lecture, I asked all the students to work out a simple
multiplication problem, namely, what is 12 times 13? After a few minutes, I ask the students to
share their work. It was surprising that only about half of the class were able to do the problem
correctly. The rest of them either did not do anything on paper or did the problem incorrectly.
The correct and incorrect work is shown below:
12
12

13
36
12
48

13
36
120
156
I displayed these two solutions on the board and picked two students to explain what was going
on in each example above and why we see two different answers.
Student 1: First multiply 3 times 12. It is 36. Write it down as the first row. Now do one times 12
(His finger is pointing to the “1” before the 3). You get 12. Write it down below the 36 and add
them. So we get 48.
Luckily, I had brought several chocolates to the classroom that day. So, I called that student and
asked him to pick 13 students in the class and distribute 12 chocolates to each of them and asked
him to keep track of the number of chocolates as he distributed them. (Little did the student
realize that I had involved him in an active learning experience!) The student started distributing
the chocolates but within a few minutes of this distribution process, he turns to me.
Student 1: I know why 48 is wrong now.
Padhu: Why?
Student 1: Because, I have more chocolates to give.
Padhu: But, why do you have more chocolates to give?
Student 1: Well, 48 is only 4 dozens and I have to count 13 dozens which is a lot more.
I was ecstatic at this point. He not only figured out the mistake himself but he used a completely
different reasoning to solve the problem. This was a great five minute teaching moment which
turned to be a discovery learning process for this student. I am glad, I kept asking “Why?” As
Albert Einstein said, “The important thing is not to stop questioning. Curiosity has its own
reason for existing.” I then called out another student to explain the other (correct) solution
displayed on the board.
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
Student 2: First multiply 3 times 12 and it is 36. Then put an imaginary zero under the 6. Then
do one times 12 and you get 12. Place the 12 before the imaginary zero. Then add the 36 and 120
to get the answer.
Even though the final answer was correct, I was shocked to hear this rote procedure that the
student presented and was especially surprised to hear about this imaginary zero. What was even
more surprising was that the majority of the class who got the correct answer explained the same
procedure that their teacher had asked them to follow. I realized that I had to have a discussion
with the teacher about the place value mathematics content that she must emphasize on rather
than asking students to remember unnecessary rules such as putting down an “imaginary zero”
that may lead to misconceptions. I also noticed one other student that refused to write anything
on paper for that problem. So I called him and the whole class watched!
Padhu: Why did you not work on the multiplication problem?
Student 3: Because, I don’t like multiplication?
Padhu: Why is that you do not like multiplication?
Student 3: Because, there are too many rules to remember. It is too difficult. That is why I hate
math.
When he said the magic words “I hate math” I realized it was another five minute teaching
moment about to happen and I was not ready to give up on it! I looked up and there was a poster
on the wall with Albert Einstein and his quote, “Do not worry about your difficulties in
Mathematics. I can assure you mine are still greater.” So, I asked the student to come up to the
board. (This is a normal practice in any class that I teach. I not only have students participate
from their seats but almost always, I will have a student come up to the board in what ever level
class I am teaching! I am known for this among students!)
Padhu: Ok, so you don’t like math. So, what do you like?
Student 3: I like drawing. I am going to become an artist one day.
Padhu: Is that so? Draw something for us.
The student did not even hesitate and within the next 30-40 seconds he drew the Statue of
Liberty like I have never seen before. This was my discovery teaching moment. He loved art, I
wanted him to love math. So, I decided to put math and art together and out came math through
art!
Padhu: (Looking at student 3) Let us do math through art. (The student looked puzzled and gave
this look as if having the words “math” and “art” in the same statement was grammatically
incorrect!)
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
I asked him to draw 12 as one line and a group of two lines (see bold lines below). Then I asked
him to draw 13 the same way but diagonally opposite on top of the lines drawn to represent 12.
12 =
13 =
12 x 13 =
Then I asked him to count the points where these lines intersected in the last picture.
12

12  13 =
13
36
120
156
1
5 6
Padhu: What do you see?
Student 3: Wow, I see 156 which is the answer to the problem. That’s so cool. I love it!
Goal accomplished! The same student who said “I hate math” apparently liked what he saw. Not
only was he thrilled about what he saw but he wanted to know if it worked for all numbers. I
love when students ask this because that makes them to abstract from computation and develop
critical thinking skills. So, I asked him to do a few more and he was so happy to realize that he
can now enjoy math through what he enjoys the most….ART! For me more than the connection
that I was able to present between mathematics and art, I was happy to tap into the artistic part of
his brain to make sense of multiplication.
As a faculty, it is important to realize that any classroom will consist of students who come with
different learning styles including auditory, visual and kinesthetic. So, any class I teach, I make
it a point to include multiple strategies to solve problems that will help the various types of
learners in the classroom. As George Bernard Shaw said, “What we want is to see the child in
pursuit of knowledge, and not knowledge in pursuit of the child.”
SETTING: Olive Garden Restaurant.
I have come with my family to have dinner. We get seated and then after a few minutes a
waitress walks towards us. I tell my wife “That face is so familiar” and my brain is doing a quick
simulation at that instant scanning through thousands of names of people that I know! As the
waitress gets closer to our table, my brain seems to have figured out that she was one of my
students from a class that I taught a few semesters prior to that. As she was distributing the
menu, she looks at me.
Waitress: Dr. Seshaiyer, how are you? Do you remember me?
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
Padhu: (It was the moment of truth!) Oh yeah, Kim right?? You were in my class three
semesters back.
Waitress: Oh wow! You remember my name.
This was a great moment for the student to see that I, as a faculty did not just treat her as a
“number” rather remembered her as a “person”. I believe it is extremely important for every
faculty to know their students very well, whatever be the size of the class. Little did Kim know
that, one of the skills I have developed over my years of teaching is that whether it is a 20 student
class or a 120 student class that I teach, it takes me a very little time to know the students in the
class by their first name. I am fortunate to have this trait in me!
Just a few days back at the Celebration of Achievements I was chatting with another faculty
member when a friendly face walks by (everyone knows him as the President of GMU, Dr. Alan
Merten). He enters into our conversation. Dr. Merten looks at the other faculty member and
points to me.
Dr. Merten: If you keep talking to Padhu, you will learn so much. I was just making a
presentation about outstanding faculty at GMU and guess what, I talked about Padhu and his
great work.
Padhu: I am honored to hear that, Dr. Merten! Thank You!
After I came back from the event I realized how important that moment was for me, for Dr.
Merten to recognize the efforts that I am involved in teaching and research at GMU. I now
realize what Kim (at Olive Garden) must have felt when I was able to recollect her name!
SETTING: A high school classroom
I have been invited by a high school teacher (who was paired with me through an Association for
Women in Mathematics Teacher Partnership program) to visit her classroom to talk to her
students about math competitions. After a great interaction, I went to have lunch with the
teacher. She mentioned that she was teaching Pre-calculus and was currently doing Differential
Equations. She said, “I wish I could make Pre-calculus more exciting for my students and have a
good answer every time they ask me “Why are we learning differential equations? Am I ever
going to use this in real-life?” I could see the frustration in the teacher who was looking for an
opportunity and advice from me to excite her students. Here was my five-minute teaching
moment and I was not going to give up on this. I spent the next five-minutes explaining to her
how one can use simple tools from Pre-Calculus to explain how to solve problems in medicine.
She was fascinated at that five minute conversation and all she wanted to know was “How can I
learn more on this?” The teacher ended up working with my undergraduate and I on a summer
research project on “Mathematical and Computational modeling of Intracranial Saccular
Aneurysms”. Several great things happened following this. The undergraduate student’s project
won a national award for outstanding undergraduate research and the results of the project was
published in one of the premier journals in applied mathematics. The teacher was able to take the
Padmanabhan Seshaiyer
Teaching Statement
Padmanabhan Seshaiyer
2/12/2016
Mathematical Sciences, GMU
work back to her classroom and present it to her high school students in the form of a lesson
study. Most importantly she connected what the students were learning in Pre-Calculus at that
time to the research project. The students were totally blown away by the teacher’s presentation
and were so eager to learn more. We were also very fortunate that our project was one of the two
projects from GMU that was selected for the Posters on the Hill event. Not only did the project
give us a chance to help promote the awareness of mathematics in fields that bridge science,
engineering and medicine but also it gave me an opportunity to meet and discuss the importance
of undergraduate research and education with Virginia Senator Mark Wanner, Congressman
Frank Wolf, Congressman Gerry Connolly and Congressman John Culberson. Little did I realize
that a five-minute discussion led to all this. To top it all, the following week, I receive a letter
signed by the Governor of Virginia, Robert F. McDonnell that stated:
“Dr. Padmanabhan Seshaiyer: On behalf of the Commonwealth of Virginia, it is with great
pleasure that I express my appreciation of your work in the field of developing computational
models and tools to address the rupture of intracranial saccular aneurysms. Your contributions
to educating Virginia high school students on the importance of Mathematics and Biology
advance a positive attitude towards the importance of education among the youth of our
Commonwealth. The insights of the research work that you shared with the students will help to
prepare them to succeed in the 21st century economy that requires increasingly high levels of
knowledge in the field of Science. Congratulations on your achievements.”
In summary…..I believe that the most important qualities of an excellent and memorable teacher
are knowledge of the subject, ability to communicate, ability to make the material being taught
interesting and most importantly having a respect for student-learning. Over the years, these
traits have helped me to develop good teaching attributes including: Having an organized course
plan; Delivering a clear lecture; Setting high expectations; Managing time inside and outside
classroom. I also believe that education is a two-way street and not a one-way monologue. So, I
try to provide a knowledge-seeking environment that provides opportunities for students to ask
questions. I also believe in going above and beyond a traditional lecture based classroom by
constantly creating knowledge holes to engage the students in a mathematical discovery learning
process. This also helps to eliminate any elevator effect (have you ever wondered why people
never talk in an elevator!). Finally, as an educator it is very important to including a sense of
humor!
In conclusion, most educational systems or textbooks in the world follow the philosophy: “Here
is the mathematics go solve the problem”. Think about how powerful and effective teaching can
be if as educators we change this philosophy to:
“Here is the problem. Let us find the mathematics to solve it!”
Padmanabhan Seshaiyer
……..Padhu