TEACHING STATEMENT
I have extensive teaching experience. I have been the instructor in 9 semester long courses and a teaching fellow assistant in 3 different courses. In addition, I have taught aspects of my own research to high school students in outreach programs and to graduate students in seminar settings. This teaching statement briefly describes my activities in each of these areas.
Course Instructor: Calculus
My first
experience as instructor occurred when I was a graduate student working toward my Masters degree
at Boston College. For 4 semesters in a row, I taught an introductory calculus for nonscience majors. The responsibilities included preparing and presenting lectures,
creating and grading exams, holding office hours and assigning final course grades. I was fortunate during this time to have continual supervision and guidance from the math department director of
graduate studies, who helped me to shape my teaching style. My hard work and commitment to teaching at Boston College was recognized when, at the completion of my Masters degree, I received the Alfred A. Bennet Mathematics Teaching Award. Moreover, while later working toward my Ph.D. at Boston University, I was invited back
to Boston College to teach a more advanced Multi-Variable Calculus course, as a part time faculty member, for one semester.
Course Instructor: Summer Terms
My post-masters teaching experience includes teaching in a
summer program organized by the office of AHANA (African-American, Hispanic,
Asian and Native American) student programs at Boston College, called The Options Through Education Program. This is a
pre-college enrichment program for educationally and financially disadvantaged AHANA students who are highly motivated. As an instructor
in this program for three summers, I taught Algebra and Pre-Calculus and provided extensive one-on-one tutoring in many areas of mathematics. In addition, I taught Algebra to a group of working adults during a summer semester in the Continuing Education Program at Fisher
College.
Teaching Assistant: Curriculum Development & Teaching with Technology
I have worked as a teaching assistant and as a text book production assistant. These and other experiences have motivated my use of technology in the classroom.
As a Graduate Teaching Fellow
at Boston University, I aided in teaching Introduction to Chaotic Dynamical
Systems, Differential Equations and Calculus II. My responsibilities in each of
these courses included holding weekly discussion sections and office hours,
grading exams and computer labs, and assigning a percentage of the final grade. Furthermore,
while a teaching fellow for Differential Equations, I took part in the curriculum
development of the course, as a text book production assistant for the book used in this class entitled \underbar{Differential Equations} by professors Paul Blanchard, Robert Devaney and Dick Hall. My duties
as production assistant included creating exercises, examples and solutions, and acting as a teaching fellow consultant.
The mathematics department at Boston University puts great emphasis on teaching with technology. Thus,
assisting in each of the computer/graphing calculator aided courses listed above greatly enriched
my integration of technology and teaching. This integration was further
developed when I substitute taught a computer based Calculus course to a
group of business students at Bentley College. These experiences proved to be beneficial when I implemented the use of a graphing calculator in the Multi-Variable Calculus course I taught at Boston College.
High School Outreach Efforts:
I have developed presentations of advanced mathematical ideas for high school students in two outreach programs organized by Professor Bob Devaney at Boston University. As a guest speaker in the Mathematics Field Day programs in 1998 and 2000, I had the privilege of teaching areas of my own research to a large group of students from Boston area high schools. Also, during
each of my years at Boston University, I presented a dynamical systems lab to
groups of high school women as part of a program designed to increase young women's
exposure to fields in math and science.
Graduate Seminar Teaching:
I have taught dynamical systems theory techniques used in my own research to graduate students at Brown University. As a guest lecturer in the Computational Neuroscience Course at Brown, I gave a tutorial on ``The Dynamics of Coupled Neural Oscillators''. Furthermore, I have presented my thesis research to the Graduate Neuroscience Group at Boston University as part of a weekly seminar series.
Philosophy and Curriculum:
One of my main philosophies on teaching is captured in a phrase many students
have heard me repeatedly say, ``if you don't know what to do, do what you know''. This phrase is meant to encourage students who doubt their ability to answer particular
problems to challenge themselves to recall what they have
learned and to try to work through problems in a logical manner. In order to do this, a student must be taught not only the necessary
formulas and steps to complete problems, but also a deeper conceptual understanding of why each is used. It is thus a challenge of a mathematics teacher to instill logical reasoning in students when approaching difficult questions; this will benefit them not only in mathematics but in all aspects of their learning.
There are many ways in which a teacher can impart a better conceptual understanding of
mathematics. One of the most important is to first attract their interest by designing problems which are relevant to the particular interest of the students in the class. I often use examples from my expertise in mathematical biology to convey and elicit enthusiasm. Also, whenever possible, emphasis should be put on both quantitative and geometric thinking. For example,
in a calculus course, I teach not only the formula for taking
a derivative of a function but also what the derivative means geometrically, and in the case of word problems, what the derivative represents realistically. Another relevant example occurs in a differential equations course, when demonstrating the solution to a differential
equation, I teach students not only how to find an explicit formula for the solution, but also how to graph the solution in a phase plane using guides such as slope fields, fixed points and eigenvectors. These examples naturally lead to the use of technology in the classroom, such as graphing calculators or computers.
In addition, students should
be continually encouraged to take advantage of help outside of the classroom, for instance during the professor's office hours, where they can identify the source of any difficulties in a more informal setting. This environment helps many students, since it is often easier to overcome difficulties in a one on one situation, and it aids the teacher by giving them a better understanding of which concepts are unclear. When students ask for help, I often
encourage them to answer their own questions after giving them hints or suggestions. I also
promote students to work together in groups; it has been my experience that students mathematical
abilities grow in a cooperative learning environment.
Through my experiences with students who have various levels of mathematical expertise, I have learned the importance of tailoring teaching to the level of the class, while still covering material required for future education. This involves continual adjustment of the pace of lectures and the length and difficulty of assignments.
I look forward to building upon my experiences, in both research and teaching, as I continue my academic career.
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