TEACHING STATEMENT

(Bharath Narayanan)

I am currently in the third and final year of my post-doctorate at the University of Arizona. This position has given me a lot of experience beyond graduate school in mathematics education and related activities. I have taught a variety of courses, gained well-developed communication skills, a broad perspective of my own field, and the ability to mentor. This definitely makes me superior to others of roughly the same experience in my field. Please allow me to describe my capabilities as a scientist and convince you that my activities show promise of continued development and professional growth, that I have the potential to direct the work of others and finally my interest in, and experience working with students from a wide variety of academic and social backgrounds.

1. Teaching Objectives - To persuade everyone to become a math major, while understanding this doesn't mean they have to become a mathematician. To make the students more familiar with the subject and less intimidated to think for themselves. In the lower level courses, I want the students who complete my course to have gained some problem solving skills and I expect to them to leave with some familiarity with the basic definitions. For the more advanced courses, I would like the students to understand some basic theoretical concepts in addition to being able to just solve problems.

2. Methodology - I believe in motivating the students to learn, especially to attend classes regularly. I always encourage them to ask questions and I try to promote student participation by including some “recitation points” through in-class quizzes. I also solve some of the assigned problems, discuss extra-credit assignments and always make the atmosphere lively and new. It does help to use a systematic method of assigning reasonable and thought provoking problems, returning them in a timely fashion with appropriate comments and corrections, and discussing the solutions in class. I always show concern by personally talking with students and being open to criticism and suggestions. I have an excellent command over the English language and have been recognized as a strong communicator by several other faculty as well as my students.

3. My teaching techniques when teaching basic skills mathematics versus teaching college level mathematics - In the beginning of the semester, I make the students understand the difference between “owning” versus “renting” the knowledge. I always include some cultural history of the subject, side-by-side with the actual mathematics, to give the pupils an idea of some of the immense struggles over the centuries to formulate the key concepts, the steady evolution of the notions of rigor and proof and the remarkable simultaneous contributions in many different fields from all the continents. When students come to my office, I take a moment to ask them something individual, like what their major is, so that they can feel more comfortable, especially when things may seem very impersonal.

4. Using computers and/or graphing calculators to enhance the teaching of mathematics - It has become clear to me that technology is a valuable aid to teach mathematics from the TI-85 calculator, Mat lab, Excel and Powerpoint presentations to the web-based approach using Java applets and WebCT. I hope to use it increasingly in my teaching career. I have used Matlab and Java programs in the Elementary Differential Equations course to teach concepts like slope fields, solution curves, radius of convergence of series solutions, stability of Laplace transforms and numerical methods. I noticed that the students showed enthusiasm while working these labs and also expressed satisfaction on getting the correct output or result, which helps to keep them interested. The course information, assignment listings, textbooks and labs were all available online. Some assignments were given online - computer graded multiple-choice questions. Please visit: http://www.math.ksu.edu/main/course_info/syllabi/previous_syllabi/math240-all-syllabi/240-u01.htm

In the Mathematics for Business Decisions course, everything was computerized – from an electronic textbook to team projects that were solved using Excel Spreadsheets with real-time data. There were preliminary and final presentations in Powerpoint. The students explored how to use computer simulations to master several mathematical concepts like approximating the distribution of a random variable, as well as several “real life” situations like running a large number of auctions and stock market analysis.

For my other courses like College Algebra, Calculus or Trigonometry, I always recommend a graphing calculator such as TI – 85. Rather than making them totally dependent on the calculators for everything, I advise the students to use them for graphing tricky functions, doing some numerical calculations like Taylor approximations and checking subtle anti-derivatives.

More recently, I taught vector calculus using Web CT, and received an extremely good response from my pupils. Colorful 3D computer animations were used to describe ideas like the Gradient and Curl of a vector field. They liked being able to continuously monitor their grades throughout the semester as well as the opportunity to access the review material and practice tests online from any computer. Their positive evaluations indicate this helped to keep them motivated and their overall performance was better than several other sections that semester.

5. Alternative modes of instruction other than technology assisted that I have used - I have experience working in the following alternative settings:

I take it as a personal challenge to interweave several of the following ingredients into each of my lectures:

Abstract mathematical concepts can be better grasped if presented using drama, music and concrete applications of the concept, thus facilitating internalization and generalization.
As a result, the pupils develop greater awareness of their learning styles and also learn not to be afraid of making mistakes to persevere in problem solving. Furthermore they began to be able to understand what was blocking their thought processes and overcame the obstruction. They also began to realize that self-confidence and the ability to generate different ideas towards solving a problem are as important as getting the right answer. Math anxiety was reduced or eliminated with this method of teaching mathematical concepts.

6. My experience in working with students, educators, and staff from diverse social and cultural backgrounds - I have always lived and worked in the environment of a globally oriented science and engineering workforce and I am acquainted with the British, Indian and American educational systems. I am especially good at reaching out to students with diverse social and cultural backgrounds and making certain to understand each individual's concerns. I feel that it is a common error for university teachers to misinterpret a student’s lack of communication skills as a lack of intellectual or analytical skills. I never let this happen.

Last year I was both a coordinator of the NSF Undergraduate Teaching Assistant program and the entry-level representative of the Undergraduate Committee. The responsibilities for the first position included the hiring process, organizing an orientation and training session for the UTA's and weekly meetings where we discussed teaching related issues. As a member of the Undergraduate committee, I also attended weekly meetings to discuss matters such as scholarship recipients, pre-requisites for new courses and the improvement of undergraduate writing skills. As a follow-up, I am actively working towards increasing the interaction among undergraduates, graduate students, postdoctoral associates, and faculty members, both pair-wise and collectively. It is important for me to succeed in integrating research and education for graduate students and postdoctoral associates, involving undergraduates in substantial learning by discovery, and developing a team approach.

7.  All the mathematics courses I have taught.  Please visit http://math.arizona.edu/~bharath/ for course details.

At Kansas State University

8. Grading Policy - I assess a student's performance by looking at their solutions to the weekly homework assignments and comparing them with other sections on their performance on the common exams. Improved test scores over previous semesters, excellent student evaluations and my receipt of the Stromberg Outstanding Graduate Teaching Assistant in Teaching Award are certainly strong indications of success. It is my belief that the best attribute of a teacher is that they should not be feared by students.

9. Student Evaluations - The anonymous teaching evaluations I conduct every semester are important since they help me to realize my better qualities as well as limits as a teacher. I have included some copies of these evaluations. The following comments made by students from various backgrounds convinced me of my excellence.

“This has been the best recitation I've had to date. Anytime I was unclear about a section of the material, I understood it when I left class. Bharath's ability to work problems out quickly and efficiently creates a sense of "flow" which is important to keep everyone on the same "sheet of music". Certainly my grade is a reflection of his ability as an instructor. It should also be noted that his accent does not hamper his abilities.”

“In my previous Calculus recitation classes, I have always ended up with a foreign teacher who was not able to communicate well with the students. I had been forced to teach myself everything. That is not the case with Narayanan. He is the only teacher I have been able to learn from and he has done a very good job. Thanks.”

“As a summer class, Bharath had to lecture the material. He did an excellent job. He went through each step and explained what needed to be done.”

“Bharath does a good job of making everything not quite as complicated. He also seems to explain what we don't understand, spending more time on it than what we do.”

“What I notice about Bharath is he has fun while teaching. He might even level with us and tell a joke every once in a while.”

“Narayanan is an excellent teacher. He explains the subject very well. This has been my best recitation teacher by far. His enthusiasm and concern for how his students are doing has made me enjoy the class more than I thought I would. He is very available and willing to help. I thank him for his time.”

“This is the third time I have taken vector calculus and the previous two times were not good experiences because the instructor was not helpful but Dr. Narayanan was exceptional!”

“Nice personality, Very down to Earth teacher. Was always willing to help you, either in class or at office hours.”

“Instructor has a good sense of humor and is willing to work with students to help them learn.” 10. “Good pace, flexible workload, considerate due dates and avoiding homework prior to exam date.Thankyou!”

 â€œI've had 4 calc teachers and Dr. Narayanan was the best one. He was helpful during office hours and patient even though I'm really bad at Calc.”