Teaching Mathematics, V NAIK

Tags: mathematics, high school students, IMOTC, Olympiad mathematics, lecture notes, high school teaching, differential calculus, Participation, Pratibha Poshak, college level mathematics, Olympiad mathematics students, students need, fellow students, group theory, holiday seasons, Mathematical Journeys, scribed notes, young students, Training Camp Medalist, International Mathematical Olympiad, teaching experience, training camp, Chennai Mathematical Institute, Medalist, AMTI, research duties, TEACHING MATHEMATICS, Olympiad, international mathematics, research priorities
Content: teaching mathematics VIPUL NAIK Abstract. I have been interested in teaching mathematics to other people, and in conveying my ideas to them. I would like to have further opportunities to teach people, and hope that my continuation in mathematics will enable me to continue with my teaching. 1. Past teaching experience 1.1. IMO Training Camp Medalist's session. The International Mathematical Olympiad is an international mathematics contest for high school students. Each participating country selects six students to represent it. In India, the selection is done in a one-month selection and training camp, held a month before the actual IMO. I have gone to the IMO twice, in 2003 and 2004. I won silver medals in both the IMOs. More detailed information about the IMO and IMOTC is available at: http://en.wikipedia.org/IMO http://en.wikipedia.org/IMOTC I have been very interested, not only in solving Olympiad problems, but also in sharing problemsolving skills. In 2004 and 2005, I was invited to give lectures to the IMO Training Camp, on account of being a former medalist. Both my sessions were appreciated greatly by the audience, which included students as well as the other Olympiad trainers. This year, I could not go for the Medalist's session, because it clashed with a summer school. However, I went to give some lectures to the departing IMO team. 1.2. AMTI training. After seeing me at the Medalist's session, one of the trainers for the Tamil Nadu region asked me if I would be interested in helping out with the training activities conducted by the AMTI (Association for Mathematics Teachers in India) in Chennai for Olympiads. I enthusiastically agreed to help, because these activities were being held close to my institute (Chennai Mathematical Institute) and I was keen to meet young students and encourage them towards Olympiad mathematics. Olympiad mathematics had been an important shaping influence in my life and I hoped that I could create a similar experience for other students. The AMTI training camp in Chennai was held for ten weeks, out of which I was able to go eight times. I trained students in grades 9 ­ 12. The students and other trainers greatly appreciated my training. I also prepared material related to the subject matter on which I had trained. Here is a letter documenting my contribution I also made it a point to maintain contact with some of the students from the camp who were keen on Olympiads as well as on pursuing mathematics in later life. I sought to provide them guidance and information on how to prepare for the Olympiads. Towards the end of the training camp, I sought feedback from the students through a feedback form. While the overall response was positive, there were a number of flaws that the students pointed out, as well as many areas of improvement that they suggested. I have tried to incorporate these lessons for further teaching opportunities. 1.3. INMO Training Camp. I was also invited for two lectures for the training camp in Chennai for the Indian National Mathematical Olympiad (INMO), the examination used to select students for the IMOTC. I drew upon my past experiences and attempted to give the students a clear and concise idea of important topics for the Olympiad that they may have neglected at the school level. 1.4. Pratibha Poshak: high school calculus. Apart from Olympiad mathematics, I have also been interested in the teaching of high school mathematics. I believe that the condition of mathematics teaching in today's high schools leaves much to be desired. Thus, when I got the opportunity to conduct classes for some high school students under the Pratibha Poshak scheme, I gladly accepted. I took about 1
5-6 classes in differential calculus and related areas. I also handed notes to the students for whatever was done in class. 1.5. Teaching little kids. The question: "how does the human mind comprehend mathematics" has always fascinated me. In this respect, I have tried to understand how children first grasp the concept of numbers. During the summer holidays last year, I spent some time teaching my five-year-old cousin the basic rules of arithmetic. In addition to teaching the rules of arithmetic, I was keen on showing him the joys, the structure and the logic of the subject. I feel that students need to be made to appreciate the patterns of mathematics right from this age. Although he did not learn a lot of new mathematics under my tutelage, he definitely started enjoying mathematics. I think the ability to enjoy mathematics is one of the most precious gifts. 2. Preparing teaching materials 2.1. Materials for AMTI, Pratibha Poshak. Both for my classes at the AMTI and for my Pratibha Poshak classes, I prepared full notes and gave them to the students. In addition, I also shared some of the differential calculus notes with a friend who is giving private tuitions for students. Further, I discussed with him possibilities for how to prepare riders and exercises for his students. 2.2. Olympiad articles. I have put up some articles for Olympiad mathematics students on my website. In addition, I also sent one Olympiad article to the magazine Samasya, where it was published. The Olympiad material that I have put up is available at: http://www.cmi.ac.in/~vipul/olymp_resources/ 2.3. Materials in college level mathematics. During my second year of college, I became interested in preparing easy-to-understand materials for areas of college mathematics. I began with a project called "Mathematical Journeys", and discussed about it with some fellow students. I completed writing the journeys in group theory, and wrote one journey in topology as well. However, due to increased pressures on my time, I had to shelve the Mathematical Journeys project temporarily. I plan to revive it later. The journeys, as they currently stand, are available at: http://www.cmi.ac.in/~vipul/mathjourneys/ I learnt a lot while attempting to prepare "journeys" in group theory. While I was already familiar with the content, I struggled in order to bring out the perspective and the motivation. Preparing the journeys helped clarify the meaning of many basic aspects of group theory to me. 2.4. Attempts to learn instructional design. Along with trying to prepare instructional content, I also attempted to learn more of the basic philosophy of instructional design. I acquired two books on instructional design, one of which was the ASTD handbook. I tried to implement in practice whatever I learnt from these books. 2.5. Scribed notes for lectures. Online lecture notes for courses taught in other universities have been of great help to me. From this year onwards, my institute started a similar practice of putting up online lecture notes. For this purpose, the instructors in some courses have asked students to submit scribed notes for some of the lectures. In my attempts at scribing lecture notes, I have tried to capture not only the content of the lecture but also the perspectives and philosophical asides of the lecturer. I am also keen on participating in scribing activities for the Microsoft Research Summer School that I attended in the summer, and hope to participate in the scribing effort during my winter vacation. 3. My further plans 3.1. Teaching experience as a research student. Some of my seniors, who are currently working towards their Ph.D.s, told me that they are assigned some teaching duties, such as conducting tutorials, setting and correcting quizzes and so on. I believe that such exposure will provide me with an opportunity to further my teaching experience as well as provide value to younger students. I look forward to the teaching experience. 3.2. Teaching duties as a post-doctoral fellow. After completing my doctorate, I plan to continue to do research in a university, so that I have the opportunity of teaching and interacting with younger students. 2
3.3. Participation in high school teaching programmes. If my research duties permit me, or during holiday seasons, I plan to work more on high school teaching aids and tools. As of now, I do not have a clear idea of the various tools available and the problems faced by high school students. I would like to get in touch with experts on mathematics education and offer my services to them insofar as it does not conflict with my research priorities. 3.4. Participation in Olympiad awareness programmes. I am also keen on supporting the Olympiad awareness programme, particularly in India, where awareness of Olympiads is poor in many areas. This support may be in the form of occasional lectures, spreading the word, or preparation of materials. While in the United States for higher study, I will use my spare time to learn more about how Olympiad awareness is spread there so that I can work better towards spreading Olympiad awareness when I get back to India. 3

V NAIK

File: teaching-mathematics.pdf
Author: V NAIK
Published: Thu Dec 28 14:21:34 2006
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