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Training for Mathematics Competitions in Taiwan: My Views Speaker: Yeong-Nan Yeh Institute of mathemetics, Academia sinica

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My association with the International Mathematical Olympiad (IMO) dated back to 1993, when I was involved with the setting of problems for selection of our national team and the training of the team. Over the past two decades, I have been an observer, leader and head of our national team. I was the Chairman of the Problems Committee when Taiwan hosted the IMO in 1998. Over this period, I solved thousands of problems used for training our national team and set some problems for the IMO and the Asian Pacific Mathematical Olympiad. 2

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I have also been involved in a number of other mathematics competitions including some organized by the government: 1. Final Contest of the National High School Competition in Mathematical Abilities 2. Selection Contest for the National Mathematical Olympiad Team 3.Asian Pacific Mathematical Olympiad 4. Team Contest of Intercity Youth Mathematics Competition 3

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and some organized by non-government bodies: 1. Tournament of the Towns (Chiu Chang Mathematics Education Foundation) 2. Taiwan Regional Mathematics League (99 Cultural and Educational Foundation) 4

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Mathematical Olympiads target at students with strong interest in mathematics to expose the nature of mathe- matics, discover their potential, cultivate rigor, flexibility and persistence in their mathematical ability. Recently, our public examination questions in mathe- matics are mostly very easy. One needs only substi- tute values into formulas and calculate to get the answers. So one must obtain near perfect scores in order to get into competitive universities. Public examination influences teaching and learning.. 5

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Students focus on how to obtain a correct answer in a few minutes and skip problems requiring in-depth understanding. Quality of education declines under such atmosphere. As the medical schools are the top preference of our parents, entering them require perfect scores in every subject at the entrance examination. To achieve this, students are required to do a lot of tests everyday, which destroy students ability in thinking independently. 6

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Many students are not permitted by their parents to participate in our selection for the national team so the students can focus on the university entrance examinations. 7

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At the end of every year, the National High School Competition in Mathematical Abilities is held. Pro- blems in this competition cover function, equation, inequality, sequence, complex number, trigonome- tric function, elementary enumeration in discrete mathematics, introductory probability and statistics, elementary calculus, analytic geometry, solid geo- metry and elementary vector. The problems in this competition are much easier than those at the IMO. Every time when I started my training sessions with students I asked who had done past problems of this competition. 8

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Only students from one school had. Similar responses were received at the training sessions for sele-ction of IMO national team when asked about experience with past IMO problems. The situation is worse with girls. Their teachers are not interested in helping students participate in mathematics competitions. This widens the gap between the performance of boys and girls in mathematics competitions at the high school level. On the other hand, there are less and less professors helping mathematics competition, particularly when compared with a decade ago. This brings difficulty to the training of the national team. 9

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Problems 3 and 6 of the IMO are always a headache to our national team with few marks scored in these two problems. Students are scared of them and focus their preparation on the remaining ones. 10

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When students participate in mathematics competitions and cannot solve a problem, there are different scenarios based on my experience from training them: 11

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1.The problem cannot be solved during the contest but can be solved when the bell rings – this means that our mathematical knowledge in our mind have not been properly organized that we cannot link it with method for solving the problem. 12

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2.The problem cannot be solved during the contest but can be solved when the solution is seen – this means that our strategies for problem-solving are not good enough and we are not aggressive enough in analyzing problems so as to understand clearly the mathematical knowledge in our mind. 13

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3.The problem cannot be solved during the contest nor after seeing the solution but can be solved after explanation by someone – this means that we do not understand thoroughly the mathematical knowledge in our mind with many facts being accepted without understanding. 14

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4.The problem cannot be solved during the contest nor after seeing the solution and even after explanation by someone – this means that our knowledge of mathematics is not enough and with much room for improvement 15

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16 Thank you for your attention!

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