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I would like to teach some young and talented pupils basics of competition mathematics. What kind of methods, topics and theorems should I teach to those who are good at school mathematics but have no experience on competitions? How accurately I should teach?

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closed as too broad by Joonas Ilmavirta, Daniel Hast, JoeTaxpayer, Benjamin Dickman, Anschewski Jul 22 '16 at 10:24

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    $\begingroup$ What are the specific competitions that they are taking? What country is this located in? What school mathematics have they completed? What is the format of the teaching? Etc w.r.t. contextual factors... $\endgroup$ – Benjamin Dickman Jul 11 '16 at 23:05
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    $\begingroup$ In addition to @BenjaminDickman excellent questions, I am wondering what you mean by "how accurately should I teach?" $\endgroup$ – Amy B Jul 12 '16 at 8:38
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    $\begingroup$ Sounds like junior high school level to me in which case I wouldn't worry about teaching theorems at all but rather get a large supply of past contest questions, and let them work on those. If it turns out that a particular piece of theory is needed, you can then cover it. The main point is that they need to learn to think hard. Try all possible angles, experiment and such. If they get stuck at a problem they should try another, and then come back to the one they couldn't solve earlier. Prepare them to the fact that contest problems can be much harder than anything they see at school. $\endgroup$ – Jyrki Lahtonen Jul 13 '16 at 23:05
  • $\begingroup$ Solving problems from mathematics competitions enhances the problem solving abilities in students. Text book problems are mostly "apply a formula to get the answer" variety, but competition problems are "discover the technique to solve a problem" variety Here more than the answer, the search for answer and the "Aha" moments are important. This gives the feeling of doing mathematics. Counting, number theory and geometry are usually within the reach of school students and I have found that students enjoy these challenges more than their usual school curriculum. $\endgroup$ – Muralidharan Jul 17 '16 at 3:41

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