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I'm teaching in China, and I have been told that I will be leading the students in mathematics competitions. I feel very ill prepared for this. I never did mathematics competitions in either high school nor university.

There will be at least five different competitions, likely more. The first is Waterloo:CEMC. Also, the student's parents send their kids to compete in competitions outside of the school's scheduled events. So, on top of coaching the 90 grade 10 (US system) students plus, grade 11 and 12; I am also to help a couple of students to do well at the Duke University Math Meet, and some various other mathematics competitions.

My question has two parts:

  1. How to coach these students when the problems themselves are challenging for myself.

  2. The bright spot, is that I have a decent budget to order books. Please, suggest titles of books to place on my order sheet and any other resources that would benefit my coaching and broaden my and the students knowledge base for mathematics competitions.

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I highly recommend Paul Zeitz, The Art and Craft of Problem Solving.

The books coauthored by Richard Rusczak on problem solving are probably excellent, though I haven't yet looked at them myself: The Art of Problem Solving, Volumes 1 and 2.

And then there are the math circle books, many of them geared to competition preparation...

You might also find James Tanton's book, Solve This!, very useful as you learn to coach math teams.

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The (university) course I took on problem solving and mathematics competitions had several problem sets with competition-level problems that were sorted into problem-solving strategies. For example, during week 3, we solved problems using the Extremal Principle and got familiar with it. In another week we solved Pigeonhole Principle problems. You might get some mileage out of such problems, depending on the level of the students.

The course was taught by Harm Derksen at the University of Michigan. The textbook used for the course was Loren C. Larson, Problem-Solving through Problems, Problem books in Mathematics, Springer, 1983 -- although I have no memory of the textbook, only of the excellent problem sets.

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You could have them work through problems on aops. It contains AMC questions as well as video lectures on the problems. Furthermore it has books and other resources you may be interested in.

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I'd like to highly recommend George Pólya's "How to Solve It". This 1945 book contains great theory and advice on how to approach hard problems in math.

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"The problems themselves are challenging for myself." That's not a bad situation to be in.

Work through the problems and figure out why they are challenging to you, Then teach the students what you have learned.

Chinese students are well trained and disciplined by their parents. They will pretty much follow where you, their teacher, leads them. Pretend that you are training for one of these contests, then pass on your knowledge to the students. Use the materials you feel would be most helpful to you.

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