The Lehigh Valley teams have had a string of extraordinary successes since 2003, but 2009 has been the most impressive ever. In February 2009, Lehigh Valley Fire began by winning first place among 154 teams in both the team-based collaborative rounds at Harvard-MIT Math Tournament. In June 2009, the Lehigh Valley team then went on to win its second national championship at ARML, this time by an astounding margin of 14 points over the nearest competitor, defending champion Phillips Exeter. In November 2009, the Lehigh Valley team capped off its year with yet another impressive first place finish in a very strong field at the Princeton University Math Tournament (PUMaC.)

How do they do it? If this were a football team or a basketball team or a hockey team, the keys to their amazing success would be a closely guarded secret. But they're a math team, and the culture of math team coaches has an incredible spirit of generosity and sharing, a tradition not found in athletics. There's a long tradition of math coaches generously sharing the materials, resources, and ideas they've developed for their teams with other coaches, and that tradition also spills over to the students as well. You can see that spirit when students from teams all over the country help one another out on Art of Problem Solving forums, for example. There is a belief that everyone benefits by encouraging and stimulating the mathematical growth of others, whether it's a teammate or a competitor from another team. That's because the ultimate prize is not a trophy or a medal or bragging rights, but rather the problem-solving skills, the camaraderie, the joy of community, the teamwork, the shared "Aha!" moments, and the esprit de corps that comes from working together on a challenging shared common goal.

So what have the Lehigh Valley math team coaches shared about the keys to their success? They've made it all an open book, and it's one well worth reading in full.

Professor Monks' general advice to students on preparing for competition is here, and it's an excellent list of books, practice problem, resources and ideas for preparation that I heartily endorse as well.

Professor and Maria Monks have also put together two extremely useful mathematical "play books," one playbook designed for MATHCOUNTS students and one playbook for high school contests. Albany Area Math Circle students should put both playbooks to good use. The MATHCOUNTS playbook is an excellent resource for those of you who are mentoring middle schoolers, and it's also the foundation upon which the high school playbook builds.

Some points Professor Monks makes are especially worth underscoring:

Perhaps the most valuable resource you have for preparing for ARML is ... each other! We have the best and friendliest mathematics students and coaches in our area on the team, all sharing a joy and passion for problem solving mathematics. If you have a question, ask a teammate!

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Naturally, attending our ARML practices is very important in order to meet and interact with your teammates. and to practice the contest itself in a group setting. Here are some ways that you can reap the most benefit from our practices and do the most good for the team.

Cooperation: With 15 students trying to work together to solve problems on the Team and Power rounds, cooperation is essential to our success. Every decision you make during these rounds should be made with the good of the team in mind. There is no room for ego and bravado. How can I help? should be your mantra. Do something useful at all times. If you are not solving a problem, you can be writing a solution. If you are not writing a solution, you can be proofreading a solution. If you are not proofreading, you can be independently verifying an answer or solution. If you are stuck ask for help. If you can offer help to someone else, offer it. If you are good with a calculator you may be able to write a useful program to check something, if you are not, partner up with one of your teammates who is.

Respect: Everyone on our team is a superb mathematics student, usually the best math student in their school or local area. It is important to respect your teammates and their mathematical ability, both in terms of trusting their mathematical judgments and also from the ordinary aspect of being collegial to others. Be supportive of each other. Provide encouragement when someone is having a bad day (everyone has good days and bad days on math contests). Experienced ARML students should provide leadership and guidance for the newcomers. More advanced students can provide mathematical guidance to students with a weaker math background.

Communication: Talk to each other during practice. Make an effort to learn each other's names. It is difficult to cooperate in a group situation when you can't refer to each other in practice. We will provide you with name tags to facilitate this. During the Team and Power rounds, talk to each other within your squads, coordinate your activities, keep your team captain informed of essential information, share insights with the entire group. Between rounds and before and after practice get to know each other.

The Lehigh Valley math teams clearly have many extraordinary individuals, but their success is even more clearly far more than the sum of their individual talents. The Lehigh Valley students have clearly learned to work effectively together on the critical collaborative skills needed to grow as a team and to create a friendly and welcoming environment that has attracted students from a large geographic area, with some team members traveling as much as 80 miles to come to weekly practices.

And above all, it's clear that Lehigh Valley shares the same philosophy I've seen in all successful coaches: the more of your mathematical knowledge and understanding that you share with others, the more you will grow mathematically yourself.