At our ARML practices we generally practice former contests as working together with your fellow teammates is something you cannot do at home. Outside of practice, how should an ARML team member study and prepare? Learning the mathematics necessary to do well on mathematics contests like ARML is a very slow and time consuming process – something we could not possibly hope to accomplish completely in our limited practice time. Thus, each student is primarily responsible for practicing and learning the necessary mathematics on their own. But how? Here are some resources and references a student can use outside of ARML practices to improve.
At the end of most practices you will be given a packet of solutions to the ARML contest we practice on that day. It is important to study these solutions to learn how to do the questions you were unable to answer.
My son Ken, daughter Maria, and I have compiled two “Playbooks”‘ of mathematical facts and formulas that are typically needed on middle and high school mathematics contests.
The High School Playbook is a continuation of the MATHCOUNTS Playbook, so a student should normally strive to learn all of the topics in the MATHCOUNTS Playbook first, and then move on to the High School Playbook topics. In addition, within each Playbook there is a star symbol next to the topics that should be learned first. The High School Playbook contains many advanced topics that are appropriate for the more difficult Olympiad contests such as USAMO and IMO, but not normally needed for ARML. Thus an ARML student should try to learn the items marked with a star in the MATHCOUNTS Playbook first, then the rest of the items in the MATHCOUNTS Playbook, and finally the items marked with a star in the High School Playbook. But they probably should not worry about the other items in the High School Playbook until they are training for USAMO.
Preparing for other high school mathematics contests is also good training for ARML. Several of the good high school math contests make both the questions and solutions available from their contests. In particular you might want to obtain and practice the following contests, which are somewhat similar to ARML in difficulty and topics.
There are many good books specifically designed for students who participate in high school contests. The Art of Problem Solving website lists many texts:
One natural progression might be as follows:
It will take a very long time to work through all of the books above, so patience is a must.
The Power Round in ARML requires that students be able to write mathematical proofs. Learning to read and write mathematical proofs is a bit like learning to play a musical instrument – it is a skill that is usually mastered over a long period of time with a substantial amount of practice. It combines several different skills: knowledge of the rules of logic, experience with mathematical conventions and notation, and a good working knowledge of English and the specific grammatical and punctuation rules that are used in mathematical exposition. That having been said, there are several ways that an ARML student can improve their proof writing and reading skills.
The Art of Problem Solving website is a “must bookmark” site for everyone involved with ARML. It brings together almost every online resource imaginable related to mathematics competitions and problem solving. There are far too many resources at that site to list here. Go to the site and check it out! Here are some ARML specific links.
In addition to my summer camp, Prove it! Math Academy, there are numerous summer math programs and training camps available for middle and high school problem solvers. Many of our team members have participated in such camps in the past and have had a very positive experience. There is a list of math programs at the Art of Problem Solving website. Follow the links on to learn more about each individual program.
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!
Keep in touch with the friends you make at LV ARML by email, online chat, text messaging, and so on. The Lehigh Valley ARML team has become a magnet program for advanced mathematics students in our area. Having such a peer group can provide you with tips about scholarships, college applications, other mathematics contests, problem solving tips and tricks, and many other things that students with your interest and aptitude for mathematics may find interesting.
OK, you’ve done your studying, participated in other contests, read books, done hundreds… no, thousands… of practice problems to get ready for ARML. What’s next? 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 calculations you may be able to compute something messy, 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. Share a cookie and some lemonade.
The Lehigh Valley ARML team has had amazing success in recent years. A large part of that success has been due to our ability to work together as a friendly, cooperative, well organized team.
The trip to Penn State is the highlight of our ARML season. All of the training and practice can now be put to good use. It is also a great opportunity for making new friends and meeting people with a similar passion for mathematics from other places. Creamery ice cream, dinner in downtown State College, games on the bus, ultimate frisbee, math talks, song contest tryouts, what could be better? During the entire weekend, keep in mind that you represent the Lehigh Valley ARML team and that your actions reflect upon both yourself and the rest of the team as well. Treat members of the other teams with respect. Show good sportsmanship. Always follow the rules of the contest, even if there is an opportunity to cheat without getting caught. It is better to lose with honor than to win with no integrity. We always have a mix of young and old students, and experienced students who have been to ARML at Penn State before and students who are there for their first time. If you are an experienced student, keep an eye out for your younger or less experienced teammates during the trip, especially with regard to navigating around campus. Also everyone should always remember that safety comes first when deciding on a game or activity.
In conclusion, as a member of the Lehigh Valley ARML team you are part of a legacy of excellence in mathematics forged by friendships and hard work of our students. By following the suggestions above, you will hopefully find your ARML experience to be equally rewarding and help to continue that legacy in the future.