Everyone gets discouraged at times in life. Sometimes the strongest students get the most discouraged of all. Such students expect a lot from themselves, and it can be hard to live up to one's own high expectations. It's important to keep things in perspective. One good way to deal with such feelings when you are struggling is to find other people who can use your help. Everybody wins when you do that: it feels good to help someone else and explaining a tricky mathematical idea can deepen your own understanding of that idea.
The best way to learn is to teach somebody else. Math circle alumna Beth Schaffer is a great example of that idea in practice.
Back when she was a Guilderland High School student coaching younger students, Beth wrote a couple of essays she has given me permission to share.
The first essay is one she wrote about her own middle school struggles, starting in sixth grade. She wrote it when she was a high school student in order to encourage the homeschoolers' middle school team she was coaching at the time--that team went on to win the state championship by the biggest margin in recent history.
Beth's essay underscores a very important lesson--don't let yourself get discouraged by comparing yourself with other students--instead, keep on working on figuring out what you can, be willing to ask questions when you can't, and encourage and help everyone around you whenever you can. Not every team can win every contest, but every team can win something far more important than contests--the ultimate prize of developing their problem-solving skills, their ability to work collaboratively, their ability to communicate mathematically, and their ability to create a mathematical community that encourages others.
Her second essay, originally written for her college applications, described the spirit of Albany Area Math Circle meetings so well that I again asked for permission to share it, which she also granted. A few details of our meetings have changed since she wrote that essay--for example, we now meet on Fridays instead of Sundays, but her essence beautifully captures the essence of what our math circle is all about.
Beth is now an MIT junior, where she continues to work with younger students through MIT's Splash Program. When she was a high school student, she participated in the Harvard-MIT Math Tournament (HMMT) as a member of Albany Area Math Circle's teams. Beth is now the tournament director of HMMT!
I'll be adding more essays from other math circle alumni and veterans later. If you have words of advice, encouragement, or inspiration for younger students that you are willing to share, please send them to me.
Beth Schaffer from MIT, manage to smile while directing a large math
tournament on a hectic day. Beth is a graduate of Guilderland High
School who competed on Albany Area Math Circle's HMMT teams
when she was in high school. The picture below shows her with some
of her high school math circle teammates at HMMT 2006.
She was co-captain of Albany Area Math Circle during her junior and
senior years of high school and also coached many younger students,
including some current members of AAMC.
HMMT is run entirely by students, and they have worked hard to
create an outstanding tournament that now attracts many of the
strongest young problem-solvers in the world. This year, students
everywhere can participate in that exciting and challenging experience
thanks to the HMMT Local on-line tournament.