As a math teacher, Mr. Carpenter's abilities are as diverse as one finds in high school. He has taught (and enjoyed teaching) the very lowest remedial math classes at our urban public high school, facilitated post-calculus classes too advanced for the school (or almost any high school) to offer, challenged our best entering freshman, and opened the eyes of seniors convinced that AP calculus would be too hard for them--all within the last three years. That is, he teaches both the most and least capable of both our most and least advanced students.

As a math coach, the most important skill is often knowing when not to interfere--in practice competitions, other students are often better equipped to explain solutions, and, as he readily admits, many of us are better at contest math than he is. This is not to say that he merely fills out contest registration forms, drives to a few competitions, and refers students to the math team: Mr. Carpenter challenges us mathematically with somewhat open-ended problems, often drawn from his area of particular expertise, physics. Besides requiring a variety of areas of mathematics, these problems help us with the transition from the highly structured world of contest mathematics to research or real-world applications. Many members of the math team had been doing contest mathematics since middle or even elementary school, so this is the most valuable practice that he--or any coach--could offer us.