Chatting recently with Amy and Tom Burd, I learned some aspects of their work as math teachers at Warren G. Harding High School. Their comments reminded me of a teaching experience that took place years ago to create history in another school.
The experience was Addison's, who was jogging around his school building through 12 inches of snow one February morning 71 years ago. His shirt was rolled up. On his abdomen was inscribed upside-down the binomial theorem, which Addison was reciting loudly as he proceeded around the building. His teacher had requested the shirt be opened and had used a marker to inscribe the theorem. He followed on Ad's heels urging him forward until the theorem was recited and explained correctly. Ad stated the theorem to his teacher's satisfaction and returned in good standing to the 11th-grade algebra classroom, surprisingly pleased with his accomplishment and admired by his classmates for learning the new equation.
A few years ago, Addison, then in his late seventies, submitted this story to the quarterly magazine of the private school he had attended in southwestern Vermont as a student years earlier. The learning experience took place in about 10 minutes. Ad expressed pleasure he and his parents had chosen this school for him to attend. He went on after graduation to greater achievements in math, natural science and education. He attained a graduate degree in geology, was employed by a major oil company and taught petroleum geology at the University of Tripoli in Libya for five years among other achievements.
I told the story to the Burds. They helped me understand mathematics, in a new way. Math consists of numbers and symbols that, in and of them have no color, weight, fragrance, sound or taste. The numbers are abstract entities that are used in a logical fashion to describe and understand observations others have previously experienced. Math formulas seem to offer no immediate practical advantage, which triggers resistance among some students. The everyday work of Amy and Tom is to help their students grasp these formulas.
The small story about Addison shows the dramatically creative intervention of an alert teacher who assisted his student to cope with a point of resistance. It features a willingness of the student to cooperate and accept his teacher's proposal to advance to a new level of understanding. Teaching and learning alike require imagination, patience, trust, willingness to work and respect.
The Burds are an energetic couple, parents of three children, all with broad interests. My guess is the adult Burds are excellent, creative teachers. An event similar to the one experienced by Addison is not possible today; the retelling, however, may introduce a new perspective between teachers, students and parents for advancement.
It is time-consuming for most students to learn, but as Tom and Amy point out, it is our full-time responsibility each day for some of us to teach and some of us to learn. Most students will not have much need for solid geometry, trigonometry or calculus. Their most likely need for math may be in calculating interest on a loan, balancing a checkbook, preparing an income tax form, computing the miles per gallon a car attains or figuring the exact quantities of ingredients to enlarge a cake recipe. Some engineers who took advanced math may not have much proof of the value of their earlier studies, either. The Burds point out the greatest value of all in math, and other high school studies, is exposure to a methodology to solve problems of life in general - how to find needed information. A knowledgeable approach to challenging situations usually leads to success, even good citizenship.
The Burds are involved in their community. They perform on stage in a local theater group; both sing in their church choir; and both are committed to the Warren City Schools system, where their children attend classes. Get to know them. They are fascinating people.
An excerpt from Malcolm Gladwell's "Outliers" reads: "We sometimes think of being good at mathematics as an innate ability. You either have it or you don't It's not so much ability as attitude. You master mathematics if you are willing to try, even doggedness."