Relationships are central to teaching, as we all know, and as class sizes creep up the ability of a teacher to have meaningful relationships with students diminishes greatly. Meaningful feedback, one of the most critical aspects of a teacher’s work, is a function of the time available divided by the number of students. Hope made a great point in her post last week that student-teacher ratios are one of the key measures of great colleges and private schools. In thinking about the student-teacher ratio, I am reminded of an interesting math problem known as the “handshake problem.” It’s about relationships – not just student-teacher relationships, but student-student relationships. All of these interactions impact the dynamic of the class.
The handshake problem is a great problem for early algebra students because it is easily understandable, slightly mind-boggling, and it is readily solved with algebra. It goes like this: Given a room with a particular number of people, how many handshakes will take place if each person shakes hands with everyone once?
We know that Person A needs to shake hands with Person B and that this will mean that B has already shaken hands with A and thus does not need to repeat this particular handshake… uh oh. Continue reading