Middle School students received the first I Love Math problem today. There is much to say about the problem-solving activities we do each year. In the coming weeks, we will say a great deal!
For today, however, I want to simply (1) share the problem and let you enjoy it with the students, and (2) let Steven Strogatz explain why he loves this problem so much. Steven Strogatz is a professor of applied mathematics at Cornell, and the author of "The Elements of Math" series which appeared in the New York Times online edition in 2010.
For today, however, I want to simply (1) share the problem and let you enjoy it with the students, and (2) let Steven Strogatz explain why he loves this problem so much. Steven Strogatz is a professor of applied mathematics at Cornell, and the author of "The Elements of Math" series which appeared in the New York Times online edition in 2010.
First, the problem:
Could the problem be any simpler? Three simple sentences. Forty-nine simple words. But plenty to think about.
Steven Strogatz was given this problem by his Uncle Irv when he was a boy. As an adult, he finds that his thoughts return to it again and again. In his book The Joy of X, a whole chapter is prompted by his memories of the bathtub problem. Strogatz says, "There are broader lessons to be learned here -- lessons about how to solve problems approximately when you can't solve them exactly, and how to solve them intuitively, for the pleasure of the Aha! moment."
Dr. Strogatz goes on, "Word problems give us practice in thinking not just about numbers, but about relationships between numbers -- how the flow rates of the faucets affect the time required to fill the tub, for example. And that is the essential next step in anyone's math education. Understandably, a lot of us have trouble with it; relationships are much more abstract than numbers. But they're also much more powerful. They express the inner logic of the world around us. Cause and effect, supply and demand, input and output, dose and response -- all involve pairs of numbers and the relationships between them. Word problems initiate us into this way of thinking."
We have many hopes, dreams and prayers for Mustard Seed's students in these days of problem solving. May they grow in this next step of abstraction, and see more of the inner logic of the world around them!
