The Tools of the Trade

“We would all be better off if functions were introduced in kindergarten and studied regularly thereafter. The concept of a function is one of the most important ideas in mathematics.”

Paul Sally 2008

I found out yesterday that Paul died last month. A great mathematician, a profound teacher, and a deeply caring math educator, Paul was a man of incisive intellect and wit. I had the good fortune to hear him in person at a University of Chicago seminar for alumni last June. Though blind and nearly deaf walking on two artificial legs, he was brilliant, funny, and transfixing. I went to the bookstore and found one of his latest books, Tools of the Trade, which he subtitled Introduction to Advanced Mathematics. It is a textbook like few others. Tiny, less than 200 pages long, and dense for he is speaking to advanced college students who seek to be mathematicians, it nonetheless captivated me, and it has been a very long time since I last took a serious math course. I cannot say I have worked my way through this book for it seeks to get students to “come to grips with the idea of proof in a serious way.” But I have returned to it again and again to gain its deep insights, for while he did not write this book for math educators, ¬†we can find in it the tools of our trade.

Paul makes it clear that functions should play a fundamental role in all math education. He constructed his book with projects to provide “Inquiry Based Learning (IBL) experience(s)…” for students. And he sought to challenge their “mathematical creativity.” So as we rethink education and particularly math education we focus our attention on those things that Paul Sally thought were fundamental: functions, Problem or Inquiry Base Learning, and of course creativity and make these the foundation of mathematics education.