Last summer, a visiting high school computer science teacher complained to an ATDP instructor that her students just didn’t seem to be grasping the concept of functions. The ATDP instructor replied, “Not only can I tell you how to teach functions, but I’ll do better than that. I’ll take you to see for yourself how first graders in Elementary Division master functions and then teach it to others.” And off they went to see Hannah Margulis-Kessel’s students performing “Mathmagic!” In Mathmagic, students are introduced to functions through a machine that “magically” transforms numbers into other numbers.
For each number that a student puts in, a different number comes out. For instance, if you put in 1, you get 3; if you put in 3, you get 5; if you put in 10, you get 12 (can you figure out this function?!). Students make guesses about the mystery rule (i.e., function) the machine is using and put in additional numbers to test their theories. By observing the mathematical patterns created by the function machine, students learn to write algebraic expressions to represent different functions, and can even program the machine with their own functions!
Watching the faces of parents and other adults as their first graders explain what a function is and why understanding functions is important is a delight to behold.