Say It with Machines

摘要

How many times have teachers drawn a picture like figure 1 on the chalkboard for their students? The image of a function as a machine has a long history (Braunfeld 1967) and has become part of the folklore of teaching mathematics in high school. Teachers make far more use of the "function machine" metaphor than could be guessed from looking at published curricula—only some textbooks use the imagery. Teachers employ pictures of machines to aid students in "guess my rule" games, to explain order of operations (fig. 2), to illustrate properties of addition and multiplication, and to help students understand iteration (fig. 3).