I asked a group of children to draw a picture of a teacher; two of them drew adults standing in front of chalkboards (Figure 3.1). In one picture the teacher seems to be talking to children who have questions about mathematics; other pictures depict adults addressing audiences that are unseen. Like a stethoscope around a doctor’s neck, or a white hat on a chef,1 a chalkboard behind a teacher sums up teaching for many people.