ABSTRACT
Suppose one asked some concerned adults, for example, parents, how multicolumn subtraction is learned in school. Their explanation would probably run something like this: The teacher tells the students how to perform the algorithm, then sets them to solving practice exercises. Perhaps the practice causes some students to realize that they hadn’t quite understood what the teacher meant. Or perhaps the teacher notices that certain students are following the wrong procedure. In either case, the teacher helps the students by telling them in more detail about the algorithm, probably by adapting the explanation to the particular exercises that the students are working on. Telling dominates both the initial instruction and the subsequent teacher-student interactions, according to this folk model of arithmetic acquisition. Winston (1978) dubbed this model “learning by being told.”
