Intuitive Beliefs, Formal Definitions and Undefined Operations: Cases of Division by Zero

In this chapter we describe a study in which we explore secondary school students’ adherence to the perform-the-operation belief in the cases of division by zero. Our aims were: (1) to examine whether secondary school students identify expressions involving division by zero as undefined or tend to perform the division operation, (2) to study the justifications given for their approach, and (3) to analyze the effects of age (grade) on their responses. A substantial number of the participants argued, in line with the perform-the-operation belief, that division by zero results in a number. This intuitive belief was also evident in the justifications of students who correctly claimed that division by zero is undefined. Performance on division by zero tasks did not improve with age. Possible causes and educational implications of these findings are described and discussed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.