Natural number bias on evaluations of the effect of multiplication and division: the role of the type of numbers

Over the last years, there is a growing interest in studying students’ difficulties with rational numbers from a cognitive/developmental perspective, focusing on the role of prior knowledge in students’ understanding of rational numbers. The present study tests the effect of the whole or natural number bias (i.e., the tendency to count on natural number knowledge to interpret information about rational numbers and deal with rational number tasks), on students’ expectations about the size (i.e., bigger or smaller) and the type (i.e., natural number or decimal) of the results of multiplication and division. Items that were congruent and incongruent with students’ assumed expectations were administered to 91 seventh and eighth graders, asking them to evaluate equalities presenting multiplication and division between given and missing numbers. The results showed that besides the already well-documented effect of the size of results (i.e., multiplication makes bigger and division makes smaller ), students tended to think that the numbers involved in multiplication and division should be of the same type (i.e., natural or non-natural, e.g., decimals). Both size and type of the numbers involved in the operations were significant factors affecting students’ evaluations, with size being stronger than type.