Creation of possible fictional worlds as a process of validation in mathematical word problem-solving and mathematical modeling activities

Abstract

This paper aims to report a new aspect of mathematical modeling processes from the viewpoints of validation and the fictionality of word problems. Validation is a stage in a modeling process and comparison between two stages in a modeling cycle. Word problems are inherently fictional because they are expected to contain information necessary to construct at least one consistent fictional situation. Through the observation of an eighth-grade mathematics class, we identified the existence of an overlooked type of validation: creation of possible fictional worlds. We observed that some students validated their real results in comparison wmoith fictional worlds they created. Such fictional worlds were built not from the information the word problem contains, but from the students’ common sense. In addition, we hypothesized that the students’ conceptually rich imagination ability promotes their validating ability.