Cultural relevance of validation during mathematical modeling and word problem-solving: Reconceptualizing validation as an integration of possible fictional worlds

Ippo Ishibashi, Yusuke Uegatani

Research output: Contribution to journalArticlepeer-review

Abstract

This study proposes a theoretical view for bridging mathematical modeling and word problem-solving activities. We introduce and elaborate on two theoretical ideas of the fictionality of word problems and the creation of possible fictional worlds. A world described by a word problem exists only fictionally (or potentially). A fictional world includes any imaginable world, any model for the real world, and any mathematical model. We developed a semi-open problem based on these theoretical ideas and observed Japanese eighth-grade students’ activity when solving it in an experimental lesson. Consequently, we identified a theoretically overlooked type of validation: considering the cultural relevance of solutions. The most important implication we draw from our observation is that the current definition of validation as a comparison between two stages in modeling should be extended to consider the integration of a target into a base possible fictional world.

Original languageEnglish
Article number100934
JournalJournal of Mathematical Behavior
Volume66
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Creation of possible fictional worlds
  • Fictionality of word problems
  • Mathematical modeling
  • Mathematical word problem-solving
  • Validation

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

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