How can mathematical modeling facilitate mathematical inquiries? Focusing on the abductive nature of modeling

Abstract

The purpose of this study is to investigate the nature of mathematical modeling and identify characteristics of mathematical inquiries triggered by mathematical modeling. We investigated three cases of mathematical inquiries facilitated by mathematical modeling. As a result of this study, we revealed the abductive nature of mathematical modeling. We also determined that mathematical inquiries triggered by mathematical modeling have abductive, recursive, analogical, and context-dependent aspects.