수학적 모델링 과정에서 수학적 기호의 의미작용 분석

Abstract

This study aims to analyze the process of mathematical modeling, focusing on how students generate mathematical representations and how the generation and modification of these representations relate to the mathematical modeling process. Particularly, this study examines, from Peirce's semiotic perspective, which characteristic among iconic, indexical, or symbolic, are prominently manifested in the mathematical representations generated by students during the modeling process, and how these characteristics are related to mathematical modeling. The results revealed that both the building and verification of mathematical models, as well as their application and generalization, are confirmed. In this process, depending on whether the focus is initially placed on the iconic or indexical aspects of the representation, inappropriate mathematical models can be built, which has been identified as one of the major challenges in students' mathematical modeling. Additionally, it was observed that students often focus on the symbolic aspect of algebraic expressions and apply conventional mathematical procedures they have previously learned in similar contexts. Finally, the study also noted instances where students achieved rapid generalization by analyzing the values derived from the use of mathematical models in an indexical manner.