수학적 모델링에서 가추적 사고의 역할과 의의

Abstract

The importance of considering students' thinking processes in mathematical modeling teaching and learning has been emphasized. The need for an in-depth analysis of the role of abduction in mathematical modeling has recently been raised, though a detailed investigation has never been done. In this study, we theoretically examined the role and the working process of abductive reasoning in mathematical modeling activities. Based on our examination, we uncovered educational implications of abduction in mathematical modeling. For purposes of this paper, we defined abductive reasoning in mathematical modeling as “a thought that leads to proposing a possible effective explanation based on an understanding of the phenomenon, consequently to deriving a suitable mathematical model”. In addition, we analyzed the integrated process and characteristics of abductive reasoning, including overcoded abduction, undercoded abduction, creative abduction, and meta abduction used in the modeling process. This study uncovered major findings regarding the educational potential of abduction in modeling in several ways. First, the abductive reasoning process can improve students' accessibility to mathematical modeling tasks. Second, meta-abduction can support students' mathematization in modeling. Third, students' mathematical creativity can be expanded through the abductive reasoning process used in modeling. In conclusion, substantial higher-level learning is expected to be implemented at schools through mathematical modeling teaching and learning methods that reflect the abductive reasoning process.