The Process of Mathematical Modeling: A Conceptual Framework for Mathematics Education

Abstract

            Mathematical modeling is a crucial process in mathematics learning that connects mathematical knowledge with real-world situations. However, the modeling processes presented in the literature are diverse and fragmented, which has led to a lack of systematic understanding of the shared core of the mathematical modeling process. The purpose of this study is to synthesize the mathematical modeling process based on internationally recognized research and conceptual frameworks in mathematics education. A conceptual analysis and comparative examination of existing modeling frameworks were employed as the basis for the synthesis.           The synthesis resulted in a mathematical modeling process consisting of five stages: understanding the real-world situation, simplifying, defining mathematical model, using mathematics, and explaining results. This process is conceptualized as dynamic and iterative, reflecting the nature of mathematical modeling as an epistemic activity in which learners continuously make decisions and revise their ideas. In addition, the synthesized framework helps organize knowledge related to the mathematical modeling process in a more coherent manner and elevates the role of simplification in making assumptions as a key theoretical component of modeling.           This study contributes theoretically to mathematics education by offering a conceptual framework that can serve as a foundation for the design of instructional activities, the analysis of students’ thinking processes, and future research on mathematical modeling.