New Perspectives in Science Education

Mathematical formalization is a critical component of mathematical modelling in engineering education, requiring students to identify relevant quantities, establish relationships, select appropriate mathematical structures, and express them symbolically. Difficulties in these actions may prevent students from constructing a suitable mathematical model, even when they possess the necessary mathematical knowledge. This paper proposes a theoretically grounded framework for interactive pedagogical support aimed at addressing difficulties arising during mathematical formalization. The framework distinguishes four sequential actions: identification of relevant quantities (I), recognition of relationships (R), selection of a mathematical structure (P), and formal mathematical representation (F). Interpretation (INT) and verification (V) are considered independent diagnostic dimensions rather than successive stages of formalization. The proposed approach connects observable student difficulties with specific instructional objectives and interactive learning activities. It emphasizes the use of targeted questions, comparison of alternative representations, collaborative discussion, and guided exploration, with the selection of support adjusted according to students' responses. The framework is illustrated through mathematical modelling tasks involving systems of linear equations, optimization using functions of one variable, and differential equations. These examples demonstrate how pedagogical support can be adapted to different mathematical structures while maintaining a consistent diagnostic principle. The contribution of the paper is a structured approach to selecting and adjusting interactive support during mathematical formalization, rather than an empirical evaluation of its effectiveness.

 

Keywords: mathematical formalization, mathematical modelling, interactive pedagogical support, engineering education, scaffolding.

 

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