Abstract:

Mathematical modelling has been described as an iterative process that plays a central role in connecting mathematics with real-world contexts, enabling students to interpret situations, make predictions and attribute meaning to mathematical concepts. Therefore, investigating and understanding how students engage with each phase of this process is essential to identify challenges and improve modelling-oriented classroom practices.

In this regard, a qualitative study with an interpretative and descriptive approach was conducted based on a case study of a pair of 8th grade students. The analysis of results focused on the strategies and representations mobilized throughout the modelling tasks, guided by the research question: What procedures and steps do students follow when engaging in the mathematical modelling process involving affine functions? The modelling process was analyzed around its main phases – problem interpretation, translation into mathematical language, mathematical model construction, exploration of representations, interpretation of results and validation.

The results indicate that students were generally able to go through all the phases of the process and to identify the type of function underlying the situations. However, transitions between the real-world context and mathematical representations were often fragile and not always fluid, particularly in the formulation of algebraic expressions.

Difficulties were especially evident in the validation phase, as students rarely evaluated the adequacy of results within their context, revealing some challenges in coordinating mathematical results with the contextual meaning of the situation. These findings highlight persistent challenges in articulating the mathematical and real worlds and point to the need for practices that explicitly support validation within the modelling cycle.

Keywords:

Mathematics, mathematical modelling, basic education.